__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?
7054 x 9779
Think step by step. | To solve the long multiplication equation \(7054 \times 9779\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7054\) by each digit of \(9779\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \(9779\)... | 68981066 | What is the solution to the long multiplication equation below?
7054 x 9779
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication process and accurately computes the final result. Both the long multiplication and verification methods yield the same final value, 68,981,066, which corresponds to the ground truth solution. | 203 | 0 | To solve the long multiplication equation \(7054 \times 9779\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7054\) by each digit of \(9779\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \(9779\)... | [
{
"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 \\(7054 \\times 9779\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(7054\\) by each digit of \\(9779\\) (considering their place values) and then... | 413 | 413 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6756 x 8442
Think step by step. | To solve the multiplication problem \( 6756 \times 8442 \), we can 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 \( 8442 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | 57034152 | What is the solution to the long multiplication equation below?
6756 x 8442
Think step by step. | true | The solution correctly follows the long multiplication procedure, multiplying each digit of 8442 by 6756 and summing the partial products accurately to arrive at the final result of 57034152, which matches the ground truth. | 204 | 0 | To solve the multiplication problem \( 6756 \times 8442 \), we can 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 \( 8442 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | [
{
"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 8442 \\), 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 ... | 362 | 384 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6915 x 8524
Think step by step. | To solve the long multiplication equation \(6915 \times 8524\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(8524\) as \(8000 + 500 + 20 + 4\) and multiply each term by \(6915\)... | 58943460 | What is the solution to the long multiplication equation below?
6915 x 8524
Think step by step. | false | The solution obtained is formatted incorrectly with commas separating the thousands whereas the ground truth does not use commas. However, both represent the same numerical value. Nonetheless, since the formatting differs, the judge's evaluation is that it is incorrect. | 205 | 0 | To solve the long multiplication equation \(6915 \times 8524\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(8524\) as \(8000 + 500 + 20 + 4\) and multiply each term by \(6915\)... | [
{
"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 \\(6915 \\times 8524\\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subg... | 198 | 220 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1479 x 7958
Think step by step. | To solve the long multiplication problem \(1479 \times 7958\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(1479\) by each digit of \(7958\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Bre... | 11769882 | What is the solution to the long multiplication equation below?
1479 x 7958
Think step by step. | false | The calculated result of the multiplication is 11,769,882, whereas the ground truth solution is 11,769,882. The two results appear to be the same, hence the solution is correct. | 206 | 0 | To solve the long multiplication problem \(1479 \times 7958\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(1479\) by each digit of \(7958\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Bre... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\(1479 \\times 7958\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(1479\\) by each digit of \\(7958\\) (from right to left), shift the partial re... | 256 | 278 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7033 x 6743
Think step by step. | To solve the multiplication \( 7033 \times 6743 \), 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 \( 6743 \) as \( 6000 + 700 + 40 + 3 \). Then, multiply \( 7033 \) by each of these components:
\... | 47423519 | What is the solution to the long multiplication equation below?
7033 x 6743
Think step by step. | true | The solution correctly applied the long multiplication method, broke down the components accurately, and added all the results correctly. The final result of 47423519 is indeed equal to the ground truth solution. | 207 | 0 | To solve the multiplication \( 7033 \times 6743 \), 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 \( 6743 \) as \( 6000 + 700 + 40 + 3 \). Then, multiply \( 7033 \) by each of these components:
\... | [
{
"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 \\( 7033 \\times 6743 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve... | 214 | 228 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7458 x 8775
Think step by step. | To solve the multiplication problem \(7458 \times 8775\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(8775\) as \(8000 + 700 + 70 + 5\) and multiply \(7458\) by each component separately.
\[
7458 \times 8775 = 7458 \times (... | 65443950 | What is the solution to the long multiplication equation below?
7458 x 8775
Think step by step. | true | The solution correctly applies the long multiplication method to compute the product of 7458 and 8775, resulting in a final answer of 65,443,950, which matches the provided ground truth solution of 65443950 (ignoring commas). Therefore, the solution is correct. | 208 | 0 | To solve the multiplication problem \(7458 \times 8775\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(8775\) as \(8000 + 700 + 70 + 5\) and multiply \(7458\) by each component separately.
\[
7458 \times 8775 = 7458 \times (... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\(7458 \\times 8775\\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to... | 222 | 214 | -8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2145 x 4527
Think step by step. | To solve the long multiplication equation \(2145 \times 4527\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2145\) by each digit of \(4527\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | 9710415 | What is the solution to the long multiplication equation below?
2145 x 4527
Think step by step. | true | The solution follows a correct method for long multiplication using the distributive property. It breaks down the multiplication into manageable components, calculates each part accurately, and sums the results correctly, yielding the final answer of 9,710,415, which matches the ground truth solution. | 209 | 0 | To solve the long multiplication equation \(2145 \times 4527\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2145\) by each digit of \(4527\) (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 \\(2145 \\times 4527\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\(2145\\) by each digit of \\(4527\\) (considering their place val... | 205 | 213 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5117 x 4451
Think step by step. | To solve the multiplication problem \(5117 \times 4451\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5117\) by each digit of \(4451\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
5117 ... | 22775767 | What is the solution to the long multiplication equation below?
5117 x 4451
Think step by step. | true | The solution computes the multiplication of 5117 and 4451 correctly using the long multiplication method. The final total calculated is 22,775,767, which matches the ground truth value of 22775767 when considering the formatting of the output (the inclusion or exclusion of commas does not change the numeric value). | 210 | 0 | To solve the multiplication problem \(5117 \times 4451\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5117\) by each digit of \(4451\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
5117 ... | [
{
"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 \\(5117 \\times 4451\\), 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 ... | 212 | 226 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6007 x 6195
Think step by step. | To solve the long multiplication equation \(6007 \times 6195\), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:
### Step 1: Break down the multiplier (6195)
We can express \(6195\) as \(6000 + 100 + 90 + 5\). This allows us to multiply \(... | 37213365 | What is the solution to the long multiplication equation below?
6007 x 6195
Think step by step. | true | The solution provided for the multiplication of 6007 and 6195 is accurate. The method of using the distributive property to break down the multiplication into manageable parts, as well as the verification through standard long multiplication, confirms that the final result of 37,213,365 is indeed correct. The formattin... | 211 | 0 | To solve the long multiplication equation \(6007 \times 6195\), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:
### Step 1: Break down the multiplier (6195)
We can express \(6195\) as \(6000 + 100 + 90 + 5\). This allows us to 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": "To solve the long multiplication equation \\(6007 \\times 6195\\), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:",
"equation": "",
"finished": true,
"output": "",
... | 268 | 284 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9869 x 4779
Think step by step. | To solve the long multiplication equation \( 9869 \times 4779 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9869 \) by each digit of \( 4779 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 47163951 | What is the solution to the long multiplication equation below?
9869 x 4779
Think step by step. | true | The solution correctly applied the distributive property of multiplication over addition to break down the multiplication of 9869 and 4779, calculated each part accurately, and summed the results to arrive at the correct final answer of 47163951, which matches the ground truth solution. | 212 | 0 | To solve the long multiplication equation \( 9869 \times 4779 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9869 \) by each digit of \( 4779 \) (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 \\( 9869 \\times 4779 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9869 \\) by each digit of \\( 4779 \\) (considering their pla... | 353 | 374 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7050 x 1453
Think step by step. | To solve the long multiplication equation \( 7050 \times 1453 \), 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 (1453)
We can express \( 1453 \) as:
\[ 1453 = 1000 + 400 + 50 + 3 \]
### Step 2: Multiply 7050 ... | 10243650 | What is the solution to the long multiplication equation below?
7050 x 1453
Think step by step. | true | The solution correctly applies the distributive property of multiplication and computes each partial product accurately. The final result is consistent with both the step-by-step breakdown and the standard long multiplication method, confirming that the answer is correct. | 214 | 0 | To solve the long multiplication equation \( 7050 \times 1453 \), 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 (1453)
We can express \( 1453 \) as:
\[ 1453 = 1000 + 400 + 50 + 3 \]
### Step 2: Multiply 7050 ... | [
{
"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 \\( 7050 \\times 1453 \\), 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_typ... | 236 | 236 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4723 x 9599
Think step by step. | To solve the multiplication \( 4723 \times 9599 \), we can use the **distributive property of multiplication over addition** to simplify the calculation. Here's a step-by-step breakdown:
### Step 1: Rewrite the multiplier
Notice that \( 9599 \) is very close to \( 10,000 \). Specifically:
\[ 9599 = 10,000 - 401 \]
##... | 45336077 | What is the solution to the long multiplication equation below?
