__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?
7319 x 4444
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7319** and **4444**. 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... | 32525636 | What is the solution to the long multiplication equation below?
7319 x 4444
Think step by step. | true | The submitted solution correctly applies the method of long multiplication, accurately calculates the individual products, and aggregates them properly to arrive at the final product of 7319 and 4444. The final answer provided is consistent with the ground truth solution. | 304 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **7319** and **4444**. 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: **7319** and **4444**. 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... | 788 | 796 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3520 x 4629
Think step by step. | To solve the multiplication problem \( 3520 \times 4629 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (3520) by each digit of the multiplier (4629) and then summing the partial results. Here's a step-by-step solution:
###... | 16294080 | What is the solution to the long multiplication equation below?
3520 x 4629
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication and arrives at the sum of partial products accurately, matching the ground truth solution. | 305 | 0 | To solve the multiplication problem \( 3520 \times 4629 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (3520) by each digit of the multiplier (4629) and then summing the partial results. Here's a step-by-step solution:
###... | [
{
"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 \\( 3520 \\times 4629 \\), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (3520) by each digit of the multiplier (4629) and then summ... | 371 | 328 | -43 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3909 x 1312
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two large numbers: 3909 and 1312. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down into simpl... | 5128608 | What is the solution to the long multiplication equation below?
3909 x 1312
Think step by step. | true | The solution provided a detailed explanation of the long multiplication process, correctly computed the product of 3909 and 1312, and verified the result through addition. The final answer matched the ground truth solution, confirming its correctness. | 306 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two large numbers: 3909 and 1312. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down into simpl... | [
{
"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 simple multiplication of two large numbers: 3909 and 1312. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"outp... | 844 | 849 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6010 x 2062
Think step by step. | To solve the long multiplication equation \(6010 \times 2062\), 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 (2062) by each digit of the first number (6010) and then summing the results.
### Step 1... | 12392620 | What is the solution to the long multiplication equation below?
6010 x 2062
Think step by step. | true | The solution is correct; it effectively uses the distributive property to break down the multiplication into manageable parts and accurately computes the final result, matching the ground truth value. | 307 | 0 | To solve the long multiplication equation \(6010 \times 2062\), 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 (2062) by each digit of the first number (6010) and then summing the results.
### 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 \\(6010 \\times 2062\\), 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 (2062) by each digit of the ... | 194 | 216 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2696 x 3930
Think step by step. | To solve the long multiplication equation \(2696 \times 3930\), 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 multiplication
We can express \(3930\) as \(4000 - 70\), so:
\[
2696 \times 3930 = 2696 \ti... | 10595280 | What is the solution to the long multiplication equation below?
2696 x 3930
Think step by step. | true | The solution correctly details the steps of the calculation using both the distributive property and standard long multiplication. The final answer matches the ground truth solution. | 308 | 0 | To solve the long multiplication equation \(2696 \times 3930\), 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 multiplication
We can express \(3930\) as \(4000 - 70\), so:
\[
2696 \times 3930 = 2696 \ti... | [
{
"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 2696 x 3930, 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": "",
"ste... | 255 | 211 | -44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8676 x 1037
Think step by step. | To solve the long multiplication problem \( 8676 \times 1037 \), we'll break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1037)
The multiplier \( 1037 \) can be expressed as:
\[ 1037 = 1000 + 30 + 7 \]
### Step 2: Multi... | 8997012 | What is the solution to the long multiplication equation below?
8676 x 1037
Think step by step. | true | The provided solution accurately breaks down the multiplication of 8676 and 1037 using the distributive property, correctly computes each multiplication step, and correctly adds the partial results to yield the final answer of 8997012. The final boxed answer matches the ground truth solution. | 309 | 0 | To solve the long multiplication problem \( 8676 \times 1037 \), we'll break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1037)
The multiplier \( 1037 \) can be expressed as:
\[ 1037 = 1000 + 30 + 7 \]
### Step 2: Multi... | [
{
"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 \\( 8676 \\times 1037 \\), we'll break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:",
"equation": "",
"finished": true,
"output": "",
"step_type"... | 259 | 262 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3432 x 5724
Think step by step. | To solve the multiplication problem \(3432 \times 5724\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3432\) by each digit of \(5724\) (from right to left), keeping track of the place values by adding zeros as we go.
\[
\beg... | 19644768 | What is the solution to the long multiplication equation below?
3432 x 5724
Think step by step. | true | The solution correctly follows the long multiplication method, breaking down the multiplication into manageable parts and adding all the partial results accurately. The final answer of 19,644,768 matches the given ground truth solution. | 310 | 0 | To solve the multiplication problem \(3432 \times 5724\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3432\) by each digit of \(5724\) (from right to left), keeping track of the place values by adding zeros as we go.
\[
\beg... | [
{
"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 3432 x 5724, 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... | 195 | 217 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7226 x 5906
Think step by step. | To solve the long multiplication equation \( 7226 \times 5906 \), 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 all the partial produc... | 42676756 | What is the solution to the long multiplication equation below?
7226 x 5906
Think step by step. | true | The provided solution correctly applies the distributive property to break down the multiplication of 7226 and 5906. Each step clearly shows the computation of the partial products and their corresponding sums. Upon evaluating the final total, it matches the ground truth solution of 42676756 when formatted correctly (w... | 311 | 0 | To solve the long multiplication equation \( 7226 \times 5906 \), 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 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 \\( 7226 \\times 5906 \\), 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, accou... | 232 | 237 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8781 x 5763
Think step by step. | To solve the long multiplication equation \( 8781 \times 5763 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8781 \) by each digit of \( 5763 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | 50604903 | What is the solution to the long multiplication equation below?
8781 x 5763
Think step by step. | true | The solution provided has correctly calculated each step of the long multiplication using the distributive property, leading to the final sum of 50,604,903, which matches the ground truth solution of 50604903. | 312 | 0 | To solve the long multiplication equation \( 8781 \times 5763 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8781 \) by each digit of \( 5763 \) (considering their place values) and then sum the results.
### Step 1: Break down 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 long multiplication equation \\( 8781 \\times 5763 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8781 \\) by each digit of \\( 5763 \\) (considering their place values) an... | 329 | 329 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3435 x 1486
Think step by step. | To solve the multiplication problem \(3435 \times 1486\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3435\) by each digit of \(1486\), starting from the rightmost digit (units place), and shift the partial results accordingl... | 5104410 | What is the solution to the long multiplication equation below?
3435 x 1486
Think step by step. | true | The provided solution correctly uses the long multiplication method and accurately calculates the value of 3435 multiplied by 1486, resulting in the correct answer of 5104410. | 313 | 0 | To solve the multiplication problem \(3435 \times 1486\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3435\) by each digit of \(1486\), starting from the rightmost digit (units place), and shift the partial results accordingl... | [
{
"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 3435 x 1486, 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... | 252 | 272 | 20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7677 x 3383
Think step by step. | To solve the multiplication problem \( 7677 \times 3383 \), 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 \( 3383 \) as \( 3000 + 300 + 80 + 3 \). This allows us to multiply \( 7677 \) by each com... | 25971291 | What is the solution to the long multiplication equation below?
7677 x 3383
Think step by step. | true | The solution correctly applies the long multiplication method, breaks down the multiplication into manageable parts, accurately calculates each component, and sums the results correctly. The final result matches the ground truth solution. | 314 | 0 | To solve the multiplication problem \( 7677 \times 3383 \), 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 \( 3383 \) as \( 3000 + 300 + 80 + 3 \). This allows us to multiply \( 7677 \) by each com... | [
{
"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 \\( 7677 \\times 3383 \\), 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 ... | 235 | 242 | 7 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7140 x 1565
Think step by step. | To solve the multiplication problem \(7140 \times 1565\), 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 (1565)
We can express \(1565\) as:
\[
1565 = 1000 + 500 + 60 + 5
\]
### Step 2: Multiply 7140 by eac... | 11174100 | What is the solution to the long multiplication equation below?
7140 x 1565
Think step by step. | true | The solution correctly applies the distributive property of multiplication, accurately breaks down the multiplier and computes the partial products properly, and sums them to arrive at the correct final answer of 11,174,100, which matches the ground truth solution. | 315 | 0 | To solve the multiplication problem \(7140 \times 1565\), 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 (1565)
We can express \(1565\) as:
\[
1565 = 1000 + 500 + 60 + 5
\]
### Step 2: Multiply 7140 by eac... | [
{
"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 \\(7140 \\times 1565\\), 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": ... | 161 | 175 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6898 x 3904
Think step by step. | To solve the long multiplication equation \( 6898 \times 3904 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6898 \) by each digit of \( 3904 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 26929792 | What is the solution to the long multiplication equation below?
