__source_repo string | question string | eval_solution string | solution string | eval_internal_cot string | raw_eval_prompt string | judge_correct bool | judge_reasoning string | __orig_idx int64 | __chunk_idx int64 | eval_solution__chunked string | eval_prompt list | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | To solve the long multiplication equation \( 5761 \times 7525 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7525)
We can express \( 7525 \) as \( 8000 - 475 \). This allows us to rewrite the multiplic... | 43351525 | What is the solution to the long multiplication equation below?
5761 x 7525
Think step by step. | true | The solution accurately followed the steps of breaking down the multiplication using the distributive property, calculated the intermediate products correctly, and performed the final subtraction accurately. The format of the answer is consistent with the ground truth solution, confirming its correctness. | 0 | 0 | To solve the long multiplication equation \( 5761 \times 7525 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7525)
We can express \( 7525 \) as \( 8000 - 475 \). This allows us to rewrite the multiplic... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 5761 x 7525, we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thoug... | 200 | 230 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together.
### Step 1: Break down t... | 28275338 | What is the solution to the long multiplication equation below?
7826 x 3613
Think step by step. | true | The solution provided correctly follows the procedure for long multiplication using the distributive property, and the calculations are accurate. The final result matches the ground truth solution. | 1 | 0 | To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together.
### Step 1: Break down t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(7826 \\times 3613\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(7826\\) by each digit of \\(3613\\) (considering their place val... | 306 | 308 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | To solve the multiplication problem \( 8767 \times 6409 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6409 \) as \( 6000 + 400 + 0 + 9 \). This allows us to multiply \( 8767 \) by each component separately a... | 56187703 | What is the solution to the long multiplication equation below?
8767 x 6409
Think step by step. | true | The solution correctly performed long multiplication by breaking down the number 6409 and then computing each component. The addition of all partial results was accurately performed, resulting in the correct final product of 56187703. The boxed format is maintained properly. | 2 | 0 | To solve the multiplication problem \( 8767 \times 6409 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6409 \) as \( 6000 + 400 + 0 + 9 \). This allows us to multiply \( 8767 \) by each component separately a... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 8767 \\times 6409 \\), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": ... | 208 | 222 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall... | 19863352 | What is the solution to the long multiplication equation below?
5266 x 3772
Think step by step. | true | The solution provided by the judge correctly calculates the product of 5,266 and 3,772 and achieves the same result as the ground truth solution, which is 19,863,352. All steps of the multiplication, addition of partial results, and alternative methods were accurately executed. The final numerical representation was al... | 3 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true... | 1,025 | 1,044 | 19 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | To solve the long multiplication equation \( 8764 \times 3293 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8764 \) by each digit of \( 3293 \) (starting from the right) and then sum the results, taking into account the place value... | 28859852 | What is the solution to the long multiplication equation below?
8764 x 3293
Think step by step. | true | The provided solution correctly computes the multiplication of 8764 and 3293 using the distributive property and confirms the result with long multiplication. The final answer matches the ground truth (28859852), albeit with formatting differences (commas vs. no commas). Thus, the answer is correct. | 4 | 0 | To solve the long multiplication equation \( 8764 \times 3293 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8764 \) by each digit of \( 3293 \) (starting from the right) and then sum the results, taking into account the place value... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8764 \\times 3293 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8764 \\) by each digit of \\( 3293 \\) (starting from the rig... | 460 | 374 | -86 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4353 x 3257
Think step by step. | To solve the long multiplication equation \(4353 \times 3257\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \(4353\) by each digit of \(3257\) (from right to left), shifting the partial results appropriately ba... | 14177721 | What is the solution to the long multiplication equation below?
4353 x 3257
Think step by step. | true | The solution provided follows the long multiplication method correctly, breaking down the problem into manageable steps and accurately performing the calculations for each digit. The final result of 14177721 is verified through both addition of partial products and using the distributive property, matching the ground t... | 5 | 0 | To solve the long multiplication equation \(4353 \times 3257\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \(4353\) by each digit of \(3257\) (from right to left), shifting the partial results appropriately ba... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(4353 \\times 3257\\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subg... | 436 | 467 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7232 x 7540
Think step by step. | To solve the long multiplication equation \(7232 \times 7540\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(7540\) as \(7000 + 500 + 40\) and multiply \(7232\) by each of these comp... | 54529280 | What is the solution to the long multiplication equation below?
7232 x 7540
Think step by step. | true | The solution provided matches the ground truth solution, both arriving at the final result of 54,529,280. The calculations are correctly detailed and verified through standard long multiplication. | 6 | 0 | To solve the long multiplication equation \(7232 \times 7540\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(7540\) as \(7000 + 500 + 40\) and multiply \(7232\) by each of these comp... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(7232 \\times 7540\\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \\(7540\\) ... | 256 | 276 | 20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2001 x 3275
Think step by step. | To solve the multiplication problem \( 2001 \times 3275 \), we can use the **distributive property of multiplication over addition**, which allows us to break down the calculation into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3275 \) as... | 6553275 | What is the solution to the long multiplication equation below?
2001 x 3275
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts. All calculations for each component are accurately performed, and the summation of the results is correct. The final answer of 6,553,275 matches the ground truth solution. | 7 | 0 | To solve the multiplication problem \( 2001 \times 3275 \), we can use the **distributive property of multiplication over addition**, which allows us to break down the calculation into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3275 \) as... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 2001 \\times 3275 \\), we can use the **distributive property of multiplication over addition**, which allows us to break down the calculation into simpler, more manageable parts. Here's a step-by-step solution:",
"equ... | 257 | 283 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | 12478965 | What is the solution to the long multiplication equation below?
2955 x 4223
Think step by step. | true | The solution correctly provides a detailed breakdown of the multiplication of 2955 and 4223, along with verification steps using alternative methods. The final answer matches the ground truth solution, confirming the accuracy of the calculations. | 8 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
... | 904 | 921 | 17 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1369 x 6277
Think step by step. | To solve the long multiplication equation \(1369 \times 6277\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying \(1369\) by each digit of \(6277\) (considering their place values) and then adding the partial results.
### Step 1: Break down the m... | 8593213 | What is the solution to the long multiplication equation below?
1369 x 6277
Think step by step. | true | The solution accurately uses the distributive property to break down the multiplication and correctly calculates each step, resulting in the correct final answer. The final answer of 8,593,213 matches the ground truth solution. | 9 | 0 | To solve the long multiplication equation \(1369 \times 6277\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying \(1369\) by each digit of \(6277\) (considering their place values) and then adding the partial results.
### Step 1: Break down the m... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1369 \\times 6277\\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying \\(1369\\) by each digit of \\(6277\\) (considering their place values) a... | 208 | 234 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5748 x 7995
Think step by step. | To solve the long multiplication equation \( 5748 \times 7995 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7995)
Notice that \( 7995 \) is very close to \( 8000 \). We can express \( 7995 \) as:
\[
7995 ... | 45955260 | What is the solution to the long multiplication equation below?
5748 x 7995
Think step by step. | true | The solution correctly used the distributive property and verified the multiplication step by step, arriving at the final answer of 45955260, which matches the ground truth solution. | 10 | 0 | To solve the long multiplication equation \( 5748 \times 7995 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (7995)
Notice that \( 7995 \) is very close to \( 8000 \). We can express \( 7995 \) as:
\[
7995 ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 5748 \\times 7995 \\), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplier (7995)\nNotice that \\( 7995 \\) i... | 233 | 263 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2817 x 7157
Think step by step. | To solve the long multiplication equation \(2817 \times 7157\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7157) by the first number (2817) and then summing the results, taking into account the p... | 20161269 | What is the solution to the long multiplication equation below?
2817 x 7157
Think step by step. | false | The solution arrived at by the method outlined results in 20,161,269, which does not match the ground truth solution of 20,161,269 without the comma formatting. Also, it appears the comma in the formatting was interpreted incorrectly in the final answer comparison—making it less directly comparable and potentially caus... | 12 | 0 | To solve the long multiplication equation \(2817 \times 7157\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7157) by the first number (2817) and then summing the results, taking into account the p... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 2817 x 7157, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7157) by the first number (2817) and th... | 257 | 295 | 38 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4356 x 4180
Think step by step. | To solve the multiplication problem \(4356 \times 4180\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(4180\) can be written as \(4000 + 100 + 80\). So, we can rewrite the multiplicatio... | 18208080 | What is the solution to the long multiplication equation below?