4723 x 9599
Think step by step. | true | The solution correctly applies the distributive property of multiplication and verifies the result through step-by-step calculations and an alternate method of long multiplication, leading to the final answer matching the ground truth solution. | 215 | 0 | To solve the multiplication \( 4723 \times 9599 \), we can use the **distributive property of multiplication over addition** to simplify the calculation. Here's a step-by-step breakdown:
### Step 1: Rewrite the multiplier
Notice that \( 9599 \) is very close to \( 10,000 \). Specifically:
\[ 9599 = 10,000 - 401 \]
##... | [
{
"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 \\( 4723 \\times 9599 \\), we can use the **distributive property of multiplication over addition** to simplify the calculation. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_... | 283 | 292 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8624 x 2990
Think step by step. | To solve the long multiplication equation \( 8624 \times 2990 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 2990 \) can be expressed as \( 3000 - 10 \). This allows us ... | 25785760 | What is the solution to the long multiplication equation below?
8624 x 2990
Think step by step. | true | The solution provided uses the distributive property correctly to compute the product of 8624 and 2990, and the final answer matches the ground truth solution of 25785760. | 216 | 0 | To solve the long multiplication equation \( 8624 \times 2990 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 2990 \) can be expressed as \( 3000 - 10 \). This allows us ... | [
{
"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": "### Step 1: Break down the multiplier\nThe multiplier \\( 2990 \\) can be expressed as \\( 3000 - 10 \\). This allows us to rewrite the multiplication as:\n\\[8624 \\times 2990 = 8624 \\times (3000 - 10)\\]",
"equation": "",
"finished": true,
"output... | 174 | 221 | 47 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3500 x 7636
Think step by step. | To solve the multiplication problem \( 3500 \times 7636 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. This means we can multiply \(... | 26726000 | What is the solution to the long multiplication equation below?
3500 x 7636
Think step by step. | false | The final answer in the solution provided is formatted with commas incorrectly, suggesting it is a different number than the ground truth solution. The ground truth solution does not have the comma formatting and is written as 26726000. | 217 | 0 | To solve the multiplication problem \( 3500 \times 7636 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. This means we can 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": "To solve the multiplication problem \\( 3500 \\times 7636 \\), 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",
"subg... | 328 | 354 | 26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6006 x 7795
Think step by step. | To solve the long multiplication equation \(6006 \times 7795\), 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 numbers
Express \(6006\) and \(7795\) in terms of their place values:
- \(6006 = 6000 + 6\)
- \(7795 = 800... | 46816770 | What is the solution to the long multiplication equation below?
6006 x 7795
Think step by step. | true | The calculations provided in the solution are correct, and the final answer of 46816770 matches the ground truth solution. The steps followed the distributive property appropriately, and the verification through standard long multiplication confirms the result. | 218 | 0 | To solve the long multiplication equation \(6006 \times 7795\), 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 numbers
Express \(6006\) and \(7795\) in terms of their place values:
- \(6006 = 6000 + 6\)
- \(7795 = 800... | [
{
"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 6006 x 7795, 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... | 249 | 274 | 25 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2187 x 6115
Think step by step. | To solve the long multiplication equation \( 2187 \times 6115 \), 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 the results.
### Step 1: B... | 13373505 | What is the solution to the long multiplication equation below?
2187 x 6115
Think step by step. | false | The provided solution states the final result as 13,372,505, while the ground truth solution is 13,373,505. There is a discrepancy in the final result, indicating an error in the calculation. | 219 | 0 | To solve the long multiplication equation \( 2187 \times 6115 \), 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 the results.
### Step 1: 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": "To solve the long multiplication equation \\( 2187 \\times 6115 \\), 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... | 318 | 328 | 10 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5187 x 3469
Think step by step. | To solve the long multiplication equation \(5187 \times 3469\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5187\) by each digit of \(3469\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Br... | 17993703 | What is the solution to the long multiplication equation below?
5187 x 3469
Think step by step. | true | The solution provided follows the correct steps for long multiplication, breaking down the calculation into manageable parts and following the appropriate rules of arithmetic. The final result matches the ground truth solution of 17993703. | 220 | 0 | To solve the long multiplication equation \(5187 \times 3469\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5187\) by each digit of \(3469\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: 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": "To solve the long multiplication equation \\(5187 \\times 3469\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\(5187\\) by each digit of \\(3469\\) (from right to left), shift the partial r... | 280 | 286 | 6 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4211 x 9924
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4211** and **9924**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplicati... | 41789964 | What is the solution to the long multiplication equation below?
4211 x 9924
Think step by step. | true | The solution provided correctly follows the steps for long multiplication and arrives at the correct final result of 41,789,964, which matches the ground truth solution. | 221 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **4211** and **9924**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplicati... | [
{
"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: **4211** and **9924**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem into smaller, more manageable pa... | 800 | 808 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3547 x 9953
Think step by step. | To solve the multiplication \( 3547 \times 9953 \), 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 \( 9953 \) as \( 10000 - 47 \). This allows us to rewrite the multiplication as:
\[
3547 \times 99... | 35303291 | What is the solution to the long multiplication equation below?
3547 x 9953
Think step by step. | false | The provided solution gives the result as 35,303,291 with formatting including commas. The ground truth solution is 35303291 without commas. However, both values represent the same number. Therefore, the solution is evaluated as incorrect due to formatting; the consistent presentation of numbers should align with the g... | 222 | 0 | To solve the multiplication \( 3547 \times 9953 \), 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 \( 9953 \) as \( 10000 - 47 \). This allows us to rewrite the multiplication as:
\[
3547 \times 99... | [
{
"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 \\( 3547 \\times 9953 \\), we can use the **long multiplication** method. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Setup a plan to solve... | 221 | 221 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8741 x 7780
Think step by step. | To solve the long multiplication equation \( 8741 \times 7780 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 7780 \) as \( 8000 - 220 \). This allows us to rewrite the multiplication as:
\[
8741 \times 7... | 68004980 | What is the solution to the long multiplication equation below?
8741 x 7780
Think step by step. | true | The provided solution accurately calculates the product of 8741 and 7780 through correct step-by-step multiplication and follows through with the proper arithmetic operations, leading to the final answer which matches the ground truth solution. | 223 | 0 | To solve the long multiplication equation \( 8741 \times 7780 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 7780 \) as \( 8000 - 220 \). This allows us to rewrite the multiplication as:
\[
8741 \times 7... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8741 \\times 7780 \\), 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\nWe can express \\( 7780 \\) as \\( 8000 - 220 \\... | 247 | 283 | 36 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2837 x 5814
Think step by step. | To solve the long multiplication equation \(2837 \times 5814\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2837\) by each digit of \(5814\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | 16494318 | What is the solution to the long multiplication equation below?
2837 x 5814
Think step by step. | true | The solution provided was calculated correctly, and after carrying out the steps of multiplication, the final sum also matches the ground truth solution of 16494318. Both the multiplication method and the final result are correct. | 224 | 0 | To solve the long multiplication equation \(2837 \times 5814\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2837\) by each digit of \(5814\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 2837 x 5814, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 2837 by each digit of 5814, accounting for place values, and then sum the resul... | 249 | 286 | 37 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9459 x 8007
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: 9,459 and 8,007. 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 ... | 75738213 | What is the solution to the long multiplication equation below?
9459 x 8007
Think step by step. | true | The solution correctly calculates the product of 9,459 and 8,007 through detailed step-by-step breakdown, including verification through long multiplication and addition of partial products. The final answer matches the ground truth solution. | 225 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9,459 and 8,007. 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 ... | [
{
"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: 9,459 and 8,007. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 722 | 730 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3019 x 3108
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3019** and **3108**. 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 (3108) by the first ... | 9383052 | What is the solution to the long multiplication equation below?
3019 x 3108
Think step by step. | true | The solution correctly computes the product of 3019 and 3108 using the long multiplication method and verifies it with the distributive property, confirming that the final answer is accurate. | 226 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3019** and **3108**. 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 (3108) by the first ... | [
{
"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: **3019** and **3108**. 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... | 964 | 964 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4966 x 6573
Think step by step. | To solve the long multiplication equation \( 4966 \times 6573 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4966 \) by each digit of \( 6573 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 32641518 | What is the solution to the long multiplication equation below?
4966 x 6573
Think step by step. | true | The calculated final result of 32,641,518 matches the ground truth solution of 32641518, when considering formatting. The formatting difference (with commas in the solution but not in the ground truth) does not affect the numerical value, thus the solution is correct. | 227 | 0 | To solve the long multiplication equation \( 4966 \times 6573 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4966 \) by each digit of \( 6573 \) (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 \\( 4966 \\times 6573 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 4966 \\) by each digit of \\( 6573 \\) (considering their pla... | 323 | 325 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9394 x 1203
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: 9,394 and 1,203. 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... | 11300982 | What is the solution to the long multiplication equation below?
9394 x 1203
Think step by step. | true | The provided solution correctly computes the product of 9,394 and 1,203 using both the distributive property and traditional long multiplication methods, yielding the final result of 11,300,982, which matches the ground truth solution. | 228 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9,394 and 1,203. 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: 9,394 and 1,203. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 649 | 691 | 42 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8493 x 5775
Think step by step. | To solve the long multiplication equation \( 8493 \times 5775 \), 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 (5775)
We can express \( 5775 \) as \( 5000 + 700 + 70 + 5 \). This allows us to multiply \( 8493... | 49047075 | What is the solution to the long multiplication equation below?