6898 x 3904
Think step by step. | true | The solution correctly calculates the product of 6898 and 3904, step by step, using the distributive property and verifying the calculation with both methods (distributive multiplication and long multiplication). The final computed result matches the ground truth solution exactly. | 316 | 0 | To solve the long multiplication equation \( 6898 \times 3904 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6898 \) by each digit of \( 3904 \), 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 6898 x 3904, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 6898 by each digit of 3904, accounting for place values, and then sum the resul... | 210 | 7,131 | 6,921 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4534 x 3124
Think step by step. | To solve the long multiplication equation \(4534 \times 3124\), 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 \(4534\) by each digit of \(3124\) (from right to left), shifting the partial results appropriately ba... | 14164216 | What is the solution to the long multiplication equation below?
4534 x 3124
Think step by step. | true | The provided solution correctly applies the long multiplication method step by step, detailing each multiplication with the respective place shifts. The final sum of the partial products is accurate, verifying that the computed answer is indeed 14164216, which matches the ground truth solution. | 317 | 0 | To solve the long multiplication equation \(4534 \times 3124\), 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 \(4534\) by each digit of \(3124\) (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 4534 x 3124, 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... | 383 | 386 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9475 x 8808
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two large numbers: 9,475 and 8,808. 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 meth... | 83455800 | What is the solution to the long multiplication equation below?
9475 x 8808
Think step by step. | true | The provided solution accurately calculates the product of 9,475 and 8,808 using detailed steps and verification methods, ultimately arriving at the correct result of 83,455,800, which matches the ground truth solution. | 318 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two large numbers: 9,475 and 8,808. 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 meth... | [
{
"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 simple multiplication of two large numbers: 9,475 and 8,808. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"ou... | 904 | 1,004 | 100 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5607 x 5438
Think step by step. | To solve the long multiplication equation \(5607 \times 5438\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5607\) by each digit of \(5438\) (from right to left), shift the partial results appropriately, and then add them together.
#... | 30490866 | What is the solution to the long multiplication equation below?
5607 x 5438
Think step by step. | true | The solution correctly follows the distributive property of multiplication, performs the multiplications accurately, and sums the partial products to arrive at the correct final answer, which matches the ground truth. | 319 | 0 | To solve the long multiplication equation \(5607 \times 5438\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5607\) by each digit of \(5438\) (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 equation 5607 x 5438, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 5607 by each digit of 5438 (from right to left), shift the partial results appr... | 284 | 275 | -9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4769 x 5487
Think step by step. | To solve the long multiplication equation \( 4769 \times 5487 \), 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 \( 4769 \) by each digit of \( 5487 \) (from right to left), shifting the partial results accordingl... | 26167503 | What is the solution to the long multiplication equation below?
4769 x 5487
Think step by step. | true | The solution correctly follows the long multiplication method and accurately computes the product of 4769 and 5487, resulting in 26167503, which matches the ground truth. | 320 | 0 | To solve the long multiplication equation \( 4769 \times 5487 \), 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 \( 4769 \) by each digit of \( 5487 \) (from right to left), shifting the partial results accordingl... | [
{
"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 4769 x 5487, 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 a p... | 243 | 5,700 | 5,457 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4947 x 4493
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4947** and **4493**. 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. I recall that long multiplication involves multiply... | 22226871 | What is the solution to the long multiplication equation below?
4947 x 4493
Think step by step. | true | The provided solution correctly calculates the multiplication of 4947 and 4493 step-by-step, breaking it down into manageable partial products. Each step is verified with consistent results, and the final result matches the ground truth solution of 22226871. | 321 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4947** and **4493**. 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. I recall that long multiplication involves multiply... | [
{
"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: **4947** and **4493**. 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... | 870 | 881 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6418 x 1671
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6418** and **1671**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | 10724478 | What is the solution to the long multiplication equation below?
6418 x 1671
Think step by step. | true | The solution correctly identifies the product of 6418 and 1671 as 10,724,478. It thoroughly details each step of the multiplication process, confirms the result using both a breakdown of operations and standard long multiplication, and matches the ground truth solution. | 322 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **6418** and **1671**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | [
{
"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: **6418** and **1671**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 843 | 851 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2064 x 4108
Think step by step. | To solve the long multiplication equation \(2064 \times 4108\), 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 adding the partial results.
#... | 8478912 | What is the solution to the long multiplication equation below?
2064 x 4108
Think step by step. | true | The solution provided correctly details the steps of breaking down the long multiplication of 2064 by 4108 using the distributive property and accurately calculates each partial product. The final total of 8,478,912 matches the ground truth solution of 8478912, confirming the correctness of the solution. | 323 | 0 | To solve the long multiplication equation \(2064 \times 4108\), 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 adding 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 long multiplication equation \\(2064 \\times 4108\\), 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... | 207 | 225 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7698 x 1692
Think step by step. | To solve the long multiplication equation \( 7698 \times 1692 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7698 \) by each digit of \( 1692 \) (considering their place values) and then add the results together.
### Step 1: Break ... | 13025016 | What is the solution to the long multiplication equation below?
7698 x 1692
Think step by step. | true | The solution provided follows the correct steps of breaking down the multiplication using the distributive property and accurately calculates the result. The final calculated answer of 13,025,016 matches the ground truth solution, 13025016, when formatted without a comma. Therefore, the solution is correct. | 324 | 0 | To solve the long multiplication equation \( 7698 \times 1692 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7698 \) by each digit of \( 1692 \) (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 \\( 7698 \\times 1692 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7698 \\) by each digit of \\( 1692 \\) (considering their pla... | 307 | 316 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8095 x 6733
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8095** and **6733**. 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) ... | 54503635 | What is the solution to the long multiplication equation below?
8095 x 6733
Think step by step. | true | The provided solution arrives at the final result of 54,503,635, which matches the ground truth solution of 54503635, albeit with formatting variations (scientific notation vs standard form). Therefore, the solution is considered correct. | 325 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **8095** and **6733**. 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: **8095** and **6733**. 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... | 632 | 660 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7808 x 1869
Think step by step. | To solve the long multiplication equation \( 7808 \times 1869 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7808 \) by each digit of \( 1869 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | 14593152 | What is the solution to the long multiplication equation below?
7808 x 1869
Think step by step. | true | The solution provided matches the ground truth solution after breaking down the multiplication and adding the partial results accurately. The calculations and summation steps were correctly followed, leading to the correct product of the multiplication. | 326 | 0 | To solve the long multiplication equation \( 7808 \times 1869 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7808 \) by each digit of \( 1869 \) (considering their place values) and then sum the results.
### Step 1: Break down 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 long multiplication equation \\( 7808 \\times 1869 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7808 \\) by each digit of \\( 1869 \\) (considering their place values) an... | 188 | 196 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8611 x 5758
Think step by step. | To solve the long multiplication problem \( 8611 \times 5758 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8611 \) by each digit of \( 5758 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | 49582138 | What is the solution to the long multiplication equation below?
8611 x 5758
Think step by step. | true | The solution correctly follows the steps of long multiplication using the distributive property. Each multiplication step is accurate, and the final total matches the ground truth solution when formatted without commas. | 327 | 0 | To solve the long multiplication problem \( 8611 \times 5758 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8611 \) by each digit of \( 5758 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | [
{
"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 \\( 8611 \\times 5758 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8611 \\) by each digit of \\( 5758 \\) (considering their place values) and... | 405 | 401 | -4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6478 x 5105
Think step by step. | To solve the long multiplication equation \( 6478 \times 5105 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6478) by each digit of the multiplier (5105) and then summing the partial results.
### Step 1: Break... | 33070190 | What is the solution to the long multiplication equation below?
6478 x 5105
Think step by step. | true | The solution correctly calculates the result of the multiplication using both the distributive property and standard long multiplication. The final result presented as boxed is in accordance with the ground truth solution, confirming it is accurate. | 328 | 0 | To solve the long multiplication equation \( 6478 \times 5105 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6478) by each digit of the multiplier (5105) 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 \\( 6478 \\times 5105 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6478) by each digit of the multiplier (5... | 236 | 245 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9532 x 7086
Think step by step. | To solve the long multiplication equation \(9532 \times 7086\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9532) by each digit of the multiplier (7086), starting from the rightmost digit, and then summing up th... | 67543752 | What is the solution to the long multiplication equation below?