4356 x 4180
Think step by step. | true | The solution provided arrives at the final product of 4356 times 4180, which is correctly calculated as 18208080. The breakdown of multiplication into simpler parts and the addition of partial products are accurate, confirming the correctness of the solution. | 13 | 0 | To solve the multiplication problem \(4356 \times 4180\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(4180\) can be written as \(4000 + 100 + 80\). So, we can rewrite the multiplicatio... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 4356 x 4180, we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
... | 190 | 6,951 | 6,761 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2699 x 2608
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2699** and **2608**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 7038992 | What is the solution to the long multiplication equation below?
2699 x 2608
Think step by step. | true | The solution methodically breaks down the multiplication of 2699 and 2608 using the long multiplication method, verifying each step along the way. The intermediate calculations are correct, and the final result of 7,038,992 matches the ground truth solution. | 14 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2699** and **2608**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2699** and **2608**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 747 | 750 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7990 x 1250
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7990** and **1250**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be simplified using the **distributive property of multiplication over add... | 9987500 | What is the solution to the long multiplication equation below?
7990 x 1250
Think step by step. | false | The calculated result in the solution is 9,987,500, but the ground truth solution states that the answer should be 9,987,500 without the extra 0. The ground truth solution is incorrect; both the judge's evaluation and the solution provided result in 9,987,500. | 15 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **7990** and **1250**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be simplified using the **distributive property of multiplication over add... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **7990** and **1250**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be simplified ... | 757 | 785 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8751 x 9132
Think step by step. | To solve the multiplication problem \( 8751 \times 9132 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8751 \) by each digit of \( 9132 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 79914132 | What is the solution to the long multiplication equation below?
8751 x 9132
Think step by step. | true | The solution correctly follows the long multiplication method step by step and arrives at the final result, which matches the ground truth solution of 79914132. | 16 | 0 | To solve the multiplication problem \( 8751 \times 9132 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8751 \) by each digit of \( 9132 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 8751 \\times 9132 \\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding ... | 514 | 536 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8906 x 5378
Think step by step. | To solve the long multiplication equation \( 8906 \times 5378 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8906 \) by each digit of \( 5378 \), starting from the rightmost digit, and then sum all the partial products.
### Step 1:... | 47896468 | What is the solution to the long multiplication equation below?
8906 x 5378
Think step by step. | true | The provided solution accurately calculates the product of 8906 and 5378 using the distributive property of multiplication. Both the breakdown of the multiplication and the final answer match the ground truth solution of 47896468. | 17 | 0 | To solve the long multiplication equation \( 8906 \times 5378 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8906 \) by each digit of \( 5378 \), starting from the rightmost digit, and then sum all the partial products.
### Step 1:... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8906 \\times 5378 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8906 \\) by each digit of \\( 5378 \\), starting from the rig... | 407 | 413 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7525 x 5029
Think step by step. | To solve the long multiplication equation \(7525 \times 5029\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together.
### Step 1... | 37843225 | What is the solution to the long multiplication equation below?
7525 x 5029
Think step by step. | false | The solution concluded with the multiplication result of 37,842,225, while the ground truth solution is 37,843,225. Therefore, the provided solution is incorrect. | 18 | 0 | To solve the long multiplication equation \(7525 \times 5029\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together.
### Step 1... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(7525 \\times 5029\\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their pl... | 313 | 315 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5668 x 3310
Think step by step. | To solve the long multiplication equation \( 5668 \times 3310 \), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3310 \) as \( 3000 + 300 + 10 \). This allows us to multiply \( 5668 \... | 18761080 | What is the solution to the long multiplication equation below?
5668 x 3310
Think step by step. | true | The solution calculated the multiplication of 5668 and 3310 correctly using the distributive property. The step-by-step breakdown adds up the partial results accurately and matches the ground truth solution when formatted, confirming that both are the same value (18761080). Therefore, the solution is correct. | 19 | 0 | To solve the long multiplication equation \( 5668 \times 3310 \), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3310 \) as \( 3000 + 300 + 10 \). This allows us to multiply \( 5668 \... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 5668 \\times 3310 \\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"ste... | 205 | 225 | 20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9756 x 3998
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9756** and **3998**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the **long multiplication** m... | 39004488 | What is the solution to the long multiplication equation below?
9756 x 3998
Think step by step. | true | The solution effectively applies the distributive property to break down the multiplication and verifies the calculations step by step. Both the breakdown using the distributive method and the standard long multiplication yield the same final result of 39,004,488, which matches the ground truth solution. | 20 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9756** and **3998**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the **long multiplication** m... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **9756** and **3998**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process... | 473 | 481 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9108 x 7472
Think step by step. | To solve the long multiplication equation \(9108 \times 7472\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | 68054976 | What is the solution to the long multiplication equation below?
9108 x 7472
Think step by step. | true | The solution provided correctly follows the steps of long multiplication using the distributive property and arrives at the correct answer. The formatting of the final answer is only different because of the presence of commas, but the numerical value matches the ground truth solution. | 21 | 0 | To solve the long multiplication equation \(9108 \times 7472\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 9108 x 7472, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partia... | 247 | 286 | 39 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9247 x 2916
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9247** and **2916**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 92... | 26964252 | What is the solution to the long multiplication equation below?
9247 x 2916
Think step by step. | true | The calculated solution matches the ground truth solution when the comma is removed, confirming the multiplication of 9247 and 2916 is correct. | 22 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9247** and **2916**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 92... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **9247** and **2916**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into s... | 711 | 719 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3063 x 2473
Think step by step. | To solve the multiplication problem \(3063 \times 2473\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3063\) by each digit of \(2473\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&3063... | 7574799 | What is the solution to the long multiplication equation below?
3063 x 2473
Think step by step. | true | The solution accurately applies the long multiplication method and correctly computes the result of multiplying 3063 by 2473. Each step is clearly outlined, and the final summation of partial products leads to the correct answer of 7574799, which matches the ground truth. | 23 | 0 | To solve the multiplication problem \(3063 \times 2473\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3063\) by each digit of \(2473\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&3063... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 3063 x 2473, we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the mu... | 235 | 269 | 34 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3872 x 9462
Think step by step. | To solve the long multiplication equation \( 3872 \times 9462 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 3872 \) by each digit of \( 9462 \), starting from the rightmost digit (units place) and moving l... | 36636864 | What is the solution to the long multiplication equation below?
3872 x 9462
Think step by step. | true | The provided solution accurately follows the steps of long multiplication, correctly breaks down the multiplication into partial products, and sums those products accurately. The final answer matches the ground truth of 36636864. | 24 | 0 | To solve the long multiplication equation \( 3872 \times 9462 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 3872 \) by each digit of \( 9462 \), starting from the rightmost digit (units place) and moving l... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3872 \\times 9462 \\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"su... | 613 | 642 | 29 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7589 x 4308
Think step by step. | To solve the long multiplication equation \( 7589 \times 4308 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7589 \) by each digit of \( 4308 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | 32693412 | What is the solution to the long multiplication equation below?
7589 x 4308
Think step by step. | true | The solution provided correctly demonstrates the step-by-step long multiplication process, accurately computes the intermediate results, and arrives at the correct final answer of 32,693,412, which matches the ground truth solution when formatted properly. | 25 | 0 | To solve the long multiplication equation \( 7589 \times 4308 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7589 \) by each digit of \( 4308 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7589 \\times 4308 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7589 \\) by each digit of \\( 4308 \\), starting from the rig... | 366 | 375 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2409 x 2084
Think step by step. | To solve the long multiplication equation \( 2409 \times 2084 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2409 \) by each digit of \( 2084 \) (considering their place values) and then add the results together.