8493 x 5775
Think step by step. | true | The solution provided for calculating the product of 8493 and 5775 has accurately followed the steps of breaking down the multiplication using the distributive property and correctly added the partial products. The final answer matches the ground truth solution. Therefore, the solution is correct. | 229 | 0 | To solve the long multiplication equation \( 8493 \times 5775 \), 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 (5775)
We can express \( 5775 \) as \( 5000 + 700 + 70 + 5 \). This allows us to multiply \( 8493... | [
{
"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 \\( 8493 \\times 5775 \\), 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_typ... | 330 | 348 | 18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9892 x 3581
Think step by step. | To solve the long multiplication equation \( 9892 \times 3581 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9892 \) by each digit of \( 3581 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 35423252 | What is the solution to the long multiplication equation below?
9892 x 3581
Think step by step. | true | The calculation methods used (distributive property and long multiplication) produced matching results. The final result of the multiplication is indeed 35423252, confirming the solution is correct. | 230 | 0 | To solve the long multiplication equation \( 9892 \times 3581 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9892 \) by each digit of \( 3581 \) (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 \\( 9892 \\times 3581 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9892 \\) by each digit of \\( 3581 \\) (considering their pla... | 306 | 280 | -26 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6284 x 4179
Think step by step. | To solve the long multiplication equation \(6284 \times 4179\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6284\) by each digit of \(4179\) (from right to left), shift the partial results appropriately, and then add them together.
#... | 26260836 | What is the solution to the long multiplication equation below?
6284 x 4179
Think step by step. | true | The solution provided correctly calculates the multiplication of 6284 and 4179 using the distributive property, showing each step and verifying the final result through standard long multiplication. The final answer matches the ground truth solution, which is 26260836. | 231 | 0 | To solve the long multiplication equation \(6284 \times 4179\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6284\) by each digit of \(4179\) (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 6284 x 4179, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 6284 by each digit of 4179 (from right to left), shift the partial results appr... | 288 | 295 | 7 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1820 x 5130
Think step by step. | To solve the long multiplication equation \( 1820 \times 5130 \), we can break it down into simpler steps using the distributive property of multiplication. Here's how to do it step by step:
### Step 1: Break down the multiplication
First, express \( 5130 \) as \( 5000 + 100 + 30 \). This allows us to multiply \( 1820... | 9336600 | What is the solution to the long multiplication equation below?
1820 x 5130
Think step by step. | true | The provided solution correctly applies the distributive property to break down the multiplication, calculates each component accurately, and adds the partial results correctly. The final answer matches the ground truth solution. | 232 | 0 | To solve the long multiplication equation \( 1820 \times 5130 \), we can break it down into simpler steps using the distributive property of multiplication. Here's how to do it step by step:
### Step 1: Break down the multiplication
First, express \( 5130 \) as \( 5000 + 100 + 30 \). This allows us to multiply \( 1820... | [
{
"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 \\( 1820 \\times 5130 \\), we can break it down into simpler steps using the distributive property of multiplication. Here's how to do it step by step:\n\n### Step 1: Break down the multiplication\nFirst, express \\( 513... | 212 | 234 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9036 x 1770
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **9036 × 1770**.
Breaking it down:
- **Multiplicand**: 9036 (the number being multiplied)
- **Multiplier**: 1770 (the number by which the multiplicand is multiplied)
### Approach to Solve the Problem... | 15993720 | What is the solution to the long multiplication equation below?
9036 x 1770
Think step by step. | true | The solution provided accurately follows the long multiplication process and confirms the final result through multiple methods, yielding the answer 15,993,720, which matches the ground truth solution. | 233 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **9036 × 1770**.
Breaking it down:
- **Multiplicand**: 9036 (the number being multiplied)
- **Multiplier**: 1770 (the number by which the multiplicand is multiplied)
### Approach to Solve the Problem... | [
{
"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: **9036 × 1770**. \n\nBreaking it down:\n- **Multiplicand**: 9036 (the number being multiplied)\n- **Multiplier**: 1770 (the number by which th... | 723 | 731 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9418 x 7242
Think step by step. | To solve the long multiplication equation \(9418 \times 7242\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9418) by each digit of the multiplier (7242), starting from the rightmost digit, and then summing up the partial res... | 68205156 | What is the solution to the long multiplication equation below?
9418 x 7242
Think step by step. | true | The solution presented matches the ground truth solution exactly. The step-by-step breakdown correctly applies the distributive property of multiplication, and the final addition of the partial products leads to the correct total of 68,205,156. | 234 | 0 | To solve the long multiplication equation \(9418 \times 7242\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9418) by each digit of the multiplier (7242), starting from the rightmost digit, and then summing up the partial res... | [
{
"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 \\(9418 \\times 7242\\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9418) by each digit of the multiplier (7242), starting ... | 262 | 271 | 9 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7767 x 2728
Think step by step. | To solve the long multiplication equation \( 7767 \times 2728 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7767 \) by each digit of \( 2728 \) (considering their place values) and then sum all the partial results.
### Step 1: Bre... | 21188376 | What is the solution to the long multiplication equation below?
7767 x 2728
Think step by step. | true | The solution correctly implements the distributive property of multiplication, breaking down the multiplier into its components. Each multiplication is executed correctly, and the final summation is accurately computed. Additionally, the verification via long multiplication confirms the correctness of the solution. Thu... | 235 | 0 | To solve the long multiplication equation \( 7767 \times 2728 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7767 \) by each digit of \( 2728 \) (considering their place values) and then sum all the partial results.
### Step 1: Bre... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7767 \\times 2728 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7767 \\) by each digit of \\( 2728 \\) (considering their pla... | 360 | 323 | -37 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4459 x 4382
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: **4459** and **4382**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I ... | 19539338 | What is the solution to the long multiplication equation below?
4459 x 4382
Think step by step. | true | The solution correctly multiplied the numbers 4459 and 4382 using the long multiplication method, breaking it down into manageable parts and summing the partial results accurately. The calculated final result matches the ground truth solution of 19539338. | 236 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: **4459** and **4382**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I ... | [
{
"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: **4459** and **4382**. The goal is to find the product of these two numbers.",
"equation": "",
"finished"... | 863 | 819 | -44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2594 x 7615
Think step by step. | To solve the multiplication problem \( 2594 \times 7615 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2594 \) by each digit of \( 7615 \), starting from the rightmost digit (units place) and moving left. Remember to add pl... | 19753310 | What is the solution to the long multiplication equation below?
2594 x 7615
Think step by step. | true | The computation of 2594 multiplied by 7615 using long multiplication is performed correctly, yielding a final result of 19753310, which matches the ground truth solution. | 237 | 0 | To solve the multiplication problem \( 2594 \times 7615 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2594 \) by each digit of \( 7615 \), starting from the rightmost digit (units place) and moving left. Remember to add pl... | [
{
"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 \\( 2594 \\times 7615 \\), 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... | 316 | 5,916 | 5,600 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2357 x 4385
Think step by step. | To solve the long multiplication equation \( 2357 \times 4385 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2357 \) by each digit of \( 4385 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 10335445 | What is the solution to the long multiplication equation below?
2357 x 4385
Think step by step. | true | The provided solution correctly applies the distributive property of multiplication, breaks down the multiplication into manageable parts, computes each part accurately, and sums the results correctly to arrive at the final answer. The final answer matches the ground truth solution of 10335445. | 238 | 0 | To solve the long multiplication equation \( 2357 \times 4385 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2357 \) by each digit of \( 4385 \) (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 \\( 2357 \\times 4385 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 2357 \\) by each digit of \\( 4385 \\) (considering their pla... | 356 | 356 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8712 x 2736
Think step by step. | To solve the long multiplication equation \( 8712 \times 2736 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8712 \) by each digit of \( 2736 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 23836032 | What is the solution to the long multiplication equation below?
8712 x 2736
Think step by step. | true | The solution correctly follows the steps of long multiplication by breaking it down using the distributive property, accurately computing each partial product, and summing them to arrive at the result. The final answer given in the solution matches the ground truth solution. | 239 | 0 | To solve the long multiplication equation \( 8712 \times 2736 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8712 \) by each digit of \( 2736 \), 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 \\( 8712 \\times 2736 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 8712 \\) by each digit of \\( 2736 \\), accounting for place ... | 315 | 315 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4325 x 8127
Think step by step. | To solve the long multiplication problem \(4325 \times 8127\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 4325 by each digit of 8127, starting from the rightmost digit, and then sum the results. Here's the step-by-step process:
### Step 1: Break d... | 35149275 | What is the solution to the long multiplication equation below?
4325 x 8127
Think step by step. | true | The solution follows a correct systematic approach to long multiplication using the distributive property, breaking down the numbers into more manageable parts, and correctly summing them to arrive at the final answer. The calculations performed at each stage are accurate, and the final computed answer of \(35,149,275\... | 240 | 0 | To solve the long multiplication problem \(4325 \times 8127\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 4325 by each digit of 8127, starting from the rightmost digit, and then sum the results. Here's the step-by-step process:
### Step 1: Break d... | [
{
"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 \\(4325 \\times 8127\\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 4325 by each digit of 8127, starting from the rightmost digit, and then sum the r... | 279 | 313 | 34 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3088 x 6809
Think step by step. | To solve the multiplication problem \( 3088 \times 6809 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We'll multiply \( 3088 \) by each digit of \( 6809 \), starting from the rightmost digit (units place), and then sum the pa... | 21026192 | What is the solution to the long multiplication equation below?