9532 x 7086
Think step by step. | false | The calculated result of the multiplication is 67,543,752, whereas the ground truth solution states that the result should be 67,543,752, but with a typo in the comparison on formatting. The answer does match, but the formatting error led to an unnecessary confusion regarding the correctness. | 329 | 0 | To solve the long multiplication equation \(9532 \times 7086\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9532) by each digit of the multiplier (7086), 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 9532 x 7086, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9532) by each digit of the multiplier (7086), starting... | 297 | 310 | 13 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6570 x 8958
Think step by step. | To solve the long multiplication equation \(6570 \times 8958\), 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 (8958)
We can express \(8958\) as:
\[
8958 = 9000 - 42
\]
This allows us to rewrite the multiplicat... | 58854060 | What is the solution to the long multiplication equation below?
6570 x 8958
Think step by step. | true | The provided solution calculated the product of 6570 and 8958 accurately using the distributive property and showed all the intermediate steps clearly. The numerical result of 58,854,060 matches the ground truth solution of 58854060. The difference in representation (with commas and without) does not affect the correct... | 330 | 0 | To solve the long multiplication equation \(6570 \times 8958\), 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 (8958)
We can express \(8958\) as:
\[
8958 = 9000 - 42
\]
This allows us to rewrite the multiplicat... | [
{
"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 6570 x 8958, 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": "thought",... | 169 | 185 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5965 x 8759
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5965** and **8759**. 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... | 52247435 | What is the solution to the long multiplication equation below?
5965 x 8759
Think step by step. | true | The solution correctly calculates the multiplication of 5965 and 8759 using long multiplication and verifies the result with a standard method. The steps are detailed, showing how the final answer matches the ground truth solution, which is also 52247435. | 331 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **5965** and **8759**. 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: **5965** and **8759**. 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... | 846 | 846 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4025 x 1602
Think step by step. | To solve the multiplication problem \( 4025 \times 1602 \), 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 (1602)
The multiplier \( 1602 \) can be expressed as:
\[ 1602 = 1000 + 600 + 2 \]
### Step 2: Mult... | 6448050 | What is the solution to the long multiplication equation below?
4025 x 1602
Think step by step. | true | The provided solution methodically breaks down the multiplication of 4025 and 1602 using the distributive property, correctly calculates each intermediate step, and sums them accurately to arrive at the final result. The final answer in the solution matches the ground truth solution. | 332 | 0 | To solve the multiplication problem \( 4025 \times 1602 \), 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 (1602)
The multiplier \( 1602 \) can be expressed as:
\[ 1602 = 1000 + 600 + 2 \]
### Step 2: 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 multiplication problem \\( 4025 \\times 1602 \\), 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"... | 182 | 188 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3564 x 2153
Think step by step. | To solve the multiplication problem \( 3564 \times 2153 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3564 \) by each digit of \( 2153 \), starting from the rightmost digit (units place) and moving left, shifting the part... | 7673292 | What is the solution to the long multiplication equation below?
3564 x 2153
Think step by step. | true | The solution provided correctly follows the long multiplication process step-by-step, leading to the accurate result of the multiplication. The partial products are calculated correctly and the final sum is also accurate, confirming that the solution is correct. | 333 | 0 | To solve the multiplication problem \( 3564 \times 2153 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3564 \) by each digit of \( 2153 \), starting from the rightmost digit (units place) and moving left, shifting 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 multiplication problem \\( 3564 \\times 2153 \\), 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 ... | 221 | 227 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6681 x 4440
Think step by step. | To solve the multiplication problem \( 6681 \times 4440 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier \( 4440 \)
Notice that \( 4440 \) can be expressed as ... | 29663640 | What is the solution to the long multiplication equation below?
6681 x 4440
Think step by step. | true | The solution correctly applies the distributive property of multiplication and performs each step accurately through breakdown, multiplication, and addition to reach the final result of 29,663,640, which matches the ground truth solution. | 334 | 0 | To solve the multiplication problem \( 6681 \times 4440 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier \( 4440 \)
Notice that \( 4440 \) can be expressed 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 \\( 6681 \\times 4440 \\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a detailed step-by-step solution:",
"equation": "",
"finis... | 231 | 249 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1161 x 8831
Think step by step. | To solve the multiplication problem \( 1161 \times 8831 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1161 \) by each digit of \( 8831 \), starting from the rightmost digit (units place), and then sum the results.
\[
\beg... | 10252791 | What is the solution to the long multiplication equation below?
1161 x 8831
Think step by step. | false | The solution arrived at a final answer of 10,252,791, while the ground truth solution provided is 10,252,791. The digits match, but the formatting and presentation of the answer suggest a possibility of miscounting or a transcription error. There might be a discrepancy regarding leading zeros or formatting, but as per ... | 335 | 0 | To solve the multiplication problem \( 1161 \times 8831 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1161 \) by each digit of \( 8831 \), starting from the rightmost digit (units place), and then sum the results.
\[
\beg... | [
{
"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 \\( 1161 \\times 8831 \\), 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... | 212 | 226 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1707 x 5402
Think step by step. | To solve the long multiplication equation \(1707 \times 5402\), 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, adjusting for place value, and then adding the partial results.
###... | 9221214 | What is the solution to the long multiplication equation below?
1707 x 5402
Think step by step. | true | The solution provided shows an accurate step-by-step process of breaking down the multiplication and using the distributive property to calculate the product of 1707 and 5402. The final answer of 9221214 matches the ground truth solution. | 336 | 0 | To solve the long multiplication equation \(1707 \times 5402\), 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, adjusting for place value, and then adding 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 long multiplication equation 1707 x 5402, 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, adjusting for place... | 193 | 211 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1449 x 7095
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1449** and **7095**. At first glance, this seems complex because both numbers are in the thousands. Breaking it down using the **long multiplication** method should make it manageable. Long multiplication involves multiplying each digit of th... | 10280655 | What is the solution to the long multiplication equation below?
1449 x 7095
Think step by step. | true | The solution provided correctly computes the product of 1449 and 7095 using long multiplication, verified through multiple approaches. All intermediate steps and final calculations are accurate, leading to the correct final result of 10,280,655. | 337 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1449** and **7095**. At first glance, this seems complex because both numbers are in the thousands. Breaking it down using the **long multiplication** method should make it manageable. Long multiplication involves multiplying each digit of 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 multiply two large numbers: **1449** and **7095**. At first glance, this seems complex because both numbers are in the thousands. Breaking it down using the **long multiplication** method should make it manageabl... | 940 | 948 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5336 x 8562
Think step by step. | To solve the long multiplication equation \(5336 \times 8562\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
5336
× 8562
________
```
### Step 2: Multiply 5336 by each digit of 8562, starting from the rightmost ... | 45686832 | What is the solution to the long multiplication equation below?
5336 x 8562
Think step by step. | true | The long multiplication was executed correctly and all intermediate calculations and the final sum were verified accurately. | 338 | 0 | To solve the long multiplication equation \(5336 \times 8562\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
5336
× 8562
________
```
### Step 2: Multiply 5336 by each digit of 8562, starting from the rightmost ... | [
{
"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 5336 × 8562, 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... | 497 | 497 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4763 x 4483
Think step by step. | To solve the long multiplication equation \( 4763 \times 4483 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4763 \) by each digit of \( 4483 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 21352529 | What is the solution to the long multiplication equation below?
4763 x 4483
Think step by step. | true | The solution correctly applies the distributive property of multiplication to break down the calculation of 4763 times 4483 into manageable parts, multiplies these parts accurately, and sums the results correctly. The final answer matches the ground truth solution when presented without commas. | 339 | 0 | To solve the long multiplication equation \( 4763 \times 4483 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4763 \) by each digit of \( 4483 \), 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 \\( 4763 \\times 4483 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 4763 \\) by each digit of \\( 4483 \\), accounting for place ... | 276 | 278 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4333 x 1206
Think step by step. | To solve the multiplication problem \(4333 \times 1206\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(1206\) as \(1000 + 200 + 6\). This allows us to multiply \(4333\) by each component separately and then add the results.
... | 5225598 | What is the solution to the long multiplication equation below?
4333 x 1206
Think step by step. | true | The solution correctly follows the long multiplication method and breaks down the multiplication step-by-step, providing accurate calculations and an accurate final answer. The final answer matches the ground truth solution. | 340 | 0 | To solve the multiplication problem \(4333 \times 1206\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(1206\) as \(1000 + 200 + 6\). This allows us to multiply \(4333\) by each component separately and then add the 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 \\(4333 \\times 1206\\), we can use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe can express \\(1206\\) as \\(1000 + 200 + 6\\). This allows us to multip... | 153 | 169 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1966 x 3555
Think step by step. | To solve the multiplication \( 1966 \times 3555 \), 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 (3555)
Express \( 3555 \) as \( 4000 - 445 \). This simplifies the multiplication because multiplying by \(... | 6989130 | What is the solution to the long multiplication equation below?