### Step 1: Break ... | 5020356 | What is the solution to the long multiplication equation below?
2409 x 2084
Think step by step. | true | The solution provided correctly breaks down the multiplication of 2409 and 2084 using the distributive property and combines the results accurately, resulting in the final answer of 5,020,356, which matches the ground truth solution. | 26 | 0 | To solve the long multiplication equation \( 2409 \times 2084 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2409 \) by each digit of \( 2084 \) (considering their place values) and then add the results together.
### Step 1: Break ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 2409 \\times 2084 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 2409 \\) by each digit of \\( 2084 \\) (considering their pla... | 301 | 304 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5127 x 3393
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5127** and **3393**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) ... | 17395911 | What is the solution to the long multiplication equation below?
5127 x 3393
Think step by step. | true | The given solution accurately breaks down the multiplication of 5127 and 3393 using long multiplication, calculates all partial products correctly, and sums them up to arrive at the correct final answer of 17395911, which matches the ground truth solution. | 27 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **5127** and **3393**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **5127** and **3393**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves m... | 783 | 794 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2618 x 3358
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2618** and **3358**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number by the entire fir... | 8791244 | What is the solution to the long multiplication equation below?
2618 x 3358
Think step by step. | true | The solution provided thoroughly details the steps to multiply the two numbers (2618 and 3358) using long multiplication, breaking down each part correctly and combining the results accurately. The final product matches the ground truth solution of 8791244. | 28 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2618** and **3358**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number by the entire fir... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2618** and **3358**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves m... | 804 | 887 | 83 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6819 x 9738
Think step by step. | To solve the long multiplication equation \( 6819 \times 9738 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \( 9738 \) as \( 9000 + 700 + 30 + 8 \), and then multiply \( 6819 \... | 66403422 | What is the solution to the long multiplication equation below?
6819 x 9738
Think step by step. | true | The solution presents a detailed breakdown of the long multiplication process and arrives at the correct final answer of 66,403,422, which matches the ground truth solution of 66403422. Hence, the solution is correct. | 29 | 0 | To solve the long multiplication equation \( 6819 \times 9738 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \( 9738 \) as \( 9000 + 700 + 30 + 8 \), and then multiply \( 6819 \... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6819 \\times 9738 \\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"su... | 269 | 285 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3507 x 6774
Think step by step. | To solve the long multiplication equation \( 3507 \times 6774 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results togethe... | 23756418 | What is the solution to the long multiplication equation below?
3507 x 6774
Think step by step. | true | The solution correctly uses the distributive property of multiplication to break down the multiplication problem, computes each step correctly, and sums all partial results accurately to arrive at the final answer. The final result matches the ground truth solution. | 30 | 0 | To solve the long multiplication equation \( 3507 \times 6774 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results togethe... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3507 \\times 6774 \\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their ... | 255 | 311 | 56 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2439 x 2497
Think step by step. | To solve the long multiplication equation \(2439 \times 2497\), we'll use the **standard multiplication method**, breaking it down into simpler, more manageable steps. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(2497\) as \(2000 + 400 + 90 + 7\) and m... | 6090183 | What is the solution to the long multiplication equation below?
2439 x 2497
Think step by step. | true | The provided solution correctly calculates the product of 2439 and 2497 using the standard multiplication method, correctly breaking down the components and summing the partial results. The final answer is presented in the boxed format and matches the ground truth solution. | 31 | 0 | To solve the long multiplication equation \(2439 \times 2497\), we'll use the **standard multiplication method**, breaking it down into simpler, more manageable steps. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(2497\) as \(2000 + 400 + 90 + 7\) and m... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 2439 x 2497, we'll use the **standard multiplication method**, breaking it down into simpler, more manageable steps. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "th... | 236 | 279 | 43 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2173 x 6346
Think step by step. | To solve the long multiplication equation \(2173 \times 6346\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2173\) by each digit of \(6346\), starting from the rightmost digit, and then sum the results, taking care to align the number... | 13789858 | What is the solution to the long multiplication equation below?
2173 x 6346
Think step by step. | true | The solution correctly applies the distributive property of multiplication and provides accurate intermediate results for each multiplication, leading to an accurate final addition of these results. The final answer matches the ground truth solution. | 32 | 0 | To solve the long multiplication equation \(2173 \times 6346\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2173\) by each digit of \(6346\), starting from the rightmost digit, and then sum the results, taking care to align the number... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(2173 \\times 6346\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(2173\\) by each digit of \\(6346\\), starting from the rightmost... | 319 | 322 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3419 x 9827
Think step by step. | To solve the long multiplication problem \( 3419 \times 9827 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3419 \) by each digit of \( 9827 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | 33598513 | What is the solution to the long multiplication equation below?
3419 x 9827
Think step by step. | false | The computed total of 33,666,893 does not match the ground truth solution of 33,598,513. Therefore, the solution is incorrect. | 33 | 0 | To solve the long multiplication problem \( 3419 \times 9827 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3419 \) by each digit of \( 9827 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 3419 \\times 9827 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 3419 \\) by each digit of \\( 9827 \\), accounting for place values, and th... | 283 | 295 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2703 x 5036
Think step by step. | To solve the long multiplication equation \( 2703 \times 5036 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (5036) by each digit of the first number (2703) and then adding all the partial product... | 13612308 | What is the solution to the long multiplication equation below?
2703 x 5036
Think step by step. | true | The solution provided is correct. The calculated result of the multiplication is accurately derived step by step, and matches the ground truth solution when expressed in a standard numerical format. | 34 | 0 | To solve the long multiplication equation \( 2703 \times 5036 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (5036) by each digit of the first number (2703) and then adding all the partial product... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 2703 \\times 5036 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (5036) by each digit of th... | 348 | 348 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9531 x 7373
Think step by step. | To solve the long multiplication equation \(9531 \times 7373\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9531) by each digit of the multiplier (7373), considering their place values, and then summing the part... | 70272063 | What is the solution to the long multiplication equation below?
9531 x 7373
Think step by step. | true | The final answer provided in the solution matches the ground truth solution of 70272063. The solution correctly applied the distributive property of multiplication, broke down the numbers accurately, and confirmed the result through standard long multiplication, resulting in consistent and correct computation. | 35 | 0 | To solve the long multiplication equation \(9531 \times 7373\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9531) by each digit of the multiplier (7373), considering their place values, and then summing the part... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 9531 x 7373, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9531) by each digit of the multiplier (7373), consider... | 277 | 319 | 42 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5443 x 4753
Think step by step. | To solve the long multiplication equation \(5443 \times 4753\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | 25870579 | What is the solution to the long multiplication equation below?
5443 x 4753
Think step by step. | true | The provided solution accurately follows the steps for long multiplication, properly breaks down the multiplication into manageable parts, and sums these parts correctly to arrive at the final product of 5443 and 4753, which matches the ground truth solution. | 36 | 0 | To solve the long multiplication equation \(5443 \times 4753\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(5443 \\times 4753\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, conside... | 269 | 275 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6448 x 4737
Think step by step. | To solve the long multiplication equation \(6448 \times 4737\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results together.... | 30544176 | What is the solution to the long multiplication equation below?
6448 x 4737
Think step by step. | true | The solution provided uses the distributive property correctly and accurately calculates the products of each component and the sums of the partial results. The final answer matches the ground truth solution. | 37 | 0 | To solve the long multiplication equation \(6448 \times 4737\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results together.... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(6448 \\times 4737\\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their pl... | 192 | 209 | 17 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2428 x 2498
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2428** and **2498**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effecti... | 6065144 | What is the solution to the long multiplication equation below?
2428 x 2498
Think step by step. | true | The given solution provides a detailed step-by-step calculation of the product of 2428 and 2498, using various methods including the distributive property, standard long multiplication, and an alternative method. Each step has been checked for accuracy, and the final result matches the ground truth solution of 6065144. | 38 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2428** and **2498**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effecti... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2428** and **2498**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process... | 954 | 986 | 32 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1950 x 9500
Think step by step. | To solve the multiplication \( 1950 \times 9500 \), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the distributive property of multiplication to simplify the calculation. Notice that \( 9500 \) can be written as \( 10,000 - 500 \... | 18525000 | What is the solution to the long multiplication equation below?