3088 x 6809
Think step by step. | true | The provided solution accurately computed the multiplication of 3088 and 6809 using the long multiplication method, and the final result matches the ground truth solution. | 241 | 0 | To solve the multiplication problem \( 3088 \times 6809 \), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We'll multiply \( 3088 \) by each digit of \( 6809 \), starting from the rightmost digit (units place), and then sum the pa... | [
{
"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 \\( 3088 \\times 6809 \\), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe'll multiply \\( 3088 \\) by each digit of \\( 6809 \\), ... | 330 | 332 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3683 x 1212
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: 3683 and 1212. 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 it down us... | 4463796 | What is the solution to the long multiplication equation below?
3683 x 1212
Think step by step. | false | The solution provided calculated the product of 3683 and 1212 as 4,463,796, which is correct. However, the ground truth solution inaccurately states it as 4463796 without the comma and incorrectly interprets the value. The mistake lies in the ground truth format, which may mislead regarding numerical accuracy despite t... | 242 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 3683 and 1212. 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 it down us... | [
{
"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: 3683 and 1212. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ""... | 776 | 787 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5683 x 7714
Think step by step. | To solve the long multiplication problem \( 5683 \times 7714 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5683 \) by each digit of \( 7714 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | 43838662 | What is the solution to the long multiplication equation below?
5683 x 7714
Think step by step. | false | The solution calculated the result as 43,838,662, but the ground truth solution shows the result as 43,838,662. Due to a discrepancy here, the formats are not consistent (the commas in the solution format), but the numeric value calculated is correct when ignoring formatting. It should be judged as incorrect due to for... | 243 | 0 | To solve the long multiplication problem \( 5683 \times 7714 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5683 \) by each digit of \( 7714 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 5683 \\times 7714 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5683 \\) by each digit of \\( 7714 \\), accounting for place values, and th... | 303 | 264 | -39 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2678 x 6440
Think step by step. | To solve the long multiplication equation \( 2678 \times 6440 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6440 \) as \( 6000 + 400 + 40 \). This allows us to multiply \( 2678 \) by each component separately an... | 17246320 | What is the solution to the long multiplication equation below?
2678 x 6440
Think step by step. | true | The provided solution follows the correct steps for long multiplication, including breaking down the multiplication into manageable components, performing the calculations accurately, and adding the partial results correctly. The final result of 17246320 matches the ground truth solution. | 244 | 0 | To solve the long multiplication equation \( 2678 \times 6440 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6440 \) as \( 6000 + 400 + 40 \). This allows us to multiply \( 2678 \) by each component separately an... | [
{
"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 \\( 2678 \\times 6440 \\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \\( 6440 \\) as \\( 6000 + 400 + 40 \\). T... | 344 | 366 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5395 x 7976
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5395** and **7976**. 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.
### Breaking Down the Multipli... | 43030520 | What is the solution to the long multiplication equation below?
5395 x 7976
Think step by step. | true | The solution provided accurately describes the process of multiplying the numbers 5395 and 7976 using the long multiplication method, following it step by step, and consistently arrives at the correct final product of 43030520, which matches the ground truth solution. | 245 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **5395** and **7976**. 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.
### Breaking Down the Multipli... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **5395** and **7976**. 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... | 741 | 752 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8826 x 3854
Think step by step. | To solve the multiplication problem \( 8826 \times 3854 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8826 \) by each digit of \( 3854 \), starting from the rightmost digit (units place), and shift the partial results acco... | 34015404 | What is the solution to the long multiplication equation below?
8826 x 3854
Think step by step. | true | The calculated result using the long multiplication method is correct and matches the ground truth solution of 34015404. | 246 | 0 | To solve the multiplication problem \( 8826 \times 3854 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8826 \) by each digit of \( 3854 \), 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 \\( 8826 \\times 3854 \\), 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... | 830 | 875 | 45 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7764 x 2683
Think step by step. | To solve the long multiplication equation \( 7764 \times 2683 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7764 \) by each digit of \( 2683 \), accounting for place value, and then sum the results.
### Step 1: Break down the mult... | 20830812 | What is the solution to the long multiplication equation below?
7764 x 2683
Think step by step. | true | The solution methodically breaks down the multiplication using the distributive property, performs each individual calculation correctly, and sums them up to arrive at a final answer. The formatting may differ (using commas vs not), but the numerical result is effectively the same. | 247 | 0 | To solve the long multiplication equation \( 7764 \times 2683 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7764 \) by each digit of \( 2683 \), accounting for place value, and then sum the results.
### Step 1: Break down the mult... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7764 \\times 2683 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7764 \\) by each digit of \\( 2683 \\), accounting for place ... | 393 | 379 | -14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7230 x 7293
Think step by step. | To solve the long multiplication equation \( 7230 \times 7293 \), 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 (7293)
Express \( 7293 \) as \( 7000 + 200 + 90 + 3 \). This allows us to multiply \( 7230 \)... | 52728390 | What is the solution to the long multiplication equation below?
7230 x 7293
Think step by step. | true | The solution provided correctly breaks down the multiplication problem and adds all the parts accurately, resulting in the final answer of 52,728,390. The formatting with commas does not affect the numerical value. Since the ground truth solution is also 52728390 (without commas), the answers match and the solution is ... | 248 | 0 | To solve the long multiplication equation \( 7230 \times 7293 \), 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 (7293)
Express \( 7293 \) as \( 7000 + 200 + 90 + 3 \). This allows us to multiply \( 7230 \)... | [
{
"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 \\( 7230 \\times 7293 \\), 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... | 296 | 293 | -3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1413 x 8175
Think step by step. | To solve the long multiplication equation \(1413 \times 8175\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | 11551275 | What is the solution to the long multiplication equation below?
1413 x 8175
Think step by step. | false | The solution provided calculated the multiplication of 1413 and 8175 as 11,551,275, whereas the ground truth solution states that the result should be 11,551,275, indicating a typo in how it is presented. However, the numbers do not match and thus the provided solution is incorrect. The formatting in the final answer s... | 249 | 0 | To solve the long multiplication equation \(1413 \times 8175\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1413 \\times 8175\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, conside... | 235 | 235 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1810 x 5158
Think step by step. | To solve the long multiplication equation \(1810 \times 5158\), 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 (5158)
We can express \(5158\) as:
\[
5158 = 5000 + 100 + 50 + 8
\]
### Step 2: Multiply 1810 ... | 9335980 | What is the solution to the long multiplication equation below?
1810 x 5158
Think step by step. | true | The solution provided correctly breaks down the multiplication of 1810 by 5158 using the distributive property, accurately calculating each partial product and summing them up to arrive at the correct total of 9335980. The final boxed answer matches the ground truth solution. | 250 | 0 | To solve the long multiplication equation \(1810 \times 5158\), 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 (5158)
We can express \(5158\) as:
\[
5158 = 5000 + 100 + 50 + 8
\]
### Step 2: Multiply 1810 ... | [
{
"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 \\(1810 \\times 5158\\), 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_t... | 184 | 198 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2999 x 5564
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2999** and **5564**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | 16686436 | What is the solution to the long multiplication equation below?
2999 x 5564
Think step by step. | true | The provided solution goes through a comprehensive breakdown of the multiplication of 2999 and 5564 using the long multiplication method, successfully arriving at the correct answer of 16686436, which matches the ground truth solution. | 251 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2999** and **5564**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **2999** and **5564**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 2,014 | 2,277 | 263 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6488 x 3807
Think step by step. | To solve the long multiplication equation \(6488 \times 3807\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6488\) by each digit of \(3807\) (from right to left), shifting the partial results appropriately, and then add them together.... | 24699816 | What is the solution to the long multiplication equation below?
6488 x 3807
Think step by step. | false | The calculated answer is 24,699,816, while the ground truth solution is 24,699,816. The discrepancy is in the representation; the formatting of the boxed/written answer appears correct but doesn't match the ground truth. Thus, while the numerical calculation is consistent, if interpreted against the final answer repres... | 252 | 0 | To solve the long multiplication equation \(6488 \times 3807\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(6488\) by each digit of \(3807\) (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 6488 x 3807, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 6488 by each digit of 3807 (from right to left), shifting the partial results a... | 263 | 263 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6626 x 7913
Think step by step. | To solve the multiplication problem \(6626 \times 7913\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6626\) by each digit of \(7913\) (from right to left), shifting the partial results appropriately based on the digit's plac... | 52431538 | What is the solution to the long multiplication equation below?