1966 x 3555
Think step by step. | true | The solution correctly applies the distributive property, calculates intermediate products accurately, sums them correctly, and performs the final subtraction to arrive at the correct final result of 6989130. | 341 | 0 | To solve the multiplication \( 1966 \times 3555 \), 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 (3555)
Express \( 3555 \) as \( 4000 - 445 \). This simplifies the multiplication because multiplying by \(... | [
{
"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 \\( 1966 \\times 3555 \\), 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... | 291 | 291 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7945 x 9508
Think step by step. | To solve the long multiplication equation \( 7945 \times 9508 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7945) by each digit of the multiplier (9508) and then summing the partial results.
### Step 1: Break... | 75541060 | What is the solution to the long multiplication equation below?
7945 x 9508
Think step by step. | true | The proposed solution correctly calculates the product of 7945 and 9508 using the distributive property and confirms it with long multiplication, arriving at the correct answer of 75,541,060. This matches the ground truth solution provided. | 342 | 0 | To solve the long multiplication equation \( 7945 \times 9508 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7945) by each digit of the multiplier (9508) 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 \\( 7945 \\times 9508 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7945) by each digit of the multiplier (9... | 307 | 307 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1176 x 2159
Think step by step. | To solve the multiplication problem \( 1176 \times 2159 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1176 \) by each digit of \( 2159 \), starting from the rightmost digit (units place) and moving left. Remember to accou... | 2538984 | What is the solution to the long multiplication equation below?
1176 x 2159
Think step by step. | true | The provided solution correctly applies the long multiplication method, calculates each partial product accurately, and sums them to find the correct final result. The final answer matches the ground truth solution. | 343 | 0 | To solve the multiplication problem \( 1176 \times 2159 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1176 \) by each digit of \( 2159 \), starting from the rightmost digit (units place) and moving left. Remember to accou... | [
{
"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 \\( 1176 \\times 2159 \\), 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 ... | 226 | 232 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6754 x 3608
Think step by step. | To solve the long multiplication equation \( 6754 \times 3608 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6754 \) by each digit of \( 3608 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
T... | 24368432 | What is the solution to the long multiplication equation below?
6754 x 3608
Think step by step. | true | The provided solution correctly breaks down the multiplication using the distributive property of multiplication. Each step is accurately calculated, leading to the final result of 24,368,432, which matches the ground truth solution exactly. The verification through standard long multiplication confirms the calculation... | 344 | 0 | To solve the long multiplication equation \( 6754 \times 3608 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6754 \) by each digit of \( 3608 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
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 \\( 6754 \\times 3608 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 6754 \\) by each digit of \\( 3608 \\), accounting for place values, and t... | 364 | 364 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5628 x 4761
Think step by step. | To solve the multiplication problem \(5628 \times 4761\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5628\) by each digit of \(4761\) (from right to left), shifting the partial results accordingly.
\[
\begin{array}{r}
\phan... | 26794908 | What is the solution to the long multiplication equation below?
5628 x 4761
Think step by step. | true | The solution follows the long multiplication method correctly, detailing each step of the multiplication and the addition of the partial products. The final computed value matches the ground truth solution, confirming its correctness. | 345 | 0 | To solve the multiplication problem \(5628 \times 4761\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5628\) by each digit of \(4761\) (from right to left), shifting the partial results accordingly.
\[
\begin{array}{r}
\phan... | [
{
"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 \\(5628 \\times 4761\\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding th... | 394 | 418 | 24 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3443 x 8080
Think step by step. | To solve the multiplication problem \(3443 \times 8080\), 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 multiplication
Notice that \(8080\) can be written as \(8000 + 80\). So, we can rewrite the m... | 27819440 | What is the solution to the long multiplication equation below?
3443 x 8080
Think step by step. | true | The solution correctly applies the distributive property to break down and compute the multiplication of 3443 and 8080. The intermediate calculations for both parts of the multiplication are accurate, leading to the correct final sum. Thus, the final answer of 27,819,440 matches the ground truth solution. | 346 | 0 | To solve the multiplication problem \(3443 \times 8080\), 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 multiplication
Notice that \(8080\) can be written as \(8000 + 80\). So, we can rewrite 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 multiplication problem \\(3443 \\times 8080\\), 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": ""... | 193 | 211 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6392 x 1910
Think step by step. | To solve the long multiplication equation \( 6392 \times 1910 \), we can break it down into simpler steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 1910 \) can be written as \( 2000 - 90 \). This allows us to use the distributive property of multiplication over ... | 12208720 | What is the solution to the long multiplication equation below?
6392 x 1910
Think step by step. | true | The provided solution correctly breaks down the multiplication using the distributive property, carries out each step accurately, and verifies the final result using long multiplication. Both the solution and the ground truth are equivalent, confirming the correctness of the solution. | 347 | 0 | To solve the long multiplication equation \( 6392 \times 1910 \), we can break it down into simpler steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 1910 \) can be written as \( 2000 - 90 \). This allows us to use the distributive property of multiplication over ... | [
{
"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 \\( 6392 \\times 1910 \\), 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... | 381 | 378 | -3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8249 x 3329
Think step by step. | To solve the long multiplication equation \( 8249 \times 3329 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8249 \) by each digit of \( 3329 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 27460921 | What is the solution to the long multiplication equation below?
8249 x 3329
Think step by step. | true | The solution correctly applies the distributive property of multiplication over addition to compute the product of 8249 and 3329. All steps of the multiplication and addition are performed accurately, leading to the correct final answer of 27,460,921, which matches the ground truth solution. | 348 | 0 | To solve the long multiplication equation \( 8249 \times 3329 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8249 \) by each digit of \( 3329 \) (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 \\( 8249 \\times 3329 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8249 \\) by each digit of \\( 3329 \\) (considering their pla... | 243 | 245 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3132 x 1281
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: 3132 and 1281. 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... | 4012092 | What is the solution to the long multiplication equation below?
3132 x 1281
Think step by step. | true | The solution correctly calculated the product of 3132 and 1281 using two methods: long multiplication and the box method. Both methods confirmed the final result as 4,012,092, which matches the ground truth solution provided. | 349 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 3132 and 1281. 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: 3132 and 1281. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ""... | 793 | 794 | 1 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4707 x 6926
Think step by step. | To solve the multiplication problem \( 4707 \times 6926 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4707 \) by each digit of \( 6926 \), starting from the rightmost digit (units place), and shift the partial results acco... | 32600682 | What is the solution to the long multiplication equation below?
4707 x 6926
Think step by step. | true | The step-by-step breakdown and calculations in the solution show a correct long multiplication process, leading to the correct final answer of 32,600,682, which matches the ground truth solution. | 350 | 0 | To solve the multiplication problem \( 4707 \times 6926 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4707 \) by each digit of \( 6926 \), starting from the rightmost digit (units place), and shift the partial results acco... | [
{
"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 \\( 4707 \\times 6926 \\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding ... | 492 | 501 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9643 x 7497
Think step by step. | To solve the multiplication problem \(9643 \times 7497\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9643\) by each digit of \(7497\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&9643... | 72293571 | What is the solution to the long multiplication equation below?
9643 x 7497
Think step by step. | false | The provided solution calculates the product of 9643 and 7497 using long multiplication and arrives at 72,281,571, which does not match the ground truth solution of 72,293,571. This indicates a computational error in either the partial results or the final sum. | 351 | 0 | To solve the multiplication problem \(9643 \times 7497\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9643\) by each digit of \(7497\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&9643... | [
{
"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 \\(9643 \\times 7497\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe'll multiply \\(9643\\) by each digit of \\(7497\\) (from right to left), ... | 491 | 505 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1110 x 5110
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two numbers: 1110 and 5110. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking them down using the distributiv... | 5672100 | What is the solution to the long multiplication equation below?
1110 x 5110
Think step by step. | true | The calculation steps clearly detailed the multiplication process correctly and arrived at the final result of 5,672,100, which matches the ground truth solution of 5672100 (the same value with formatting differences). The verification methods used also confirmed the correctness of the calculations. | 353 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two numbers: 1110 and 5110. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking them down using the distributiv... | [
{
"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 numbers: 1110 and 5110. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": "",
... | 511 | 511 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3450 x 3848
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3450** and **3848**. 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) ... | 13275600 | What is the solution to the long multiplication equation below?
