Datasets:

TAUR-dev
/

v3_4d_eval

question string	solution string	eval_prompt string	eval_solution string	raw_eval_prompt string	judge_correct bool	judge_reasoning string
What is the solution to the long multiplication equation below? 5761 x 7525 Think step by step.	43351525	What is the solution to the long multiplication equation below? 5761 x 7525 Think step by step.	To solve the long multiplication equation \( 5761 \times 7525 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution: ### Step 1: Break down the multiplier (7525) We can express \( 7525 \) as \( 8000 - 475 \). This allows us to rewrite the multiplic...	What is the solution to the long multiplication equation below? 5761 x 7525 Think step by step.	true	The solution accurately followed the steps of breaking down the multiplication using the distributive property, calculated the intermediate products correctly, and performed the final subtraction accurately. The format of the answer is consistent with the ground truth solution, confirming its correctness.
What is the solution to the long multiplication equation below? 7826 x 3613 Think step by step.	28275338	What is the solution to the long multiplication equation below? 7826 x 3613 Think step by step.	To solve the long multiplication equation \(7826 \times 3613\), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \(7826\) by each digit of \(3613\) (considering their place values) and then add the results together. ### Step 1: Break down t...	What is the solution to the long multiplication equation below? 7826 x 3613 Think step by step.	true	The solution provided correctly follows the procedure for long multiplication using the distributive property, and the calculations are accurate. The final result matches the ground truth solution.
What is the solution to the long multiplication equation below? 8767 x 6409 Think step by step.	56187703	What is the solution to the long multiplication equation below? 8767 x 6409 Think step by step.	To solve the multiplication problem \( 8767 \times 6409 \), we'll break it down using the long multiplication method. Here's a step-by-step solution: ### Step 1: Break down the multiplication We can express \( 6409 \) as \( 6000 + 400 + 0 + 9 \). This allows us to multiply \( 8767 \) by each component separately a...	What is the solution to the long multiplication equation below? 8767 x 6409 Think step by step.	true	The solution correctly performed long multiplication by breaking down the number 6409 and then computing each component. The addition of all partial results was accurately performed, resulting in the correct final product of 56187703. The boxed format is maintained properly.
What is the solution to the long multiplication equation below? 5266 x 3772 Think step by step.	19863352	What is the solution to the long multiplication equation below? 5266 x 3772 Think step by step.	### Understanding the Problem First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 5,266 and 3,772. The goal is to find the product of these two numbers. ### Breaking Down the Multiplication Multiplying large numbers directly can be complex, so I recall...	What is the solution to the long multiplication equation below? 5266 x 3772 Think step by step.	true	The solution provided by the judge correctly calculates the product of 5,266 and 3,772 and achieves the same result as the ground truth solution, which is 19,863,352. All steps of the multiplication, addition of partial results, and alternative methods were accurately executed. The final numerical representation was al...
What is the solution to the long multiplication equation below? 8764 x 3293 Think step by step.	28859852	What is the solution to the long multiplication equation below? 8764 x 3293 Think step by step.	To solve the long multiplication equation \( 8764 \times 3293 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 8764 \) by each digit of \( 3293 \) (starting from the right) and then sum the results, taking into account the place value...	What is the solution to the long multiplication equation below? 8764 x 3293 Think step by step.	true	The provided solution correctly computes the multiplication of 8764 and 3293 using the distributive property and confirms the result with long multiplication. The final answer matches the ground truth (28859852), albeit with formatting differences (commas vs. no commas). Thus, the answer is correct.
What is the solution to the long multiplication equation below? 4353 x 3257 Think step by step.	14177721	What is the solution to the long multiplication equation below? 4353 x 3257 Think step by step.	To solve the long multiplication equation \(4353 \times 3257\), we'll break it down step by step using the long multiplication method. Here's how it works: ### Step 1: Break down the multiplication We'll multiply \(4353\) by each digit of \(3257\) (from right to left), shifting the partial results appropriately ba...	What is the solution to the long multiplication equation below? 4353 x 3257 Think step by step.	true	The solution provided follows the long multiplication method correctly, breaking down the problem into manageable steps and accurately performing the calculations for each digit. The final result of 14177721 is verified through both addition of partial products and using the distributive property, matching the ground t...
What is the solution to the long multiplication equation below? 7232 x 7540 Think step by step.	54529280	What is the solution to the long multiplication equation below? 7232 x 7540 Think step by step.	To solve the long multiplication equation \(7232 \times 7540\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution: ### Step 1: Break down the multiplication We can express \(7540\) as \(7000 + 500 + 40\) and multiply \(7232\) by each of these comp...	What is the solution to the long multiplication equation below? 7232 x 7540 Think step by step.	true	The solution provided matches the ground truth solution, both arriving at the final result of 54,529,280. The calculations are correctly detailed and verified through standard long multiplication.