6626 x 7913
Think step by step. | true | The solution provided accurately follows the long multiplication method and correctly calculates the final product of 6626 and 7913. The final answer in both the solution and ground truth is 52,431,538, hence confirming its correctness. | 253 | 0 | To solve the multiplication problem \(6626 \times 7913\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(6626\) by each digit of \(7913\) (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 6626 x 7913, 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... | 201 | 217 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1875 x 4456
Think step by step. | To solve the long multiplication equation \(1875 \times 4456\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1875) by each digit of the multiplier (4456) and then summing the partial results.
### Step 1: Break d... | 8355000 | What is the solution to the long multiplication equation below?
1875 x 4456
Think step by step. | true | The solution follows the correct steps of multiplying using the distributive property, sums the partial products accurately, and validates the final result through verification. The numerical result matches the ground truth solution of 8355000. | 254 | 0 | To solve the long multiplication equation \(1875 \times 4456\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1875) by each digit of the multiplier (4456) and then summing the partial results.
### Step 1: Break d... | [
{
"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 \\(1875 \\times 4456\\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1875) by each digit of the multiplier (445... | 279 | 282 | 3 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7323 x 1892
Think step by step. | To solve the long multiplication equation \( 7323 \times 1892 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7323) by each digit of the multiplier (1892), starting from the rightmost digit, and then summing up ... | 13855116 | What is the solution to the long multiplication equation below?
7323 x 1892
Think step by step. | false | The solution provided gives an incorrect format for the answer by including commas incorrectly. The ground truth solution does not contain thousand separators, while the solution does. Both calculations result in the correct numerical value, but the presentation of the answer must match the ground truth format without ... | 255 | 0 | To solve the long multiplication equation \( 7323 \times 1892 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7323) by each digit of the multiplier (1892), starting from the rightmost digit, and then summing up ... | [
{
"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 \\( 7323 \\times 1892 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7323) by each digit of the multiplier (1... | 279 | 265 | -14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4923 x 3354
Think step by step. | To solve the long multiplication equation \(4923 \times 3354\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(3354\) as \(3000 + 300 + 50 + 4\) and multiply each term by \(4923\)... | 16511742 | What is the solution to the long multiplication equation below?
4923 x 3354
Think step by step. | false | The solution provided is '16,511,742' which includes a comma, while the ground truth solution is '16511742' without a comma. In numerical terms, both represent the same value, but the formats are incorrect. The formats must match. | 256 | 0 | To solve the long multiplication equation \(4923 \times 3354\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication using the distributive property
We can express \(3354\) as \(3000 + 300 + 50 + 4\) and multiply each term by \(4923\)... | [
{
"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 \\(4923 \\times 3354\\), we'll break it down step by step using the **long multiplication method**. Here's how it works:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subg... | 313 | 342 | 29 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9269 x 4036
Think step by step. | To solve the long multiplication equation \( 9269 \times 4036 \), 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 t... | 37409684 | What is the solution to the long multiplication equation below?
9269 x 4036
Think step by step. | true | The presented solution correctly uses the distributive property to break down the multiplication of 9269 and 4036, arriving at the correct final result of 37409684. The verification step via long multiplication confirms this result, matching the ground truth solution, which indicates that the calculation is accurate. | 257 | 0 | To solve the long multiplication equation \( 9269 \times 4036 \), 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 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 \\( 9269 \\times 4036 \\), 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, shift... | 341 | 323 | -18 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2411 x 3537
Think step by step. | To solve the multiplication problem \( 2411 \times 3537 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2411 \) by each digit of \( 3537 \), starting from the rightmost digit, and then sum the results.
\[
\begin{align*}
&2... | 8527707 | What is the solution to the long multiplication equation below?
2411 x 3537
Think step by step. | true | The solution provided uses a correct long multiplication procedure and arrives at the correct total. The total calculated as 8527707 matches the ground truth solution. | 258 | 0 | To solve the multiplication problem \( 2411 \times 3537 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2411 \) by each digit of \( 3537 \), starting from the rightmost digit, and then sum the results.
\[
\begin{align*}
&2... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 2411 \\times 3537 \\), 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... | 293 | 262 | -31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7200 x 4882
Think step by step. | To solve the long multiplication equation \(7200 \times 4882\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \(7200 \times 4882\) as:
\[
7200 \times 4882 = 7200 \times (5000 - 118)
\]
T... | 35150400 | What is the solution to the long multiplication equation below?
7200 x 4882
Think step by step. | true | The solution provided correctly calculates the product of 7200 and 4882 using the distributive property and breaks down the multiplication into manageable parts. The final result of 35,150,400 matches the ground truth solution of 35150400, confirming that the solution is accurate. | 259 | 0 | To solve the long multiplication equation \(7200 \times 4882\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \(7200 \times 4882\) as:
\[
7200 \times 4882 = 7200 \times (5000 - 118)
\]
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 \\(7200 \\times 4882\\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication using the distributive property\nWe can express \\(7200 \\ti... | 216 | 238 | 22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9986 x 3028
Think step by step. | To solve the long multiplication equation \( 9986 \times 3028 \), 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 (3028)
The multiplier \( 3028 \) can be expressed as:
\[ 3028 = 3000 + 20 + 8 \]
### Step 2: Mul... | 30237608 | What is the solution to the long multiplication equation below?
9986 x 3028
Think step by step. | true | The solution provided correctly utilizes the distributive property to break down the multiplication into manageable parts, calculates the products accurately, and sums them to arrive at the final answer. The final result matches the ground truth solution of 30237608. | 260 | 0 | To solve the long multiplication equation \( 9986 \times 3028 \), 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 (3028)
The multiplier \( 3028 \) can be expressed as:
\[ 3028 = 3000 + 20 + 8 \]
### Step 2: 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 \\( 9986 \\times 3028 \\), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplier (3028)\nThe multiplier \\( 3028 \\... | 216 | 221 | 5 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2092 x 3723
Think step by step. | To solve the long multiplication equation \(2092 \times 3723\), 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 toget... | 7788516 | What is the solution to the long multiplication equation below?
2092 x 3723
Think step by step. | true | The solution provided correctly follows the method of breaking down the multiplication using the distributive property and accurately calculates and sums the partial results to arrive at the correct final product of 2092 multiplied by 3723. | 261 | 0 | To solve the long multiplication equation \(2092 \times 3723\), 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 toget... | [
{
"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 \\(2092 \\times 3723\\), 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, appropr... | 220 | 220 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1923 x 4380
Think step by step. | To solve the long multiplication equation \(1923 \times 4380\), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(4380\) can be written as \(4000 + 300 + 80 + 0\). Multiplying \(1923\) by each of these components simplifies the ca... | 8422740 | What is the solution to the long multiplication equation below?
1923 x 4380
Think step by step. | true | The solution provided includes detailed steps of the long multiplication, breaking the numbers down into manageable components and summing the results, which leads to the correct final answer of 8,422,740. This matches the ground truth solution provided. | 262 | 0 | To solve the long multiplication equation \(1923 \times 4380\), we can break it down into simpler steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(4380\) can be written as \(4000 + 300 + 80 + 0\). Multiplying \(1923\) by each of these components simplifies the ca... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(1923 \\times 4380\\), we can break it down into simpler steps. Here's a detailed, step-by-step solution:\n\n### Step 1: Break down the multiplication\nNotice that \\(4380\\) can be written as \\(4000 + 300 + 80 + 0\\)... | 288 | 332 | 44 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5642 x 3722
Think step by step. | To solve the long multiplication equation \( 5642 \times 3722 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5642 \) by each digit of \( 3722 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | 20999524 | What is the solution to the long multiplication equation below?
5642 x 3722
Think step by step. | false | The solution provided arrived at a result of 20,999,524, which does not match the ground truth solution of 20,999,524 provided, indicating that the solution method or final result was inaccurately calculated. | 263 | 0 | To solve the long multiplication equation \( 5642 \times 3722 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5642 \) by each digit of \( 3722 \) (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 \\( 5642 \\times 3722 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5642 \\) by each digit of \\( 3722 \\) (considering their place values) an... | 374 | 376 | 2 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5008 x 6795
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5008** and **6795**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication: The Distri... | 34029360 | What is the solution to the long multiplication equation below?
5008 x 6795
Think step by step. | true | The provided solution accurately breaks down the multiplication of 5008 and 6795 into partial steps using the distributive property, arrives at the correct partial products, and correctly sums them to obtain the final result of 34029360. Additionally, the verification using the standard algorithm confirms the same resu... | 264 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **5008** and **6795**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication: The Distri... | [
{
"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: **5008** and **6795**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the proces... | 862 | 889 | 27 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1299 x 9319
Think step by step. | To solve the multiplication \( 1299 \times 9319 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 9319 \) as \( 9000 + 300 + 10 + 9 \). This allows us to multiply \( 1299 \) by each component separately and then add the resul... | 12105381 | What is the solution to the long multiplication equation below?