1950 x 9500
Think step by step. | true | The solution calculates the multiplication of 1950 and 9500 correctly and arrives at the same result as the ground truth solution, which is 18525000. The methods used to verify the calculations confirm that the answer is indeed correct. | 39 | 0 | To solve the multiplication \( 1950 \times 9500 \), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the distributive property of multiplication to simplify the calculation. Notice that \( 9500 \) can be written as \( 10,000 - 500 \... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication \\( 1950 \\times 9500 \\), we can break it down into simpler steps. Here's a detailed, step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to so... | 241 | 241 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9213 x 2411
Think step by step. | To solve the long multiplication problem \( 9213 \times 2411 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9213 \) by each digit of \( 2411 \), accounting for place values, and then sum the results.
### Step 1: Break down the mult... | 22212543 | What is the solution to the long multiplication equation below?
9213 x 2411
Think step by step. | false | The solution arrived at a total of 22,212,543, but this is incorrect. The ground truth solution is 22,212,543, which is simply the number 2212543 with an additional placeholder for a million. The thousands digit is incorrectly calculated in the summation. Therefore, the provided solution has an arithmetic error. | 40 | 0 | To solve the long multiplication problem \( 9213 \times 2411 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9213 \) by each digit of \( 2411 \), accounting for place values, and then sum the results.
### Step 1: Break down the mult... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 9213 \\times 2411 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9213 \\) by each digit of \\( 2411 \\), accounting for place v... | 435 | 7,233 | 6,798 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1129 x 9352
Think step by step. | To solve the multiplication problem \(1129 \times 9352\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(1129\) by each digit of \(9352\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | 10558408 | What is the solution to the long multiplication equation below?
1129 x 9352
Think step by step. | true | The solution provided uses the long multiplication method correctly and arrives at the final answer, which matches the ground truth solution when formatted appropriately (ignoring comma placement). Therefore, the solution is correct. | 41 | 0 | To solve the multiplication problem \(1129 \times 9352\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(1129\) by each digit of \(9352\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(1129 \\times 9352\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to ... | 177 | 208 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9560 x 8678
Think step by step. | To solve the long multiplication equation \(9560 \times 8678\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8678) by each digit of the first number (9560) and then adding all the partial products ... | 82961680 | What is the solution to the long multiplication equation below?
9560 x 8678
Think step by step. | true | The solution correctly breaks down the multiplication into partial products using the distributive property, computes each partial product accurately, and adds them together correctly to reach the final answer of 82,961,680, which matches the ground truth solution. | 42 | 0 | To solve the long multiplication equation \(9560 \times 8678\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8678) by each digit of the first number (9560) and then adding all the partial products ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(9560 \\times 8678\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8678) by each digit of the ... | 240 | 268 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4864 x 9604
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4864** and **9604**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process.
### Breaking Down the Second Number (9604)
Looking at *... | 46713856 | What is the solution to the long multiplication equation below?
4864 x 9604
Think step by step. | true | The solution correctly computes the multiplication of 4864 and 9604 step by step using different methods, arriving at the consistent final result of 46,713,856, which matches the ground truth solution. | 43 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4864** and **9604**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process.
### Breaking Down the Second Number (9604)
Looking at *... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4864** and **9604**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process... | 427 | 438 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4552 x 4506
Think step by step. | To solve the long multiplication equation \( 4552 \times 4506 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (4506)
The multiplier \( 4506 \) can be expressed as:
\[ 4506 = 4000 + 500 + 6 \]
### Step 2... | 20511312 | What is the solution to the long multiplication equation below?
4552 x 4506
Think step by step. | true | The calculated product of 4552 and 4506, which is 20511312, matches the ground truth solution. The method used was correct as it applied the distributive property properly, and all partial results were accurately computed and summed. | 44 | 0 | To solve the long multiplication equation \( 4552 \times 4506 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (4506)
The multiplier \( 4506 \) can be expressed as:
\[ 4506 = 4000 + 500 + 6 \]
### Step 2... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 4552 \\times 4506 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step... | 230 | 230 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9333 x 4285
Think step by step. | To solve the long multiplication equation \( 9333 \times 4285 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9333) by each digit of the multiplier (4285) and then summing the partial results.
### Step 1: Break... | 39991905 | What is the solution to the long multiplication equation below?
9333 x 4285
Think step by step. | false | The solution provided calculated the product of 9333 and 4285 as 39,991,905, whereas the ground truth solution gives the result as 39991905 without the comma. Both represent the same numerical value, but one includes commas while the other does not, which is a formatting discrepancy; hence, the evaluation is based on s... | 45 | 0 | To solve the long multiplication equation \( 9333 \times 4285 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9333) by each digit of the multiplier (4285) and then summing the partial results.
### Step 1: Break... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9333 \\times 4285 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9333) by each digit of the multiplier (4... | 291 | 303 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3696 x 5575
Think step by step. | To solve the multiplication \( 3696 \times 5575 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5575)
Express \( 5575 \) as \( 5000 + 500 + 70 + 5 \). This allows us to multiply \( 3696 \) by each compo... | 20605200 | What is the solution to the long multiplication equation below?
3696 x 5575
Think step by step. | false | The solution provided calculates the final result as 20,605,200, but the ground truth solution indicates that the correct answer should be 20,605,200 without the formatting of the commas. However, both answers are actually the same numerically. Thus, while the answer format may differ due to the presence of commas, the... | 46 | 0 | To solve the multiplication \( 3696 \times 5575 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5575)
Express \( 5575 \) as \( 5000 + 500 + 70 + 5 \). This allows us to multiply \( 3696 \) by each compo... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication \\( 3696 \\times 5575 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thoug... | 299 | 303 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8083 x 9284
Think step by step. | To solve the long multiplication problem \( 8083 \times 9284 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8083 \) by each digit of \( 9284 \), starting from the rightmost digit, and then sum the results, taking care to shift each ... | 75042572 | What is the solution to the long multiplication equation below?
8083 x 9284
Think step by step. | true | The solution provided correctly breaks down the multiplication of 8083 and 9284 using the distributive property, accurately calculates each partial product, adds them up correctly, and confirms the final result matches the ground truth of 75042572. | 47 | 0 | To solve the long multiplication problem \( 8083 \times 9284 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8083 \) by each digit of \( 9284 \), starting from the rightmost digit, and then sum the results, taking care to shift each ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 8083 \\times 9284 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8083 \\) by each digit of \\( 9284 \\), starting from the righ... | 474 | 480 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3195 x 8200
Think step by step. | To solve the long multiplication equation \( 3195 \times 8200 \), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 8200 \) can be written as \( 82 \times 100 \). So, we can rewrite the multiplication as:
\[
3195 \times 8200 = 3195 \times ... | 26199000 | What is the solution to the long multiplication equation below?
3195 x 8200
Think step by step. | false | The solution provided states that the final result of the multiplication is 26,199,000, while the ground truth solution is 26,199,000 (both formulations actually point to the same number). The number formatting differs due to the use of commas versus not adding a comma for the ground truth. However, since both refer to... | 48 | 0 | To solve the long multiplication equation \( 3195 \times 8200 \), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 8200 \) can be written as \( 82 \times 100 \). So, we can rewrite the multiplication as:
\[
3195 \times 8200 = 3195 \times ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3195 \\times 8200 \\), we can break it down into simpler steps. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nNotice that \\( 8200 \\) can be written as \\( 82 \\times 100 \\). So, we ... | 267 | 275 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9464 x 6401
Think step by step. | To solve the multiplication problem \( 9464 \times 6401 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 6401 \) can be expressed as:
\[ 6401 = 6000 + 400 + 0 + 1 \]
### Step 2: Multipl... | 60579064 | What is the solution to the long multiplication equation below?
9464 x 6401
Think step by step. | true | The solution provided accurately applies the distributive property of multiplication to break down the calculation of 9464 multiplied by 6401. Each component is correctly calculated and the final summation of the partial products leads to the correct final answer of 60579064. Thus, we can conclude that the solution is ... | 49 | 0 | To solve the multiplication problem \( 9464 \times 6401 \), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 6401 \) can be expressed as:
\[ 6401 = 6000 + 400 + 0 + 1 \]
### Step 2: Multipl... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 9464 \\times 6401 \\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type"... | 246 | 246 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4561 x 9726
Think step by step. | To solve the multiplication problem \(4561 \times 9726\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(4561\) by each digit of \(9726\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | 44360286 | What is the solution to the long multiplication equation below?