3450 x 3848
Think step by step. | true | The provided solution successfully details the steps of long multiplication, accurately calculates and adds all the partial products, and verifies the final result using an alternative method. The final answer (13,275,600) matches the ground truth solution. | 354 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3450** and **3848**. 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: **3450** and **3848**. 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... | 1,054 | 1,067 | 13 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7597 x 9379
Think step by step. | To solve the long multiplication equation \( 7597 \times 9379 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
7597
× 9379
-------
```
### Step 2: Multiply 7597 by each digit of 9379, starting from the right ... | 71252263 | What is the solution to the long multiplication equation below?
7597 x 9379
Think step by step. | true | The solution correctly follows the long multiplication method step-by-step, and accurately calculates the result of 7597 times 9379. The final answer presented matches the ground truth solution, confirming its correctness. | 355 | 0 | To solve the long multiplication equation \( 7597 \times 9379 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
7597
× 9379
-------
```
### Step 2: Multiply 7597 by each digit of 9379, 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 \\( 7597 \\times 9379 \\), 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... | 268 | 270 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3322 x 5559
Think step by step. | To solve the long multiplication equation \( 3322 \times 5559 \), 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, appropriately shifted, and then adding all the partial results tog... | 18466998 | What is the solution to the long multiplication equation below?
3322 x 5559
Think step by step. | true | The provided solution correctly breaks down the multiplication using the distributive property, calculates each partial product accurately, and adds them up correctly to arrive at the final result of 18,466,998, which matches the ground truth solution. | 356 | 0 | To solve the long multiplication equation \( 3322 \times 5559 \), 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, appropriately shifted, and then adding all the partial results 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 \\( 3322 \\times 5559 \\), 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, appro... | 366 | 399 | 33 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2646 x 3200
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **2646 × 3200**.
At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly. I recall that breaking down the multiplication into simpler, ... | 8467200 | What is the solution to the long multiplication equation below?
2646 x 3200
Think step by step. | true | The solution provided correctly follows the steps of multiplication and verification, arriving at the correct final product of 8,467,200. | 357 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **2646 × 3200**.
At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly. I recall that breaking down the multiplication into simpler, ... | [
{
"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 problem: **2646 × 3200**. \n\nAt first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly.... | 580 | 597 | 17 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1332 x 9737
Think step by step. | To solve the long multiplication equation \(1332 \times 9737\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1332) by each digit of the multiplier (9737), starting from the rightmost digit, and then summing up th... | 12969684 | What is the solution to the long multiplication equation below?
1332 x 9737
Think step by step. | true | The solution provided uses the distributive property correctly to break down the multiplication of 1332 and 9737 into manageable pieces and sums them accurately. The step-by-step verification confirms the final answer of 12969684, which matches the ground truth solution. | 358 | 0 | To solve the long multiplication equation \(1332 \times 9737\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1332) by each digit of the multiplier (9737), 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 \\(1332 \\times 9737\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1332) by each digit of the multiplier (973... | 311 | 315 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7200 x 6145
Think step by step. | To solve the long multiplication equation \(7200 \times 6145\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \(7200 \times 6145\) as:
\[
7200 \times 6145 = 7200 \times (6000 +... | 44244000 | What is the solution to the long multiplication equation below?
7200 x 6145
Think step by step. | true | The solution provided accurately follows the steps of long multiplication and arrives at the correct final result of 44,244,000, which matches the ground truth solution of 44244000. Therefore, the solution is correct. | 359 | 0 | To solve the long multiplication equation \(7200 \times 6145\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \(7200 \times 6145\) as:
\[
7200 \times 6145 = 7200 \times (6000 +... | [
{
"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 \\(7200 \\times 6145\\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:\n\n### Step 1: Break down the multiplication using the distributive property\nWe can express \\... | 321 | 365 | 44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8000 x 1716
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication problem: **8000 × 1716**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't approach it systematically.
### Breaking Down the Numbers
I recall that breaki... | 13728000 | What is the solution to the long multiplication equation below?
8000 x 1716
Think step by step. | true | The solution correctly demonstrates the multiplication of 8000 and 1716, going through a detailed step-by-step explanation that confirms the calculation results in 13,728,000. This matches the ground truth solution of 13728000. | 360 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication problem: **8000 × 1716**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't approach it systematically.
### Breaking Down the Numbers
I recall that breaki... | [
{
"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 simple multiplication problem: **8000 × 1716**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't approach it systemat... | 649 | 672 | 23 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7254 x 8804
Think step by step. | To solve the multiplication problem \( 7254 \times 8804 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7254 \) by each digit of \( 8804 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
... | 63864216 | What is the solution to the long multiplication equation below?
7254 x 8804
Think step by step. | false | The solution presented has a formatting issue in the final answer by including commas. The ground truth solution '63864216' does not have commas. Though the numerical value calculated is correct, the final answer format does not match the ground truth. | 361 | 0 | To solve the multiplication problem \( 7254 \times 8804 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7254 \) by each digit of \( 8804 \), 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 \\( 7254 \\times 8804 \\), 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 ... | 239 | 253 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1723 x 1321
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 1723 and 1321. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 1723 by each digit of 1321, starting from the rightmost digit, and then add all ... | 2276083 | What is the solution to the long multiplication equation below?
1723 x 1321
Think step by step. | true | The provided solution correctly follows the long multiplication method, breaking down the multiplication into manageable parts and verifying the result through multiple methods. After performing the calculations step by step and adding the partial products, the final result of 2276083 matches the ground truth solution. | 362 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: 1723 and 1321. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 1723 by each digit of 1321, starting from the rightmost digit, and then add all ... | [
{
"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: 1723 and 1321. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 1723 by each digit o... | 894 | 894 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7300 x 9977
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **7300** and **9977**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem using the distributive property of multiplication over addition can simplify the calculation... | 72832100 | What is the solution to the long multiplication equation below?
7300 x 9977
Think step by step. | true | The solution correctly calculates the product of 7300 and 9977 using both the distributive property and long multiplication, arriving at the final answer of 72,832,100. This matches the ground truth solution. | 363 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **7300** and **9977**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem using the distributive property of multiplication over addition can simplify the calculation... | [
{
"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: **7300** and **9977**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem using the distributive property ... | 462 | 483 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7679 x 7863
Think step by step. | To solve the long multiplication equation \( 7679 \times 7863 \), 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 (7863) by each digit of the first number (7679) and then summing the results.
### Step... | 60379977 | What is the solution to the long multiplication equation below?
7679 x 7863
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication into components, accurately computes each partial product, and sums them correctly. The final result matches the ground truth solution of 60379977. | 364 | 0 | To solve the long multiplication equation \( 7679 \times 7863 \), 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 (7863) by each digit of the first number (7679) and then summing the results.
### Step... | [
{
"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 \\( 7679 \\times 7863 \\), 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 (7863) by each digit of th... | 285 | 285 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4891 x 1576
Think step by step. | To solve the multiplication problem \( 4891 \times 1576 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4891 \) by each digit of \( 1576 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 7708216 | What is the solution to the long multiplication equation below?
4891 x 1576
Think step by step. | true | The provided solution breaks down the multiplication correctly using both the long multiplication method and then verifies the final answer through addition of partial products, which matches the ground truth solution of 7708216. | 365 | 0 | To solve the multiplication problem \( 4891 \times 1576 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4891 \) by each digit of \( 1576 \), 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 \\( 4891 \\times 1576 \\), 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... | 287 | 301 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7306 x 2953
Think step by step. | To solve the long multiplication equation \(7306 \times 2953\), 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... | 21574618 | What is the solution to the long multiplication equation below?
7306 x 2953
Think step by step. | true | The solution correctly uses the distributive property of multiplication and verifies the result with the traditional long multiplication method, arriving at the same final result as the ground truth. | 366 | 0 | To solve the long multiplication equation \(7306 \times 2953\), 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 7306 x 2953, 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... | 281 | 285 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5907 x 3215
Think step by step. | To solve the long multiplication equation \(5907 \times 3215\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5907\) by each digit of \(3215\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | 18991005 | What is the solution to the long multiplication equation below?
5907 x 3215
Think step by step. | false | The calculated result of 18,990,975 is incorrect. The ground truth solution is 18,991,005. There is a discrepancy of 30, indicating an error in the steps or calculations performed in the solution. | 367 | 0 | To solve the long multiplication equation \(5907 \times 3215\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5907\) by each digit of \(3215\) (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 5907 x 3215, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 5907 by each digit of 3215 (considering their place values) and then sum the re... | 212 | 240 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5136 x 4072
Think step by step. | To solve the long multiplication equation \(5136 \times 4072\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5136\) by each digit of \(4072\) (from right to left), shifting the partial results appropriately, and then add them together.... | 20913792 | What is the solution to the long multiplication equation below?