1299 x 9319
Think step by step. | false | The computed answer of 12,105,381 does not match the ground truth solution of 12,105,381. The discrepancy, although they seem identical, indicates that a formatting or computational error occurred; hence, the correct answer should be 12,105,381. | 265 | 0 | To solve the multiplication \( 1299 \times 9319 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 9319 \) as \( 9000 + 300 + 10 + 9 \). This allows us to multiply \( 1299 \) by each component separately and then add the resul... | [
{
"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 \\( 1299 \\times 9319 \\), 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 \\( 9319 \\) as \\( 9000 + 300 + 10 + 9 \\). This allows us to mul... | 320 | 320 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9518 x 6327
Think step by step. | To solve the long multiplication problem \(9518 \times 6327\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9518\) by each digit of \(6327\) (from right to left), shift the partial results appropriately, and then add them together.
##... | 60220386 | What is the solution to the long multiplication equation below?
9518 x 6327
Think step by step. | true | The solution provided correctly uses the distributive property to break down the multiplication into manageable parts, calculates each part accurately, and adds the results correctly. The final answer matches the ground truth solution. | 266 | 0 | To solve the long multiplication problem \(9518 \times 6327\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9518\) by each digit of \(6327\) (from right to left), shift the partial results appropriately, and then add them together.
##... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem 9518 x 6327, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 9518 by each digit of 6327 (from right to left), shift the partial results appro... | 324 | 364 | 40 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2076 x 1670
Think step by step. | To solve the multiplication problem \( 2076 \times 1670 \), 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 \( 1670 \) as \( 1000 + 600 + 70 \). This allows us to multiply \... | 3466920 | What is the solution to the long multiplication equation below?
2076 x 1670
Think step by step. | true | The provided solution effectively breaks down the multiplication into manageable steps and correctly applies the distributive property. Each multiplication and addition step has been verified, and the final total matches the ground truth solution of 3466920. | 267 | 0 | To solve the multiplication problem \( 2076 \times 1670 \), 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 \( 1670 \) as \( 1000 + 600 + 70 \). This allows us to 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": "To solve the multiplication problem \\( 2076 \\times 1670 \\), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplication\nWe can express \... | 349 | 360 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7229 x 8414
Think step by step. | To solve the long multiplication equation \( 7229 \times 8414 \), 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 (8414) by each digit of the first number (7229) and then summing the results.
### Step... | 60824806 | What is the solution to the long multiplication equation below?
7229 x 8414
Think step by step. | true | The solution accurately follows the steps of long multiplication using the distributive property and correctly computes each intermediate product as well as the total sum. The final answer matches the ground truth solution. | 268 | 0 | To solve the long multiplication equation \( 7229 \times 8414 \), 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 (8414) by each digit of the first number (7229) 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 \\( 7229 \\times 8414 \\), 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 (8414) by each digit of th... | 317 | 348 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3795 x 3307
Think step by step. | To solve the multiplication problem \( 3795 \times 3307 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3795 \) by each digit of \( 3307 \), starting from the rightmost digit (the ones place), and then sum the partial result... | 12550065 | What is the solution to the long multiplication equation below?
3795 x 3307
Think step by step. | true | The solution correctly performs the long multiplication step-by-step, calculates the partial products accurately, and sums them correctly to arrive at the final answer of 12,550,065, which matches the ground truth solution. | 269 | 0 | To solve the multiplication problem \( 3795 \times 3307 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3795 \) by each digit of \( 3307 \), starting from the rightmost digit (the ones place), and then sum the partial result... | [
{
"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 \\( 3795 \\times 3307 \\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:",
"equation": "",
"finished": true,
"output": "",
"step_type": "thought",
"subgoal": "Understanding ... | 586 | 640 | 54 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4695 x 5227
Think step by step. | To solve the long multiplication equation \(4695 \times 5227\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 4695 by each digit of 5227, starting from the rightmost digit, and then sum the results.
### Step 1: Break down the multiplicat... | 24540765 | What is the solution to the long multiplication equation below?
4695 x 5227
Think step by step. | false | The stated final result from the solution is 24,539,765, while the ground truth solution is 24,540,765. These two values do not match, indicating that the solution given is incorrect. | 270 | 0 | To solve the long multiplication equation \(4695 \times 5227\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 4695 by each digit of 5227, starting from the rightmost digit, and then sum the results.
### Step 1: Break down 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 4695 x 5227, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 4695 by each digit of 5227, starting from the rightmost digit, and then sum the... | 289 | 3,706 | 3,417 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8915 x 7613
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8915** and **7613**. 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... | 67869895 | What is the solution to the long multiplication equation below?
8915 x 7613
Think step by step. | true | The provided solution correctly follows the steps of long multiplication, breaking down the numbers into manageable parts and systematically adding the results together. Furthermore, the verification using the grid method confirms the product of 8915 and 7613 as 67869895, which matches the ground truth solution. | 271 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **8915** and **7613**. 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: **8915** and **7613**. 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... | 923 | 931 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8288 x 5074
Think step by step. | To solve the long multiplication equation \( 8288 \times 5074 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8288) by each digit of the multiplier (5074) and then summing the partial results.
### Step 1: Break down the mul... | 42053312 | What is the solution to the long multiplication equation below?
8288 x 5074
Think step by step. | true | The provided solution correctly uses the distributive property of multiplication and verifies the result using standard long multiplication. The calculated result matches the ground truth of 42053312. | 272 | 0 | To solve the long multiplication equation \( 8288 \times 5074 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8288) by each digit of the multiplier (5074) and then summing the partial 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 \\( 8288 \\times 5074 \\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8288) by each digit of the multiplier (5074) and then... | 255 | 255 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1271 x 5397
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1271** and **5397**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | 6859587 | What is the solution to the long multiplication equation below?
1271 x 5397
Think step by step. | true | The solution correctly uses long multiplication to compute the product of 1271 and 5397, providing detailed steps for each digit multiplication, and correctly aggregates the partial results. The final value matches the ground truth solution. | 273 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **1271** and **5397**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to multiply two large numbers: **1271** and **5397**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it mana... | 714 | 725 | 11 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
1552 x 1795
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two numbers: 1552 and 1795. 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 using the distri... | 2785840 | What is the solution to the long multiplication equation below?
1552 x 1795
Think step by step. | true | The solution breaks down the multiplication accurately using both the distributive property and standard long multiplication. Each step is detailed, and the final result of 2,785,840 matches the ground truth solution of 2785840. Therefore, the solution is correct. | 274 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two numbers: 1552 and 1795. 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 using the distri... | [
{
"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 numbers: 1552 and 1795. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": "... | 733 | 761 | 28 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4717 x 2956
Think step by step. | To solve the long multiplication equation \(4717 \times 2956\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4717) by each digit of the multiplier (2956), starting from the rightmost digit, and then summing up th... | 13943452 | What is the solution to the long multiplication equation below?
4717 x 2956
Think step by step. | true | The solution provided correctly calculates the product of 4717 and 2956 through the distributive property of multiplication and correctly sums the partial products, leading to the final answer of 13,943,452. The format of the boxed answer in the solution, although with commas, corresponds to the ground truth solution, ... | 275 | 0 | To solve the long multiplication equation \(4717 \times 2956\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4717) by each digit of the multiplier (2956), 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 4717 x 2956, we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4717) by each digit of the multiplier (2956), starting... | 231 | 266 | 35 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9282 x 8328
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9282** and **8328**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication: The Distrib... | 77300496 | What is the solution to the long multiplication equation below?
9282 x 8328
Think step by step. | true | The solution correctly implements multiplication using the distributive property and verifies the steps through both traditional and lattice multiplication methods. The final answer is consistent with the ground truth solution. | 276 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **9282** and **8328**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication: The Distrib... | [
{
"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: **9282** and **8328**. 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... | 798 | 798 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8723 x 3741
Think step by step. | To solve the long multiplication equation \( 8723 \times 3741 \), 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 (3741)
We can express \( 3741 \) as:
\[ 3741 = 3000 + 700 + 40 + 1 \]
### Step 2: Multiply 8723 b... | 32632743 | What is the solution to the long multiplication equation below?
8723 x 3741
Think step by step. | true | The solution correctly calculates the product of 8723 and 3741 using the distributive property, and the final answer matches the ground truth solution after correcting for formatting (removal of the comma). Both the detailed steps and verification process are correct. | 277 | 0 | To solve the long multiplication equation \( 8723 \times 3741 \), 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 (3741)
We can express \( 3741 \) as:
\[ 3741 = 3000 + 700 + 40 + 1 \]
### Step 2: Multiply 8723 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": "To solve the long multiplication equation \\( 8723 \\times 3741 \\), 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... | 258 | 258 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8875 x 1133
Think step by step. | To solve the long multiplication equation \( 8875 \times 1133 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8875) by each digit of the multiplier (1133) and then summing the partial products.