4561 x 9726
Think step by step. | false | The solution provided calculated the product of 4561 and 9726 as 44370486, while the correct answer is 44360286. Therefore, the solution is incorrect. | 50 | 0 | To solve the multiplication problem \(4561 \times 9726\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(4561\) by each digit of \(9726\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(4561 \\times 9726\\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to ... | 253 | 296 | 43 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3816 x 7327
Think step by step. | To solve the multiplication problem \( 3816 \times 7327 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3816 \) by each digit of \( 7327 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 27959832 | What is the solution to the long multiplication equation below?
3816 x 7327
Think step by step. | true | The performed long multiplication is correct, and the formatting of the answer is merely a matter of style (with comma separators). The numerical result matches the ground truth solution of 27959832. | 51 | 0 | To solve the multiplication problem \( 3816 \times 7327 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3816 \) by each digit of \( 7327 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3816 \\times 7327 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 251 | 229 | -22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1729 x 6372
Think step by step. | To solve the multiplication \( 1729 \times 6372 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1729 \) by each digit of \( 6372 \), starting from the rightmost digit (units place), and shift the partial results accordingly.... | 11017188 | What is the solution to the long multiplication equation below?
1729 x 6372
Think step by step. | true | The calculations in the long multiplication method for the expression \( 1729 \times 6372 \) were performed correctly, resulting in the value of \( 11017188 \). This matches the ground truth solution. | 52 | 0 | To solve the multiplication \( 1729 \times 6372 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1729 \) by each digit of \( 6372 \), starting from the rightmost digit (units place), and shift the partial results accordingly.... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication 1729 x 6372, we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the question",... | 149 | 6,086 | 5,937 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9555 x 1211
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **9555** and **1211**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall that brea... | 11571105 | What is the solution to the long multiplication equation below?
9555 x 1211
Think step by step. | false | The provided solution's final answer is written in scientific notation as \(1.1571105 \times 10^7\), which is equivalent to 11571105 in decimal form. However, the solution is supposed to present the answer as an integer (11571105) without scientific notation. Therefore, while the calculated result is correct, the forma... | 53 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **9555** and **1211**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall that brea... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: **9555** and **1211**. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"out... | 550 | 553 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2516 x 4230
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 2516 and 4230. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of bre... | 10642680 | What is the solution to the long multiplication equation below?
2516 x 4230
Think step by step. | true | The solution correctly calculates the multiplication of 2516 and 4230 step-by-step using long multiplication and verifies its correctness through different methods. The final result matches the ground truth solution exactly, confirming its accuracy. | 54 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 2516 and 4230. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of bre... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 2516 and 4230. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ""... | 1,091 | 1,096 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1936 x 6998
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1936** and **6998**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be done using the **distributive property** of multiplication over additio... | 13548128 | What is the solution to the long multiplication equation below?
1936 x 6998
Think step by step. | true | The solution correctly follows the distributive property and the traditional long multiplication method, leading to the correct final product of 13,548,128. The verification step confirms this result matches the ground truth solution. | 55 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1936** and **6998**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be done using the **distributive property** of multiplication over additio... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1936** and **6998**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be done using ... | 625 | 643 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4943 x 4193
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4943** and **4193**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | 20725999 | What is the solution to the long multiplication equation below?
4943 x 4193
Think step by step. | true | The solution correctly performs the long multiplication and matches the ground truth solution (20,725,999). The calculations are thorough, and the verification step confirms the accuracy. | 56 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4943** and **4193**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4943** and **4193**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it mana... | 755 | 711 | -44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6618 x 4115
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6618** and **4115**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effecti... | 27233070 | What is the solution to the long multiplication equation below?
6618 x 4115
Think step by step. | true | The solution correctly applies the long multiplication method and verifies the result using two different approaches, confirming the final product of 6618 and 4115 as 27,233,070, which matches the ground truth solution. | 57 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **6618** and **4115**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effecti... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **6618** and **4115**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process... | 966 | 966 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5733 x 7142
Think step by step. | To solve the long multiplication problem \(5733 \times 7142\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5733\) by each digit of \(7142\), starting from the rightmost digit, and then sum the results. Here's the step-by-step solution:
### Step 1... | 40945086 | What is the solution to the long multiplication equation below?
5733 x 7142
Think step by step. | true | The solution provided accurately calculates the product of 5733 and 7142 through the distributive property and verifies the result with standard long multiplication, confirming that both methods yield the same correct result of 40945086. | 58 | 0 | To solve the long multiplication problem \(5733 \times 7142\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5733\) by each digit of \(7142\), starting from the rightmost digit, and then sum the results. Here's the step-by-step solution:
### Step 1... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem 5733 x 7142, we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 5733 by each digit of 7142, starting from the rightmost digit, and then sum the results. Here... | 339 | 300 | -39 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3706 x 3990
Think step by step. | To solve the long multiplication equation \( 3706 \times 3990 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (3990)
Notice that \( 3990 \) can be expressed as \( 4000 - 10 \). This allows... | 14786940 | What is the solution to the long multiplication equation below?
3706 x 3990
Think step by step. | true | The provided solution correctly applies the distributive property of multiplication and confirms the result with standard long multiplication. The final answer, 14,786,940, matches the given ground truth solution. | 59 | 0 | To solve the long multiplication equation \( 3706 \times 3990 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (3990)
Notice that \( 3990 \) can be expressed as \( 4000 - 10 \). This allows... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3706 \\times 3990 \\), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output"... | 291 | 307 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5317 x 8669
Think step by step. | To solve the multiplication problem \(5317 \times 8669\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5317\) by each digit of \(8669\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | 46093073 | What is the solution to the long multiplication equation below?
5317 x 8669
Think step by step. | true | The provided solution correctly breaks down the multiplication using the long multiplication method, calculating each part accurately, and correctly sums them to arrive at the final result. The steps are detailed and verify that the final answer matches the ground truth solution. | 60 | 0 | To solve the multiplication problem \(5317 \times 8669\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5317\) by each digit of \(8669\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 5317 x 8669, we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the mu... | 340 | 377 | 37 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8623 x 4551
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8623** and **4551**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | 39243273 | What is the solution to the long multiplication equation below?
8623 x 4551
Think step by step. | true | The calculation for multiplying 8623 and 4551 has been thoroughly verified using long multiplication and the distributive property. Each partial multiplication and addition step was accurately carried out and confirmed, leading to the correct solution of 39,243,273, which matches the ground truth solution. | 61 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8623** and **4551**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: **8623** and **4551**. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"out... | 794 | 794 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1028 x 1708
Think step by step. | To solve the long multiplication equation \(1028 \times 1708\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (1708) by each digit of the first number (1028) and then adding all the partial products ... | 1755824 | What is the solution to the long multiplication equation below?
1028 x 1708
Think step by step. | true | The solution provided correctly follows the step-by-step process of long multiplication, uses the distributive property accurately, and correctly adds the partial products to arrive at the final answer, which matches the ground truth solution (1755824). Therefore, the solution is correct. | 62 | 0 | To solve the long multiplication equation \(1028 \times 1708\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (1708) by each digit of the first number (1028) and then adding all the partial products ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1028 \\times 1708\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (1708) by each digit of the ... | 213 | 231 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8610 x 6263
Think step by step. | To solve the multiplication problem \( 8610 \times 6263 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express the multiplication as:
\[ 8610 \times 6263 = 8610 \times (6000 + 200 + 60 + 3) \]
### Step 2: Multiply 8610 by each compo... | 53924430 | What is the solution to the long multiplication equation below?
8610 x 6263
Think step by step. | true | The solution correctly calculates the product of 8610 and 6263 using the long multiplication method, breaking it down into manageable components, correctly matching the ground truth of 53924430. | 63 | 0 | To solve the multiplication problem \( 8610 \times 6263 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express the multiplication as:
\[ 8610 \times 6263 = 8610 \times (6000 + 200 + 60 + 3) \]
### Step 2: Multiply 8610 by each compo... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 8610 \\times 6263 \\), we can use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan ... | 271 | 271 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6492 x 4764
Think step by step. | To solve the long multiplication equation \( 6492 \times 4764 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6492 \) by each digit of \( 4764 \), accounting for the place value, and then sum the results.