5136 x 4072
Think step by step. | true | The provided solution correctly calculates the long multiplication of 5136 and 4072, and the final result of 20,913,792 matches the ground truth solution of 20913792 when the comma is removed. Therefore, the solution is correct. | 368 | 0 | To solve the long multiplication equation \(5136 \times 4072\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5136\) by each digit of \(4072\) (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 \\(5136 \\times 4072\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(5136\\) by each digit of \\(4072\\) (from right to left), shifti... | 260 | 286 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6011 x 8360
Think step by step. | To solve the long multiplication equation \(6011 \times 8360\), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(8360\) can be written as \(8000 + 300 + 60 + 0\). So, we can multiply \(6011\) by each of these components separately and then... | 50251960 | What is the solution to the long multiplication equation below?
6011 x 8360
Think step by step. | true | The solution correctly performed the steps of long multiplication by breaking down the second number into manageable parts, performing each multiplication accurately, and then correctly adding the results together. The final answer matches the ground truth solution provided. | 369 | 0 | To solve the long multiplication equation \(6011 \times 8360\), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(8360\) can be written as \(8000 + 300 + 60 + 0\). So, we can multiply \(6011\) by each of these components separately and then... | [
{
"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 \\(6011 \\times 8360\\), 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 \\(8360\\) can be written as \\(8000 + 300 + 60 + 0\\). So, we c... | 197 | 223 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5919 x 9111
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: 5919 and 9111. 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... | 53928009 | What is the solution to the long multiplication equation below?
5919 x 9111
Think step by step. | true | The provided solution correctly performs the long multiplication of the two large numbers, 5919 and 9111, step by step, and accurately arrives at the final product of 53,928,009. The reasoning is thorough, and the calculations are verified through alternative methods, consistently confirming the same result. | 370 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5919 and 9111. 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: 5919 and 9111. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
... | 842 | 842 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6040 x 3531
Think step by step. | To solve the long multiplication equation \(6040 \times 3531\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6040\) by each digit of \(3531\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | 21327240 | What is the solution to the long multiplication equation below?
6040 x 3531
Think step by step. | true | The solution correctly applies the distributive property of multiplication, breaks down the multiplier, performs each multiplication accurately, and adds the results to arrive at the correct final answer of 21327240, which matches the ground truth. | 371 | 0 | To solve the long multiplication equation \(6040 \times 3531\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6040\) by each digit of \(3531\) (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 6040 x 3531, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 6040 by each digit of 3531 (considering their place values) and then sum the re... | 217 | 230 | 13 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7554 x 7369
Think step by step. | To solve the long multiplication problem \( 7554 \times 7369 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7554 \) by each digit of \( 7369 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | 55665426 | What is the solution to the long multiplication equation below?
7554 x 7369
Think step by step. | false | The solution provided gives the final result as 55,665,426, which has a different format than the ground truth solution provided, which is 55665426. The difference is the presence of a comma in the solution but not in the ground truth. However, the numerical value calculated by the solution matches the ground truth val... | 372 | 0 | To solve the long multiplication problem \( 7554 \times 7369 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7554 \) by each digit of \( 7369 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | [
{
"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 \\( 7554 \\times 7369 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7554 \\) by each digit of \\( 7369 \\) (considering their place values) and... | 375 | 379 | 4 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4100 x 9562
Think step by step. | To solve the long multiplication equation \( 4100 \times 9562 \), we can break it down into simpler, more manageable steps. Here's how you can approach it:
### Step 1: Break down the multiplication using the distributive property
We can express \( 4100 \times 9562 \) as:
\[
4100 \times 9562 = 4100 \times (9000 + 500 +... | 39204200 | What is the solution to the long multiplication equation below?
4100 x 9562
Think step by step. | true | The provided solution breaks down the multiplication of 4100 and 9562 correctly using the distributive property, calculates each partial product accurately, and sums them to reach the final answer of 39,204,200. The solution matches the ground truth of 39204200. Therefore, the solution is correct. | 373 | 0 | To solve the long multiplication equation \( 4100 \times 9562 \), we can break it down into simpler, more manageable steps. Here's how you can approach it:
### Step 1: Break down the multiplication using the distributive property
We can express \( 4100 \times 9562 \) as:
\[
4100 \times 9562 = 4100 \times (9000 + 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 long multiplication equation \\( 4100 \\times 9562 \\), we can break it down into simpler, more manageable steps. Here's how you can approach it:\n\n### Step 1: Break down the multiplication using the distributive property\nWe can express \\( 4100 \... | 331 | 390 | 59 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9800 x 4858
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9800** and **4858**. 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 **long multiplication** method, which involves multiplyi... | 47608400 | What is the solution to the long multiplication equation below?
9800 x 4858
Think step by step. | true | The solution arrives at the correct result of multiplying 9800 and 4858, which is 47608400, by breaking down the multiplication into manageable parts and verifying the calculations through an alternative method. The detailed steps taken show thorough reasoning and proper arithmetic operations. | 374 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9800** and **4858**. 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 **long multiplication** method, which involves multiplyi... | [
{
"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: **9800** and **4858**. 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 ... | 623 | 631 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5283 x 7345
Think step by step. | To solve the long multiplication equation \(5283 \times 7345\), 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, starting from the rightmost digit, and then summing all the partial ... | 38803635 | What is the solution to the long multiplication equation below?
5283 x 7345
Think step by step. | true | The solution correctly breaks down the multiplication problem, calculates each partial product accurately, and sums them correctly to arrive at the final result. The final answer of 38803635 matches the ground truth solution. | 375 | 0 | To solve the long multiplication equation \(5283 \times 7345\), 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, starting from the rightmost digit, and then summing all the partial ... | [
{
"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 5283 x 7345, 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, starting from the r... | 247 | 293 | 46 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5144 x 7638
Think step by step. | To solve the multiplication problem \( 5144 \times 7638 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5144 \) by each digit of \( 7638 \), starting from the rightmost digit (units place) and moving left. Each partial produ... | 39289872 | What is the solution to the long multiplication equation below?
5144 x 7638
Think step by step. | true | The computation provided in the solution includes detailed steps of long multiplication, correctly processes each digit of the multiplier while accounting for place values, and adds the partial products accuracy to arrive at the final result. The final answer matches the ground truth solution, confirming that the solut... | 376 | 0 | To solve the multiplication problem \( 5144 \times 7638 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5144 \) by each digit of \( 7638 \), starting from the rightmost digit (units place) and moving left. Each partial produ... | [
{
"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 \\( 5144 \\times 7638 \\), 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... | 415 | 469 | 54 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8759 x 8442
Think step by step. | To solve the multiplication problem \( 8759 \times 8442 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8759 \) by each digit of \( 8442 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 73943478 | What is the solution to the long multiplication equation below?
8759 x 8442
Think step by step. | true | The solution provided accurately follows the long multiplication method step-by-step, leading to the correct final answer of 73943478, which matches the ground truth solution. | 377 | 0 | To solve the multiplication problem \( 8759 \times 8442 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8759 \) by each digit of \( 8442 \), 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 \\( 8759 \\times 8442 \\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understand the... | 594 | 618 | 24 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9265 x 7494
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9265** and **7494**. At first glance, this seems complex because both numbers are in the thousands. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 9265... | 69431910 | What is the solution to the long multiplication equation below?
9265 x 7494
Think step by step. | true | The solution accurately details the long multiplication steps required to multiply 9265 and 7494, along with the verification process using the distributive property. The final result of 69,431,910 matches the ground truth solution. | 378 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9265** and **7494**. At first glance, this seems complex because both numbers are in the thousands. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 9265... | [
{
"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: **9265** and **7494**. At first glance, this seems complex because both numbers are in the thousands. To tackle this, I recall that long multiplication breaks down the problem into sim... | 865 | 879 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4312 x 5413
Think step by step. | To solve the multiplication problem \(4312 \times 5413\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Write the numbers vertically
```
4312
× 5413
-------
```
### Step 2: Multiply 4312 by each digit of 5413, starting from the right
#### Multiply by 3 (unit... | 23340856 | What is the solution to the long multiplication equation below?
4312 x 5413
Think step by step. | true | The solution follows the long multiplication method correctly, and the final answer matches the ground truth. | 379 | 0 | To solve the multiplication problem \(4312 \times 5413\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Write the numbers vertically
```
4312
× 5413
-------
```
### Step 2: Multiply 4312 by each digit of 5413, starting from the right
#### Multiply by 3 (unit... | [
{
"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 \\(4312 \\times 5413\\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup the multip... | 188 | 190 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6506 x 7003
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: 6506 and 7003. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall that breaking them down ... | 45561518 | What is the solution to the long multiplication equation below?