### Step 1: Brea... | 10055375 | What is the solution to the long multiplication equation below?
8875 x 1133
Think step by step. | true | The provided solution correctly calculates the product of 8875 and 1133 using both the distributive property and verification through standard long multiplication. The final answer of 10,055,375 matches with the ground truth solution of 10055375 when formatted appropriately. | 278 | 0 | To solve the long multiplication equation \( 8875 \times 1133 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8875) by each digit of the multiplier (1133) and then summing the partial products.
### Step 1: Brea... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8875 \\times 1133 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8875) by each digit of the multiplier (1... | 241 | 241 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4176 x 4765
Think step by step. | To solve the long multiplication equation \( 4176 \times 4765 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4176 \) by each digit of \( 4765 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | 19898640 | What is the solution to the long multiplication equation below?
4176 x 4765
Think step by step. | true | The solution correctly follows the distributive property, and the individual calculations for each step of multiplication are accurately derived. After summing the partial results, the final answer matches the ground truth solution when accounting for leading zeros, confirming that the output is indeed correct. | 279 | 0 | To solve the long multiplication equation \( 4176 \times 4765 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4176 \) by each digit of \( 4765 \) (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 \\( 4176 \\times 4765 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 4176 \\) by each digit of \\( 4765 \\) (considering their pla... | 480 | 480 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7630 x 4531
Think step by step. | To solve the long multiplication equation \( 7630 \times 4531 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7630 \) by each digit of \( 4531 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | 34571530 | What is the solution to the long multiplication equation below?
7630 x 4531
Think step by step. | true | The solution correctly calculates the product of 7630 and 4531 as 34,571,530, which matches the ground truth solution of 34571530. The breakdown and verification steps are clearly illustrated and accurate. | 280 | 0 | To solve the long multiplication equation \( 7630 \times 4531 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7630 \) by each digit of \( 4531 \), 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 \\( 7630 \\times 4531 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7630 \\) by each digit of \\( 4531 \\), accounting for place ... | 353 | 353 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5619 x 1824
Think step by step. | To solve the long multiplication problem \( 5619 \times 1824 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5619 \) by each digit of \( 1824 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | 10249056 | What is the solution to the long multiplication equation below?
5619 x 1824
Think step by step. | true | The solution correctly breaks down the multiplication process using the distributive property, computes each step accurately, and confirms the final result through long multiplication. The final answer of 10,249,056 matches the ground truth solution. | 281 | 0 | To solve the long multiplication problem \( 5619 \times 1824 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5619 \) by each digit of \( 1824 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 5619 \\times 1824 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5619 \\) by each digit of \\( 1824 \\) (considering their plac... | 252 | 260 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2264 x 7700
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **2264 × 7700**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly.
### Breaking Down the Multiplication
I recall that multiplica... | 17432800 | What is the solution to the long multiplication equation below?
2264 x 7700
Think step by step. | true | The provided solution correctly evaluates the multiplication of 2264 and 7700 step by step using the distributive property and verification through standard long multiplication. The final result is accurately stated as 17,432,800, which matches the ground truth solution. | 282 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication problem: **2264 × 7700**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly.
### Breaking Down the Multiplication
I recall that multiplica... | [
{
"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: **2264 × 7700**. At first glance, it seems straightforward, but multiplying large numbers can be tricky if I don't break it down properly.",
... | 537 | 549 | 12 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8637 x 7410
Think step by step. | To solve the long multiplication equation \( 8637 \times 7410 \), 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 \( 7410 \) as \( 7000 + 400 + 10 \). This allows us to multiply \... | 64000170 | What is the solution to the long multiplication equation below?
8637 x 7410
Think step by step. | false | The given solution arrives at the final answer of 64000170, rather than the correct product, which is 64000170 according to the ground truth. Although the individual steps and the breakdown of the multiplication are correct, the final answer calculated is incorrect. Therefore, the solution is not accurate. | 283 | 0 | To solve the long multiplication equation \( 8637 \times 7410 \), 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 \( 7410 \) as \( 7000 + 400 + 10 \). This allows us to 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": "To solve the long multiplication equation 8637 x 7410, 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 7410 as 7000 + ... | 202 | 6,547 | 6,345 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4333 x 2741
Think step by step. | To solve the multiplication problem \( 4333 \times 2741 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4333 \) by each digit of \( 2741 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\... | 11876753 | What is the solution to the long multiplication equation below?
4333 x 2741
Think step by step. | false | The calculated product of 4333 and 2741 is incorrect. The solution states that the final answer is 11882753, while the ground truth solution is 11876753. Thus, the provided solution is not correct. | 284 | 0 | To solve the multiplication problem \( 4333 \times 2741 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4333 \) by each digit of \( 2741 \), 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 \\( 4333 \\times 2741 \\), 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... | 245 | 261 | 16 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3826 x 3674
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3,826** and **3,674**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 3,826 by each digit of 3,674, starting from the rightmost digit, and t... | 14056724 | What is the solution to the long multiplication equation below?
3826 x 3674
Think step by step. | true | The solution provided matches the ground truth solution exactly. The step-by-step multiplication and verification are correctly executed and confirm the final result. | 285 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **3,826** and **3,674**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 3,826 by each digit of 3,674, starting from the rightmost digit, and 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 multiply two large numbers: **3,826** and **3,674**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Essentially, I'll multiply 3,826 by e... | 857 | 857 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2552 x 8993
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2552** and **8993**. 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 ... | 22950136 | What is the solution to the long multiplication equation below?
2552 x 8993
Think step by step. | true | The provided solution accurately follows the long multiplication method for calculating the product of 2552 and 8993. Each step, including multiplication and addition of partial products, is carefully verified and correctly computed, leading to the correct final answer of 22950136. | 286 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **2552** and **8993**. 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: **2552** and **8993**. 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... | 690 | 717 | 27 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8868 x 8238
Think step by step. | To solve the long multiplication equation \( 8868 \times 8238 \), 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 summing all the partial produc... | 73054584 | What is the solution to the long multiplication equation below?
8868 x 8238
Think step by step. | true | The solution correctly computes the product of 8868 and 8238 to be 73,054,584, which matches the ground truth solution of 73054584. The solution breaks down the multiplication into manageable parts and verifies the result through two methods, confirming accuracy. | 287 | 0 | To solve the long multiplication equation \( 8868 \times 8238 \), 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 summing all the partial produc... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 8868 \\times 8238 \\), 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, adjus... | 296 | 306 | 10 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
3183 x 1368
Think step by step. | To solve the multiplication problem \( 3183 \times 1368 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3183 \) by each digit of \( 1368 \), starting from the rightmost digit (units place), and then sum the partial results.... | 4354344 | What is the solution to the long multiplication equation below?
3183 x 1368
Think step by step. | true | The solution correctly performs the long multiplication of 3183 by 1368, computes the partial products accurately, and sums them to arrive at the final answer of 4,354,344, which matches the ground truth solution of 4354344. | 288 | 0 | To solve the multiplication problem \( 3183 \times 1368 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3183 \) by each digit of \( 1368 \), starting from the rightmost digit (units place), and then sum the partial results.... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the multiplication problem \\( 3183 \\times 1368 \\), 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 ... | 219 | 218 | -1 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7514 x 5906
Think step by step. | To solve the long multiplication equation \(7514 \times 5906\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7514\) by each digit of \(5906\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | 44377684 | What is the solution to the long multiplication equation below?
7514 x 5906
Think step by step. | true | The solution provided is correct. The intermediate calculations were performed accurately, and the final result matches the ground truth, considering that formatting variations (like commas) do not affect the numerical value. | 289 | 0 | To solve the long multiplication equation \(7514 \times 5906\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7514\) by each digit of \(5906\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplic... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation 7514 x 5906, we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 7514 by each digit of 5906, accounting for place values, and then sum the resul... | 248 | 301 | 53 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7888 x 4368
Think step by step. | To solve the long multiplication equation \( 7888 \times 4368 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7888 \) by each digit of \( 4368 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | 34454784 | What is the solution to the long multiplication equation below?
7888 x 4368
Think step by step. | true | The provided solution correctly calculates the product of 7888 and 4368 and matches the ground truth solution of 34454784, including an accurate verification step. | 290 | 0 | To solve the long multiplication equation \( 7888 \times 4368 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 7888 \) by each digit of \( 4368 \) (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 \\( 7888 \\times 4368 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 7888 \\) by each digit of \\( 4368 \\) (considering their place values) an... | 340 | 297 | -43 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9778 x 2325
Think step by step. | To solve the long multiplication equation \( 9778 \times 2325 \), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:
### Step 1: Break down the multiplier (2325)
We can express \( 2325 \) as \( 2000 + 300 + 20 + 5 \). This allows us to multi... | 22733850 | What is the solution to the long multiplication equation below?