### Step 1: Break down the ... | 30927888 | What is the solution to the long multiplication equation below?
6492 x 4764
Think step by step. | true | The solution accurately follows the steps for long multiplication, breaking down the multiplication into partial products and correctly summing the results. The final calculated answer (30,927,888) matches the ground truth solution (30927888) when formatted consistently (ignoring commas). Thus, the solution is correct. | 64 | 0 | To solve the long multiplication equation \( 6492 \times 4764 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6492 \) by each digit of \( 4764 \), accounting for the place value, and then sum the results.
### Step 1: Break down the ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 6492 \\times 4764 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 6492 \\) by each digit of \\( 4764 \\), accounting for the pl... | 314 | 314 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3207 x 4398
Think step by step. | To solve the long multiplication equation \( 3207 \times 4398 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3207 \) by each digit of \( 4398 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 14104386 | What is the solution to the long multiplication equation below?
3207 x 4398
Think step by step. | true | The solution correctly describes the step-by-step process of long multiplication, and the final computed result of 14,104,386 matches the ground truth solution of 14104386. The use of the distributive property, along with accurate calculations for each step, shows a thorough understanding of the multiplication process.... | 65 | 0 | To solve the long multiplication equation \( 3207 \times 4398 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3207 \) by each digit of \( 4398 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 3207 \\times 4398 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 3207 \\) by each digit of \\( 4398 \\), accounting for place ... | 317 | 315 | -2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1333 x 4982
Think step by step. | To solve the long multiplication equation \(1333 \times 4982\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding the results together.
#... | 6641006 | What is the solution to the long multiplication equation below?
1333 x 4982
Think step by step. | false | The solution calculated 6,641,006, but the ground truth solution is written as 6641006, which appears to be a typographical error in the formatting. If both numbers represent the same value, then the solutions match; however, if we treat them as distinct based on their formatting, the first solution is incorrectly form... | 66 | 0 | To solve the long multiplication equation \(1333 \times 4982\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding the results together.
#... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1333 \\times 4982\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, account... | 250 | 252 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6549 x 3559
Think step by step. | To solve the long multiplication equation \(6549 \times 3559\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6549\) by each digit of \(3559\) (from right to left), shifting the partial results appropriately, and then add them together.... | 23307891 | What is the solution to the long multiplication equation below?
6549 x 3559
Think step by step. | true | The solution is correct. The calculation of each partial multiplication and the summation of the results are accurate, leading to the final answer of 23,307,891, which matches the ground truth solution of 23307891. | 67 | 0 | To solve the long multiplication equation \(6549 \times 3559\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6549\) by each digit of \(3559\) (from right to left), shifting the partial results appropriately, and then add them together.... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 6549 x 3559, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 6549 by each digit of 3559 (from right to left), shifting the partial results a... | 202 | 209 | 7 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4986 x 9604
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4986** and **9604**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 47885544 | What is the solution to the long multiplication equation below?
4986 x 9604
Think step by step. | true | The solution systematically calculated the multiplication of 4986 and 9604 using multiple methods (distributive property and long multiplication) and arrived at the final answer of 47885544, which matches the ground truth solution. | 68 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4986** and **9604**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4986** and **9604**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 908 | 1,001 | 93 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9973 x 7385
Think step by step. | To solve the multiplication problem \( 9973 \times 7385 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 9973 \) by each digit of \( 7385 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
... | 73650605 | What is the solution to the long multiplication equation below?
9973 x 7385
Think step by step. | false | The provided solution correctly applies the long multiplication method and arrives at a final answer of 73,665,605. However, the ground truth solution states the correct answer is 73,650,605. Therefore, the calculated answer in the solution is incorrect compared to the ground truth. | 69 | 0 | To solve the multiplication problem \( 9973 \times 7385 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 9973 \) by each digit of \( 7385 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 9973 \\times 7385 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding... | 567 | 592 | 25 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8945 x 2955
Think step by step. | To solve the long multiplication equation \( 8945 \times 2955 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8945 \) by each digit of \( 2955 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplier (2955... | 26432475 | What is the solution to the long multiplication equation below?
8945 x 2955
Think step by step. | true | The solution provided correctly breaks down the multiplication using the distributive property and sums the partial results accurately. The final answer matches the ground truth solution when formatted with or without commas. | 70 | 0 | To solve the long multiplication equation \( 8945 \times 2955 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8945 \) by each digit of \( 2955 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplier (2955... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8945 \\times 2955 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8945 \\) by each digit of \\( 2955 \\), accounting for place values, and t... | 287 | 289 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7466 x 6085
Think step by step. | To solve the long multiplication equation \(7466 \times 6085\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7466\) by each digit of \(6085\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | 45430610 | What is the solution to the long multiplication equation below?
7466 x 6085
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication into manageable parts. Each part of the multiplication is computed accurately, and the final summation of these parts yields the same answer as the ground truth solution (45430610). Therefore, the provided solution is correct. | 71 | 0 | To solve the long multiplication equation \(7466 \times 6085\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7466\) by each digit of \(6085\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 7466 x 6085, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 7466 by each digit of 6085 (considering their place values) and then sum the re... | 213 | 240 | 27 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5975 x 4676
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5975** and **4676**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 27939100 | What is the solution to the long multiplication equation below?
5975 x 4676
Think step by step. | true | The provided solution correctly performed the multiplication of 5975 and 4676 using both the long multiplication method and the distributive property, and arrived at the correct product of 27,939,100. The verification process was thorough and accurately confirmed the result. | 72 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **5975** and **4676**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **5975** and **4676**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 753 | 724 | -29 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8384 x 4784
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8384** and **4784**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts.
### Breaking Down the Multip... | 40109056 | What is the solution to the long multiplication equation below?
8384 x 4784
Think step by step. | true | The solution correctly applies the long multiplication method and verifies the result using both the distributive property and standard long multiplication. The calculations show that the result of multiplying 8384 by 4784 is indeed 40,109,056, matching the ground truth solution. | 73 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **8384** and **4784**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts.
### Breaking Down the Multip... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **8384** and **4784**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into s... | 946 | 946 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7525 x 6050
Think step by step. | To solve the long multiplication equation \( 7525 \times 6050 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Notice that \( 6050 \... | 45526250 | What is the solution to the long multiplication equation below?
7525 x 6050
Think step by step. | true | The computed final answer of 45,526,250 matches the ground truth solution of 45526250 (which is the same number expressed properly with a comma). The solution follows the correct multiplication processes and checks for accuracy. | 74 | 0 | To solve the long multiplication equation \( 7525 \times 6050 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Notice that \( 6050 \... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7525 \\times 6050 \\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal"... | 281 | 307 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1138 x 7633
Think step by step. | To solve the multiplication \( 1138 \times 7633 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7633 \) as \( 8000 - 367 \), which allows us to rewrite the multiplication as:
\[
1138 \times 7... | 8686354 | What is the solution to the long multiplication equation below?
1138 x 7633
Think step by step. | true | The provided solution correctly applied the long multiplication method and the distributive property to compute the product of 1138 and 7633. The detailed steps, including the breakdown of 7633 and the multiplications carried out, lead correctly to the final result. The value calculated in the solution matches the grou... | 75 | 0 | To solve the multiplication \( 1138 \times 7633 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7633 \) as \( 8000 - 367 \), which allows us to rewrite the multiplication as:
\[
1138 \times 7... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication \\( 1138 \\times 7633 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve... | 243 | 243 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5259 x 5394
Think step by step. | To solve the long multiplication problem \(5259 \times 5394\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5259\) by each digit of \(5394\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
We ca... | 28367046 | What is the solution to the long multiplication equation below?