6506 x 7003
Think step by step. | true | The solution accurately calculates the product of 6506 and 7003 through multiple methods, ultimately arriving at the correct final answer of 45561518. The formatting in scientific notation (4.5561518 x 10^7) is also mathematically valid as it represents the same number, just in a different format. Therefore, the soluti... | 380 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 6506 and 7003. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall that breaking them down ... | [
{
"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: 6506 and 7003. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ""... | 777 | 789 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3779 x 2653
Think step by step. | To solve the long multiplication equation \( 3779 \times 2653 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3779 \) by each digit of \( 2653 \), starting from the rightmost digit, and then sum the results, taking into account the p... | 10025687 | What is the solution to the long multiplication equation below?
3779 x 2653
Think step by step. | false | The two answers differ in formatting, but the calculated final answer of 10,025,687 (with a comma) matches the numeric value of the ground truth solution of 10025687, so the solution is effectively correct in value but fails in the presentation format. | 381 | 0 | To solve the long multiplication equation \( 3779 \times 2653 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3779 \) by each digit of \( 2653 \), starting from the rightmost digit, and then sum 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 \\( 3779 \\times 2653 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 3779 \\) by each digit of \\( 2653 \\), starting from the rig... | 342 | 342 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1707 x 8459
Think step by step. | To solve the multiplication problem \(1707 \times 8459\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \(1707\) by each digit of \(8459\) (from right to left), and then sum the results.
\[
\begin{align*}
1707 \times 8459 &= 1707 \tim... | 14439513 | What is the solution to the long multiplication equation below?
1707 x 8459
Think step by step. | false | The solution provided states the final answer as 14,439,513, which is formatted differently than the ground truth 14439513. However, upon removing the commas and comparing the two values, they are indeed the same (both equal to 14439513). The primary issue lies in the representation of the number rather than the correc... | 382 | 0 | To solve the multiplication problem \(1707 \times 8459\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \(1707\) by each digit of \(8459\) (from right to left), and then sum the results.
\[
\begin{align*}
1707 \times 8459 &= 1707 \tim... | [
{
"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 \\(1707 \\times 8459\\), 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 ... | 216 | 229 | 13 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8218 x 6065
Think step by step. | To solve the multiplication problem \( 8218 \times 6065 \), 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 (6065)
We can express \( 6065 \) as \( 6000 + 60 + 5 \). This allows us to multiply \( 8218 \) by e... | 49842170 | What is the solution to the long multiplication equation below?
8218 x 6065
Think step by step. | false | The solution incorrectly calculates the final result as 49,842,170 instead of the ground truth solution of 49,842,170 found in the ground truth, which is missing a leading zero. | 383 | 0 | To solve the multiplication problem \( 8218 \times 6065 \), 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 (6065)
We can express \( 6065 \) as \( 6000 + 60 + 5 \). This allows us to multiply \( 8218 \) by e... | [
{
"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 \\( 8218 \\times 6065 \\), 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"... | 303 | 309 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5155 x 1515
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two four-digit numbers: 5155 and 1515. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down into simpler, ... | 7809825 | What is the solution to the long multiplication equation below?
5155 x 1515
Think step by step. | true | The provided solution correctly computes the product of 5155 and 1515. The method used, which involves long multiplication along with verification through the distributive property, leads to the correct product of 7,809,825, which matches the ground truth solution. | 384 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two four-digit numbers: 5155 and 1515. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down into simpler, ... | [
{
"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 four-digit numbers: 5155 and 1515. My goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output"... | 586 | 594 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6756 x 1286
Think step by step. | To solve the multiplication problem \( 6756 \times 1286 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 6756 \) by each digit of \( 1286 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | 8688216 | What is the solution to the long multiplication equation below?
6756 x 1286
Think step by step. | false | The solution correctly breaks down the multiplication using long multiplication, but the final sum of the partial products was calculated incorrectly. The correct multiplication of 6756 and 1286 should yield 8688216, not 8690616 as calculated in the provided solution. | 385 | 0 | To solve the multiplication problem \( 6756 \times 1286 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 6756 \) by each digit of \( 1286 \), 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 \\( 6756 \\times 1286 \\), 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... | 184 | 198 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8637 x 5839
Think step by step. | To solve the long multiplication equation \( 8637 \times 5839 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8637 \) by each digit of \( 5839 \), starting from the rightmost digit, and then sum the partial results. Here's the step-by-step proces... | 50431443 | What is the solution to the long multiplication equation below?
8637 x 5839
Think step by step. | true | The solution provided accurately described the process of multiplying 8637 by 5839 using the distributive property, leading to the correct final answer of 50,431,443. The ground truth solution is equivalent to this result (50431443 without comma), confirming that the solution is correct. | 386 | 0 | To solve the long multiplication equation \( 8637 \times 5839 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8637 \) by each digit of \( 5839 \), starting from the rightmost digit, and then sum the partial results. Here's the step-by-step proces... | [
{
"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 \\( 8637 \\times 5839 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8637 \\) by each digit of \\( 5839 \\), starting from the rightmost digit,... | 440 | 471 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1031 x 8380
Think step by step. | To solve the multiplication problem \(1031 \times 8380\), 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 \(8380\) as \(8000 + 300 + 80 + 0\). Multiplying \(1031\) by each of these compon... | 8639780 | What is the solution to the long multiplication equation below?
1031 x 8380
Think step by step. | true | The provided solution accurately breaks down the multiplication of 1031 by 8380 into smaller components and correctly computes each part. The summed result matches the ground truth solution of 8639780. | 387 | 0 | To solve the multiplication problem \(1031 \times 8380\), 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 \(8380\) as \(8000 + 300 + 80 + 0\). Multiplying \(1031\) by each of these compon... | [
{
"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 1031 x 8380, 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",
... | 231 | 265 | 34 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3086 x 3265
Think step by step. | To solve the long multiplication equation \( 3086 \times 3265 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3086 \) by each digit of \( 3265 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 10075790 | What is the solution to the long multiplication equation below?
3086 x 3265
Think step by step. | true | The solution correctly applies the distributive property of multiplication over addition to calculate the product, providing accurate intermediate results and summing them correctly to reach the final result of 10075790. The verification step using traditional long multiplication confirms the correctness. | 388 | 0 | To solve the long multiplication equation \( 3086 \times 3265 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3086 \) by each digit of \( 3265 \) (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 \\( 3086 \\times 3265 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 3086 \\) by each digit of \\( 3265 \\) (considering their pla... | 356 | 356 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9061 x 4277
Think step by step. | To solve the multiplication problem \(9061 \times 4277\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9061\) by each digit of \(4277\) (from right to left), shifting the partial results appropriately based on the digit's plac... | 38753897 | What is the solution to the long multiplication equation below?
9061 x 4277
Think step by step. | true | The solution uses the long multiplication method correctly, breaking down each part of the multiplication step-by-step and accurately calculating the partial products and final sum. The final result matches the ground truth solution. | 389 | 0 | To solve the multiplication problem \(9061 \times 4277\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(9061\) by each digit of \(4277\) (from right to left), shifting the partial results appropriately based on the digit's plac... | [
{
"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 \\(9061 \\times 4277\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Break down the m... | 408 | 438 | 30 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1527 x 8940
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: 1527 and 8940. 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 concept of br... | 13651380 | What is the solution to the long multiplication equation below?
1527 x 8940
Think step by step. | true | The solution correctly follows the steps of multiplication for large numbers using the distributive property, verifies each step, and confirms the final result with a standard long multiplication method. The final numerical answer matches the provided ground truth of 13651380. | 390 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 1527 and 8940. 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 concept of br... | [
{
"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: 1527 and 8940. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ""... | 1,013 | 1,013 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9627 x 9184
Think step by step. | To solve the long multiplication problem \( 9627 \times 9184 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9627 \) by each digit of \( 9184 \), starting from the rightmost digit, and then sum the partial results. Here's how it's done step by st... | 88414368 | What is the solution to the long multiplication equation below?
9627 x 9184
Think step by step. | true | The solution follows the long multiplication method accurately and arrives at the same final product, 88414368, as given in the ground truth solution, verifying its correctness. | 391 | 0 | To solve the long multiplication problem \( 9627 \times 9184 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9627 \) by each digit of \( 9184 \), starting from the rightmost digit, and then sum the partial results. Here's how it's done step by st... | [
{
"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 \\( 9627 \\times 9184 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9627 \\) by each digit of \\( 9184 \\), starting from the rightmost digit, ... | 332 | 335 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4802 x 6949
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4802** and **6949**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number by the first number ... | 33369098 | What is the solution to the long multiplication equation below?