9778 x 2325
Think step by step. | true | The solution correctly followed the steps of breaking down the multiplication using the distributive property, accumulating partial results accurately, and verified the calculations using standard long multiplication. Both the proposed solution and the ground truth result match when formatted correctly. | 291 | 0 | To solve the long multiplication equation \( 9778 \times 2325 \), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:
### Step 1: Break down the multiplier (2325)
We can express \( 2325 \) as \( 2000 + 300 + 20 + 5 \). This allows us to 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 equation \\( 9778 \\times 2325 \\), we'll break it down step by step using the distributive property of multiplication over addition. Here's how we can approach it:",
"equation": "",
"finished": true,
"output": "",
... | 301 | 309 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
7222 x 5866
Think step by step. | To solve the long multiplication equation \( 7222 \times 5866 \), 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 summing all the partial produc... | 42364252 | What is the solution to the long multiplication equation below?
7222 x 5866
Think step by step. | true | The solution accurately breaks down the multiplication of 7222 and 5866 into manageable parts using the distributive property, calculates each partial product correctly, and sums them to arrive at the correct total, which matches the ground truth solution (42364252). Therefore, the solution is correct. | 292 | 0 | To solve the long multiplication equation \( 7222 \times 5866 \), 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 summing all the partial produc... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\( 7222 \\times 5866 \\), 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, adjus... | 282 | 313 | 31 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5446 x 4961
Think step by step. | To solve the long multiplication equation \(5446 \times 4961\), 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 results.
### Step ... | 27017606 | What is the solution to the long multiplication equation below?
5446 x 4961
Think step by step. | true | The solution correctly follows the steps of breaking down the multiplication using the distributive property, computes the intermediate products accurately, and arrives at the final result of 27,017,606, which matches the ground truth solution when formatted correctly. | 293 | 0 | To solve the long multiplication equation \(5446 \times 4961\), 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 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 \\(5446 \\times 4961\\), 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... | 274 | 295 | 21 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
6108 x 8125
Think step by step. | To solve the long multiplication equation \(6108 \times 8125\), 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 toget... | 49627500 | What is the solution to the long multiplication equation below?
6108 x 8125
Think step by step. | false | The solution correctly applied the distributive property and summed the partial products. However, the formatting of the answer uses a comma instead of a digit spacing format, leading to a slight discrepancy compared to the ground truth solution of 49627500. The final answer should match the ground truth exactly, regar... | 294 | 0 | To solve the long multiplication equation \(6108 \times 8125\), 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 toget... | [
{
"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 \\(6108 \\times 8125\\), 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, adjusti... | 302 | 280 | -22 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8822 x 7944
Think step by step. | To solve the multiplication problem \( 8822 \times 7944 \), 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 \( 7944 \) as \( 8000 - 56 \), since \( 8000 - 56 = 7944 \). This allows us to multiply \(... | 70081968 | What is the solution to the long multiplication equation below?
8822 x 7944
Think step by step. | true | The solution provided is correct because it accurately demonstrates the long multiplication process and matches the ground truth solution when formatted correctly (70081968 vs 70,081,968). The calculations and final answer align perfectly with the expected result. | 295 | 0 | To solve the multiplication problem \( 8822 \times 7944 \), 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 \( 7944 \) as \( 8000 - 56 \), since \( 8000 - 56 = 7944 \). This allows us to 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": "To solve the multiplication problem \\( 8822 \\times 7944 \\), 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 ... | 396 | 396 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8455 x 8850
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: 8,455 and 8,850. The goal is to find the product of these two numbers.
### Breaking It Down
Multiplying large numbers directly can be complex, so I recall that breaking it down using the... | 74826750 | What is the solution to the long multiplication equation below?
8455 x 8850
Think step by step. | true | The provided solution correctly calculates the product of 8,455 and 8,850 using multiple methods and arrives at the correct answer of 74,826,750. The solution details the calculations step-by-step and verifies the result through different mathematical approaches, confirming its accuracy. | 296 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,455 and 8,850. The goal is to find the product of these two numbers.
### Breaking It Down
Multiplying large numbers directly can be complex, so I recall that breaking it down using 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": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: 8,455 and 8,850. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"output": ... | 652 | 710 | 58 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
2135 x 2683
Think step by step. | To solve the long multiplication equation \(2135 \times 2683\), 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 all the partial product... | 5728205 | What is the solution to the long multiplication equation below?
2135 x 2683
Think step by step. | true | The provided solution correctly calculates the multiplication of 2135 and 2683 using the distributive property and correctly adds all the partial products to arrive at the correct sum of 5728205, which matches the ground truth solution. | 297 | 0 | To solve the long multiplication equation \(2135 \times 2683\), 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 all the partial product... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication equation \\(2135 \\times 2683\\), 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... | 206 | 226 | 20 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9058 x 2276
Think step by step. | To solve the long multiplication problem \( 9058 \times 2276 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9058 \) by each digit of \( 2276 \) (starting from the right) and then sum the partial results.
### Step 1: Break down the ... | 20616008 | What is the solution to the long multiplication equation below?
9058 x 2276
Think step by step. | true | The solution correctly follows the steps of breaking down the multiplication using the distributive property, calculating each partial product accurately, and providing a verification through standard long multiplication. The final answer of 20,616,008 matches the ground truth solution of 20616008, confirming the corre... | 298 | 0 | To solve the long multiplication problem \( 9058 \times 2276 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9058 \) by each digit of \( 2276 \) (starting from the right) and then sum the partial 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 problem \\( 9058 \\times 2276 \\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \\( 9058 \\) by each digit of \\( 2276 \\) (starting from the righ... | 359 | 359 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9389 x 7824
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: **9389** and **7824**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I ... | 73459536 | What is the solution to the long multiplication equation below?
9389 x 7824
Think step by step. | true | The submitted solution correctly demonstrates the process of multiplying the two numbers 9389 and 7824 step-by-step using long multiplication. It accurately breaks down the multiplication into parts, sums the results, and arrives at the final product which matches the ground truth solution of 73,459,536. | 299 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: **9389** and **7824**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I ... | [
{
"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: **9389** and **7824**. The goal is to find the product of these two numbers.",
"equation": "",
"finished"... | 847 | 847 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
9756 x 2568
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: **9756** and **2568**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | 25053408 | What is the solution to the long multiplication equation below?
9756 x 2568
Think step by step. | true | The solution correctly follows the long multiplication method step by step. It includes detailed breakdowns of multiplying each digit and properly handles carrying over. The final total matches the ground truth solution (25053408), confirming its accuracy. | 300 | 0 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **9756** and **2568**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "### Understanding the Problem\n\nFirst, I need to understand what the problem is asking. It's a multiplication of two large numbers: **9756** and **2568**. The goal is to find the product of these two numbers.",
"equation": "",
"finished": true,
"out... | 812 | 820 | 8 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
5786 x 6753
Think step by step. | To solve the long multiplication problem \( 5786 \times 6753 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5786 \) by each digit of \( 6753 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | 39072858 | What is the solution to the long multiplication equation below?
5786 x 6753
Think step by step. | true | The provided solution correctly applies the distributive property to calculate the product of 5786 and 6753, breaking it down into manageable parts and summing the intermediate results accurately. Both the final answer given and the ground truth solution match when written in standard form (the commas are just formatti... | 301 | 0 | To solve the long multiplication problem \( 5786 \times 6753 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5786 \) by each digit of \( 6753 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "To solve the long multiplication problem \\( 5786 \\times 6753 \\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \\( 5786 \\) by each digit of \\( 6753 \\), accounting for place values, and th... | 294 | 294 | 0 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
4689 x 5883
Think step by step. | To solve the long multiplication equation \( 4689 \times 5883 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | 27585387 | What is the solution to the long multiplication equation below?
4689 x 5883
Think step by step. | true | The solution provided correctly calculates the product of 4689 and 5883 using the distributive property of multiplication. Each step is accurately performed, leading to the correct final result of 27,585,387, which matches the ground truth solution (27585387) in value. | 302 | 0 | To solve the long multiplication equation \( 4689 \times 5883 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place values, and then summing all the partial prod... | [
{
"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 \\( 4689 \\times 5883 \\), 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... | 238 | 252 | 14 | |
TAUR-dev/v3_4d_eval__mini_all | What is the solution to the long multiplication equation below?
8998 x 2502
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8998** and **2502**. At first glance, both numbers seem a bit complex, but perhaps there's a pattern or a simplification that can make this easier.
### Breaking Down the Numbers
Looking at the numbers:
- **8998**: This is close to 9000, jus... | 22512996 | What is the solution to the long multiplication equation below?
8998 x 2502
Think step by step. | true | The solution correctly applies the distributive property and verifies the result through multiple methods, confirming that the final product of 8998 and 2502 is indeed 22,512,996, which matches the ground truth. | 303 | 0 | ### Understanding the Problem
First, I need to multiply two large numbers: **8998** and **2502**. At first glance, both numbers seem a bit complex, but perhaps there's a pattern or a simplification that can make this easier.
### Breaking Down the Numbers
Looking at the numbers:
- **8998**: This is close to 9000, jus... | [
{
"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: **8998** and **2502**. At first glance, both numbers seem a bit complex, but perhaps there's a pattern or a simplification that can make this easier.",
"equation": "",
"finishe... | 568 | 568 | 0 |
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