5259 x 5394
Think step by step. | true | The solution correctly applies the distributive property of multiplication, performs each multiplication accurately, and sums the partial products correctly. The final result is consistent with the ground truth solution, which is also represented as an unformatted integer (28367046). Therefore, the solution is correct. | 76 | 0 | To solve the long multiplication problem \(5259 \times 5394\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5259\) by each digit of \(5394\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
We ca... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem 5259 x 5394, we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 5259 by each digit of 5394 (considering their place values) and then sum the results.",
"... | 228 | 243 | 15 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7251 x 5693
Think step by step. | To solve the long multiplication equation \(7251 \times 5693\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7251\) by each digit of \(5693\) (starting from the rightmost digit) and then sum the results, taking care to shift each partial product ap... | 41279943 | What is the solution to the long multiplication equation below?
7251 x 5693
Think step by step. | true | The provided solution correctly performs long multiplication using both the distributive property and verification through standard long multiplication. The calculations are accurate, and the final answer matches the ground truth solution. | 77 | 0 | To solve the long multiplication equation \(7251 \times 5693\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7251\) by each digit of \(5693\) (starting from the rightmost digit) and then sum the results, taking care to shift each partial product ap... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 7251 x 5693, we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 7251 by each digit of 5693 (starting from the rightmost digit) and then sum the results, tak... | 263 | 307 | 44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3106 x 5132
Think step by step. | To solve the long multiplication equation \(3106 \times 5132\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
3106
× 5132
________
```
### Step 2: Multiply 3106 by each digit of 5132, starting from the right
###... | 15939992 | What is the solution to the long multiplication equation below?
3106 x 5132
Think step by step. | true | The provided solution accurately follows the long multiplication method and the calculations for each step are correct. The final result matches the ground truth solution. | 78 | 0 | To solve the long multiplication equation \(3106 \times 5132\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
3106
× 5132
________
```
### Step 2: Multiply 3106 by each digit of 5132, starting from the right
###... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 3106 x 5132, we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup... | 180 | 182 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5043 x 4258
Think step by step. | To solve the long multiplication problem \(5043 \times 4258\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5043\) by each digit of \(4258\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Bre... | 21473094 | What is the solution to the long multiplication equation below?
5043 x 4258
Think step by step. | true | The solution correctly follows the long multiplication process. The breakdown of multiplications for each component of 4258 and the subsequent addition of the partial results are accurately described and calculated. Both the step-by-step approach and the final sum confirm that the total matches the ground truth, which ... | 79 | 0 | To solve the long multiplication problem \(5043 \times 4258\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5043\) by each digit of \(4258\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Bre... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\(5043 \\times 4258\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(5043\\) by each digit of \\(4258\\) (from right to left), shift the partial re... | 239 | 255 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1576 x 9545
Think step by step. | To solve the long multiplication equation \(1576 \times 9545\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1576) by each digit of the multiplier (9545), starting from the rightmost digit, and then summing up th... | 15042920 | What is the solution to the long multiplication equation below?
1576 x 9545
Think step by step. | true | The solution correctly breaks down the multiplication using the distributive property, computes each partial product accurately, and sums them up correctly, resulting in the final answer of 15,042,920, which matches the ground truth solution. | 81 | 0 | To solve the long multiplication equation \(1576 \times 9545\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1576) by each digit of the multiplier (9545), starting from the rightmost digit, and then summing up th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1576 \\times 9545\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1576) by each digit of the multiplier (954... | 261 | 272 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7384 x 8656
Think step by step. | To solve the multiplication problem \( 7384 \times 8656 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7384 \) by each digit of \( 8656 \), starting from the rightmost digit (units place), and then sum the partial results.
... | 63915904 | What is the solution to the long multiplication equation below?
7384 x 8656
Think step by step. | true | The provided solution follows the long multiplication method correctly. Each step was outlined, providing partial products, which were then summed accurately, leading to the correct final answer of 63,915,904. The format of the answer in both the solution and ground truth matches, thereby confirming correctness. | 82 | 0 | To solve the multiplication problem \( 7384 \times 8656 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7384 \) by each digit of \( 8656 \), starting from the rightmost digit (units place), and then sum the partial results.
... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 7384 \\times 8656 \\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan t... | 179 | 193 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7073 x 8567
Think step by step. | To solve the multiplication problem \(7073 \times 8567\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7073\) by each digit of \(8567\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&7073... | 60594391 | What is the solution to the long multiplication equation below?
7073 x 8567
Think step by step. | true | The solution provided uses the long multiplication method correctly, breaks down the multiplication into appropriate parts, performs each multiplication accurately, and sums all partial results correctly to reach the final answer. The final computed product matches the ground truth solution of 60594391. | 83 | 0 | To solve the multiplication problem \(7073 \times 8567\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7073\) by each digit of \(8567\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&7073... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 7073 x 8567, we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the mu... | 204 | 234 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7474 x 5559
Think step by step. | To solve the multiplication problem \(7474 \times 5559\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7474\) by each digit of \(5559\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&\qu... | 41547966 | What is the solution to the long multiplication equation below?
7474 x 5559
Think step by step. | true | The solution correctly uses the long multiplication method to calculate the product of 7474 and 5559 step-by-step, arriving at the same result as the ground truth solution, which is 41547966. Therefore, the evaluated solution is correct. | 84 | 0 | To solve the multiplication problem \(7474 \times 5559\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7474\) by each digit of \(5559\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&\qu... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 7474 x 5559, we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the q... | 229 | 6,097 | 5,868 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7342 x 1713
Think step by step. | To solve the multiplication problem \(7342 \times 1713\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7342\) by each digit of \(1713\), starting from the rightmost digit, and shift the partial results accordingly.
\[
\begin{... | 12576846 | What is the solution to the long multiplication equation below?
7342 x 1713
Think step by step. | true | The provided solution calculated the multiplication of 7342 and 1713 using the long multiplication method step-by-step, correctly breaking down the problem into manageable parts, and arrived at the result of 12,576,846. The ground truth solution of 12576846 corresponds to the same numerical value (removing the comma do... | 85 | 0 | To solve the multiplication problem \(7342 \times 1713\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7342\) by each digit of \(1713\), starting from the rightmost digit, and shift the partial results accordingly.
\[
\begin{... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 7342 x 1713, we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the mu... | 226 | 253 | 27 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5025 x 8264
Think step by step. | To solve the long multiplication equation \(5025 \times 8264\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5025) by each digit of the multiplier (8264), starting from the rightmost digit, and then summing up th... | 41526600 | What is the solution to the long multiplication equation below?
5025 x 8264
Think step by step. | true | The solution correctly employs the distributive property to break down the multiplication and accurately calculates the partial products. The final sum is confirmed using both the distributive method and standard long multiplication, yielding the same result. | 86 | 0 | To solve the long multiplication equation \(5025 \times 8264\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5025) by each digit of the multiplier (8264), starting from the rightmost digit, and then summing up th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(5025 \\times 8264\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5025) by each digit of the multiplier (826... | 356 | 315 | -41 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6593 x 5553
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6593** and **5553**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 36610929 | What is the solution to the long multiplication equation below?
6593 x 5553
Think step by step. | true | The provided solution follows a structured approach to multiply two large numbers using the long multiplication method, which is accurately executed with correct placement of each partial product. It carefully details each step of the multiplication process, correctly adds the partial products, and verifies the final p... | 87 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **6593** and **5553**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **6593** and **5553**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 1,030 | 1,047 | 17 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9381 x 5585
Think step by step. | To solve the long multiplication equation \( 9381 \times 5585 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9381 \) by each digit of \( 5585 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 52392885 | What is the solution to the long multiplication equation below?
9381 x 5585
Think step by step. | true | The provided solution correctly applies the distributive property to perform long multiplication of 9381 and 5585. Each step is accurately calculated, and the final answer of 52,392,885 matches the ground truth solution of 52392885 when formatting is disregarded (commas are not part of the numerical value). Therefore, ... | 88 | 0 | To solve the long multiplication equation \( 9381 \times 5585 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9381 \) by each digit of \( 5585 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 9381 \\times 5585 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9381 \\) by each digit of \\( 5585 \\) (considering their pla... | 334 | 311 | -23 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3291 x 1974
Think step by step. | To solve the long multiplication equation \(3291 \times 1974\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(3291\) by each digit of \(1974\) (expressed in its expanded form: \(1000 + 900 + 70 + 4\)) and then sum the results.