4802 x 6949
Think step by step. | true | The computed result (33,369,098) from the solution matches exactly with the ground truth solution (33369098) provided. Therefore, the solution is correct. | 392 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4802** and **6949**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number by the first 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": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **4802** and **6949**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves mult... | 865 | 876 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7449 x 4104
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: 7,449 and 4,104. 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 b... | 30570696 | What is the solution to the long multiplication equation below?
7449 x 4104
Think step by step. | true | The solution correctly demonstrates the process of multiplying the two numbers 7,449 and 4,104, including breaking down the multiplication into manageable parts, verifying the result using both direct long multiplication and an alternative method. The final computed result of 30,570,696 matches the ground truth solutio... | 393 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 7,449 and 4,104. 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 b... | [
{
"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: 7,449 and 4,104. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 1,031 | 1,041 | 10 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2563 x 2251
Think step by step. | To solve the multiplication problem \(2563 \times 2251\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2563\) by each digit of \(2251\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | 5769313 | What is the solution to the long multiplication equation below?
2563 x 2251
Think step by step. | true | The solution correctly applies the long multiplication method to calculate the product of 2563 and 2251 step by step. Each multiplication step and the subsequent addition of the partial results is accurate, leading to the correct final answer of 5769313, which matches the ground truth solution. | 394 | 0 | To solve the multiplication problem \(2563 \times 2251\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2563\) by each digit of \(2251\) (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 2563 x 2251, 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... | 215 | 229 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2866 x 7353
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: 2866 and 7353. 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 the method of **lo... | 21073698 | What is the solution to the long multiplication equation below?
2866 x 7353
Think step by step. | true | The calculated product of 2866 and 7353 is correctly derived as 21,073,698, which matches the ground truth solution. The solution follows a detailed and correct method of long multiplication and verifies the result with an alternative method. | 395 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 2866 and 7353. 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 the method of **lo... | [
{
"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: 2866 and 7353. My goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": "",... | 834 | 834 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7077 x 1854
Think step by step. | To solve the multiplication problem \(7077 \times 1854\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7077\) by each digit of \(1854\), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
1... | 13120758 | What is the solution to the long multiplication equation below?
7077 x 1854
Think step by step. | true | The provided solution correctly performs the long multiplication steps and adds the partial products accurately, arriving at the correct final answer of 13120758, which matches the ground truth solution. | 396 | 0 | To solve the multiplication problem \(7077 \times 1854\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7077\) by each digit of \(1854\), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
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 multiplication problem \\(7077 \\times 1854\\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:\n\n### Step 1: Break down the multiplication\nWe'll multiply \\(7077\\) by each digit of \\(1854\\), starting from the rig... | 197 | 233 | 36 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7205 x 5127
Think step by step. | To solve the long multiplication equation \(7205 \times 5127\), 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 (5127) by the first number (7205) and then summing the results.
### Step 1: Break down t... | 36940035 | What is the solution to the long multiplication equation below?
7205 x 5127
Think step by step. | true | The solution correctly computes the long multiplication using the distributive property, and the final answer matches the ground truth solution (36940035). The steps are logically structured and the arithmetic is correct. | 397 | 0 | To solve the long multiplication equation \(7205 \times 5127\), 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 (5127) by the first number (7205) and then summing 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 \\(7205 \\times 5127\\), 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 (5127) by the first number (... | 255 | 255 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2416 x 3898
Think step by step. | To solve the long multiplication equation \(2416 \times 3898\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(2416\) by each digit of \(3898\) (starting from the rightmost digit), shift the partial results appropriately, and then add them together.
... | 9417568 | What is the solution to the long multiplication equation below?
2416 x 3898
Think step by step. | true | The solution provided yields a calculated result of 9,417,568, which matches the ground truth solution of 9417568 when formatted correctly without the additional comma. Therefore, the solution is correct. | 398 | 0 | To solve the long multiplication equation \(2416 \times 3898\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(2416\) by each digit of \(3898\) (starting from the rightmost digit), 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 equation \\(2416 \\times 3898\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(2416\\) by each digit of \\(3898\\) (starting from the rightmost digit), shif... | 309 | 333 | 24 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3781 x 7583
Think step by step. | To solve the long multiplication equation \( 3781 \times 7583 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3781 \) by each digit of \( 7583 \) (considering their place values) and then add the results together.
### Step 1: Break ... | 28671323 | What is the solution to the long multiplication equation below?
3781 x 7583
Think step by step. | true | The solution provided correctly follows the steps of long multiplication using the distributive property and arrives at the answer of 28,671,323. The formatting is consistent, and additional verification through standard long multiplication confirms the correctness. Both the solution and ground truth solution express t... | 399 | 0 | To solve the long multiplication equation \( 3781 \times 7583 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3781 \) by each digit of \( 7583 \) (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 \\( 3781 \\times 7583 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 3781 \\) by each digit of \\( 7583 \\) (considering their pla... | 398 | 380 | -18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7410 x 4626
Think step by step. | To solve the long multiplication equation \(7410 \times 4626\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7410) by each digit of the multiplier (4626), starting from the rightmost digit, and then summing up th... | 34278660 | What is the solution to the long multiplication equation below?
7410 x 4626
Think step by step. | true | The solution correctly breaks down the multiplication of 7410 by 4626 using the distributive property, calculates each partial product accurately, and correctly sums them to reach the final result of 34,278,660, which matches the ground truth solution when formatted without commas. | 400 | 0 | To solve the long multiplication equation \(7410 \times 4626\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7410) by each digit of the multiplier (4626), 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 \\(7410 \\times 4626\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7410) by each digit of the multiplier (462... | 385 | 342 | -43 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2079 x 1478
Think step by step. | To solve the multiplication problem \(2079 \times 1478\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2079\) by each digit of \(1478\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&2079... | 3072762 | What is the solution to the long multiplication equation below?
2079 x 1478
Think step by step. | true | The solution correctly follows the long multiplication method step-by-step, showing each multiplication and the subsequent addition of partial results. The final answer, 3,072,762, matches the ground truth solution of 3072762, confirming its correctness. | 401 | 0 | To solve the multiplication problem \(2079 \times 1478\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(2079\) by each digit of \(1478\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
&2079... | [
{
"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 \\(2079 \\times 1478\\), 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 ... | 193 | 207 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9364 x 1125
Think step by step. | To solve the multiplication problem \( 9364 \times 1125 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier (1125)
Notice that \( 1125 \) can be expressed as \( 1000 + 100 + 20 + 5 \). This allows us to multiply \( 9364 \) by each... | 10534500 | What is the solution to the long multiplication equation below?
9364 x 1125
Think step by step. | true | The solution provides a step-by-step breakdown of the multiplication process, correctly adding all components of the calculation and arriving at the final answer of 10,534,500. This matches the ground truth solution (10534500), thus confirming the correctness of the solution. | 402 | 0 | To solve the multiplication problem \( 9364 \times 1125 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier (1125)
Notice that \( 1125 \) can be expressed as \( 1000 + 100 + 20 + 5 \). This allows us to multiply \( 9364 \) by 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 multiplication problem \\( 9364 \\times 1125 \\), 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",
"subgo... | 256 | 263 | 7 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8386 x 2982
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: 8,386 and 2,982. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall the method of **long m... | 25007052 | What is the solution to the long multiplication equation below?
8386 x 2982
Think step by step. | true | The solution correctly uses the long multiplication method and confirms its accuracy through the distributive property. The final calculated result, 25,007,052, matches the ground truth solution. Therefore, the evaluation concludes that the solution is correct. | 403 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,386 and 2,982. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall the method of **long 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 understand what the problem is asking. It's a multiplication of two large numbers: 8,386 and 2,982. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 695 | 703 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5020 x 2160
Think step by step. | To solve the multiplication problem \(5020 \times 2160\), 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
First, express \(2160\) as \(2000 + 160\). This allows us to multiply \(5020\) by each part ... | 10843200 | What is the solution to the long multiplication equation below?
5020 x 2160
Think step by step. | true | The solution provided correctly uses the distributive property of multiplication and verifies the result through both breakdown and standard multiplication methods. The computed result of \(5020 \times 2160\) equals \(10,843,200\), which matches the ground truth answer. | 404 | 0 | To solve the multiplication problem \(5020 \times 2160\), 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
First, express \(2160\) as \(2000 + 160\). This allows us to multiply \(5020\) by each 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 multiplication problem 5020 x 2160, 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": "though... | 241 | 263 | 22 |
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