### Step 1: Break dow... | 6496434 | What is the solution to the long multiplication equation below?
3291 x 1974
Think step by step. | true | The solution follows a correct application of the distributive property for long multiplication, and all calculations are accurately performed, leading to the correct final result of 6496434, which matches the ground truth. | 89 | 0 | To solve the long multiplication equation \(3291 \times 1974\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(3291\) by each digit of \(1974\) (expressed in its expanded form: \(1000 + 900 + 70 + 4\)) and then sum the results.
### Step 1: Break dow... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(3291 \\times 1974\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(3291\\) by each digit of \\(1974\\) (expressed in its expanded form: \\(1000 ... | 173 | 173 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5829 x 6356
Think step by step. | To solve the long multiplication problem \( 5829 \times 6356 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5829 \) by each digit of \( 6356 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | 37049124 | What is the solution to the long multiplication equation below?
5829 x 6356
Think step by step. | true | The provided solution correctly follows the distributive property of multiplication and performs the calculations without errors. The final answer matches the ground truth solution. | 90 | 0 | To solve the long multiplication problem \( 5829 \times 6356 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5829 \) by each digit of \( 6356 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 5829 \\times 6356 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5829 \\) by each digit of \\( 6356 \\), starting from the righ... | 376 | 379 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6109 x 4281
Think step by step. | To solve the long multiplication equation \(6109 \times 4281\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial produc... | 26152629 | What is the solution to the long multiplication equation below?
6109 x 4281
Think step by step. | true | The provided solution correctly applies the distributive property of multiplication to break down the multiplication of 6109 and 4281 into partial products, accurately computes each multiplication, and then accurately adds the partial products to arrive at the final total of 26152629. The answer format is consistent wi... | 91 | 0 | To solve the long multiplication equation \(6109 \times 4281\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial produc... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 6109 x 4281, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for plac... | 221 | 242 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8699 x 3651
Think step by step. | To solve the long multiplication equation \( 8699 \times 3651 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8699 \) by each digit of \( 3651 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 31760049 | What is the solution to the long multiplication equation below?
8699 x 3651
Think step by step. | true | The solution calculated follows the correct steps for long multiplication, applying the distributive property accurately. Each multiplication is computed correctly, and the final addition of the partial results yields the correct total, which matches the ground truth solution of 31,760,049. | 92 | 0 | To solve the long multiplication equation \( 8699 \times 3651 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8699 \) by each digit of \( 3651 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8699 \\times 3651 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8699 \\) by each digit of \\( 3651 \\) (considering their pla... | 278 | 9,536 | 9,258 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5026 x 7624
Think step by step. | To solve the long multiplication equation \(5026 \times 7624\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5026) by each digit of the multiplier (7624), starting from the rightmost digit, and then summing up th... | 38318224 | What is the solution to the long multiplication equation below?
5026 x 7624
Think step by step. | true | The solution provided steps through the multiplication process step by step using the distributive property and correctly computes the partial products as well as their sum. Each multiplication and addition is accurate, and the final result, 38318224, matches the ground truth solution. | 93 | 0 | To solve the long multiplication equation \(5026 \times 7624\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5026) by each digit of the multiplier (7624), starting from the rightmost digit, and then summing up th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 5026 x 7624, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5026) by each digit of the multiplier (7624), starting... | 348 | 7,621 | 7,273 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6441 x 3982
Think step by step. | To solve the multiplication problem \(6441 \times 3982\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6441\) by each digit of \(3982\), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
&... | 25648062 | What is the solution to the long multiplication equation below?
6441 x 3982
Think step by step. | true | The solution follows the long multiplication method correctly. Each step involves breaking down the multiplication appropriately, and when the partial results are summed, the final answer obtained matches the ground truth solution of 25648062. | 94 | 0 | To solve the multiplication problem \(6441 \times 3982\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6441\) by each digit of \(3982\), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
&... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem 6441 x 3982, we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve the qu... | 224 | 6,611 | 6,387 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9705 x 8878
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9705** and **8878**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effective... | 86160990 | What is the solution to the long multiplication equation below?
9705 x 8878
Think step by step. | true | The provided solution correctly calculates the product of 9705 and 8878 using both long multiplication and the distributive property methods. The final result of 86,160,990 matches the ground truth solution. | 95 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9705** and **8878**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effective... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **9705** and **8878**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the pr... | 1,578 | 1,585 | 7 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9215 x 7884
Think step by step. | To solve the long multiplication problem \( 9215 \times 7884 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9215 \) by each digit of \( 7884 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | 72651060 | What is the solution to the long multiplication equation below?
9215 x 7884
Think step by step. | true | The provided solution correctly calculates the multiplication of 9215 and 7884 using the distributive property and correctly sums the partial products to arrive at the final answer. The calculated result of 72651060 matches the ground truth solution. | 96 | 0 | To solve the long multiplication problem \( 9215 \times 7884 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9215 \) by each digit of \( 7884 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 9215 \\times 7884 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9215 \\) by each digit of \\( 7884 \\), starting from the righ... | 279 | 281 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1571 x 3079
Think step by step. | To solve the long multiplication equation \(1571 \times 3079\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1571) by each digit of the multiplier (3079), considering their place values, and then summing the resu... | 4837109 | What is the solution to the long multiplication equation below?
1571 x 3079
Think step by step. | true | The solution correctly follows the long multiplication process step by step, accurately calculating each multiplication involving the components of the multiplier and summing the partial products correctly. The final answer matches the ground truth solution. | 97 | 0 | To solve the long multiplication equation \(1571 \times 3079\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1571) by each digit of the multiplier (3079), considering their place values, and then summing the resu... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 1571 x 3079, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1571) by each digit of the multiplier (3079), consider... | 207 | 234 | 27 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5246 x 8836
Think step by step. | To solve the long multiplication problem \(5246 \times 8836\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5246\) by each digit of \(8836\) (from right to left), shift the partial results appropriately, and then add them together.
##... | 46353656 | What is the solution to the long multiplication equation below?
5246 x 8836
Think step by step. | true | The solution accurately followed the long multiplication process and verified the result through both the distributive property method and standard long multiplication. The final result matches the ground truth solution after considering formatting differences (commas in the answer). Therefore, the solution is correct. | 98 | 0 | To solve the long multiplication problem \(5246 \times 8836\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5246\) by each digit of \(8836\) (from right to left), shift the partial results appropriately, and then add them together.
##... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\(5246 \\times 8836\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(5246\\) by each digit of \\(8836\\) (from right to left), shift t... | 350 | 333 | -17 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9015 x 9141
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9015 and 9141. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall th... | 82406115 | What is the solution to the long multiplication equation below?
9015 x 9141
Think step by step. | true | The provided solution accurately calculates the product of 9015 and 9141 as 82,406,115. All steps in the breakdown of multiplication are consistent and verified using multiple methods, including long multiplication and factorization, leading to the final answer matching the ground truth. | 99 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9015 and 9141. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall th... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9015 and 9141. My goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
... | 784 | 805 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2611 x 7986
Think step by step. | To solve the long multiplication equation \(2611 \times 7986\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results together.... | 20851446 | What is the solution to the long multiplication equation below?
2611 x 7986
Think step by step. | true | The solution correctly calculated the multiplication of 2611 by 7986 by breaking it down using the distributive property. It also verified the result using the long multiplication method and both methods yielded the same final result of 20,851,446. Additionally, the ground truth solution of 20,851,446 matches the calcu... | 100 | 0 | To solve the long multiplication equation \(2611 \times 7986\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results together.... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(2611 \\times 7986\\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their pl... | 302 | 302 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6274 x 7610
Think step by step. | To solve the long multiplication equation \(6274 \times 7610\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Specifically, ... | 47745140 | What is the solution to the long multiplication equation below?
6274 x 7610
Think step by step. | true | The solution correctly applied the distributive property of multiplication, accurately calculated each partial product, and summed them to obtain the correct final answer. The verification using standard long multiplication reaffirms the correctness. Both the solution and the ground truth yield the same value, 47745140... | 101 | 0 | To solve the long multiplication equation \(6274 \times 7610\), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Specifically, ... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 6274 x 7610, we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Se... | 259 | 294 | 35 |
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