What is the solution to the long multiplication equation below? 2001 x 3275 Think step by step.	6553275	What is the solution to the long multiplication equation below? 2001 x 3275 Think step by step.	To solve the multiplication problem \( 2001 \times 3275 \), we can use the distributive property of multiplication over addition, which allows us to break down the calculation into simpler, more manageable parts. Here's a step-by-step solution: ### Step 1: Break down the multiplication We can express \( 3275 \) as...	What is the solution to the long multiplication equation below? 2001 x 3275 Think step by step.	true	The solution correctly applies the distributive property to break down the multiplication into manageable parts. All calculations for each component are accurately performed, and the summation of the results is correct. The final answer of 6,553,275 matches the ground truth solution.
What is the solution to the long multiplication equation below? 2955 x 4223 Think step by step.	12478965	What is the solution to the long multiplication equation below? 2955 x 4223 Think step by step.	### Understanding the Problem First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2955 and 4223. The goal is to find the product of these two numbers. ### Breaking Down the Multiplication Multiplying large numbers directly can be complex, so I recall t...	What is the solution to the long multiplication equation below? 2955 x 4223 Think step by step.	true	The solution correctly provides a detailed breakdown of the multiplication of 2955 and 4223, along with verification steps using alternative methods. The final answer matches the ground truth solution, confirming the accuracy of the calculations.
What is the solution to the long multiplication equation below? 1369 x 6277 Think step by step.	8593213	What is the solution to the long multiplication equation below? 1369 x 6277 Think step by step.	To solve the long multiplication equation \(1369 \times 6277\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying \(1369\) by each digit of \(6277\) (considering their place values) and then adding the partial results. ### Step 1: Break down the m...	What is the solution to the long multiplication equation below? 1369 x 6277 Think step by step.	true	The solution accurately uses the distributive property to break down the multiplication and correctly calculates each step, resulting in the correct final answer. The final answer of 8,593,213 matches the ground truth solution.
What is the solution to the long multiplication equation below? 5748 x 7995 Think step by step.	45955260	What is the solution to the long multiplication equation below? 5748 x 7995 Think step by step.	To solve the long multiplication equation \( 5748 \times 7995 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution: ### Step 1: Break down the multiplier (7995) Notice that \( 7995 \) is very close to \( 8000 \). We can express \( 7995 \) as: \[ 7995 ...	What is the solution to the long multiplication equation below? 5748 x 7995 Think step by step.	true	The solution correctly used the distributive property and verified the multiplication step by step, arriving at the final answer of 45955260, which matches the ground truth solution.
What is the solution to the long multiplication equation below? 5775 x 2934 Think step by step.	16943850	What is the solution to the long multiplication equation below? 5775 x 2934 Think step by step.	To solve the long multiplication equation \( 5775 \times 2934 \), we'll break it down using the distributive property of multiplication over addition. This means we'll multiply \( 5775 \) by each digit of \( 2934 \), accounting for place values, and then sum the results. ### Step 1: Break down the multiplication E...	What is the solution to the long multiplication equation below? 5775 x 2934 Think step by step.	true	The solution provided correctly follows the process of long multiplication by breaking down the numbers and properly utilizing the distributive property. Each multiplication is carried out accurately and the final sum is calculated correctly. The final result of 16,943,850 matches the ground truth solution of 16943850 ...
What is the solution to the long multiplication equation below? 2817 x 7157 Think step by step.	20161269	What is the solution to the long multiplication equation below? 2817 x 7157 Think step by step.	To solve the long multiplication equation \(2817 \times 7157\), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (7157) by the first number (2817) and then summing the results, taking into account the p...	What is the solution to the long multiplication equation below? 2817 x 7157 Think step by step.	false	The solution arrived at by the method outlined results in 20,161,269, which does not match the ground truth solution of 20,161,269 without the comma formatting. Also, it appears the comma in the formatting was interpreted incorrectly in the final answer comparison—making it less directly comparable and potentially caus...
What is the solution to the long multiplication equation below? 4356 x 4180 Think step by step.	18208080	What is the solution to the long multiplication equation below? 4356 x 4180 Think step by step.	To solve the multiplication problem \(4356 \times 4180\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution: ### Step 1: Break down the multiplication Notice that \(4180\) can be written as \(4000 + 100 + 80\). So, we can rewrite the multiplicatio...	What is the solution to the long multiplication equation below? 4356 x 4180 Think step by step.	true	The solution provided arrives at the final product of 4356 times 4180, which is correctly calculated as 18208080. The breakdown of multiplication into simpler parts and the addition of partial products are accurate, confirming the correctness of the solution.
What is the solution to the long multiplication equation below? 2699 x 2608 Think step by step.	7038992	What is the solution to the long multiplication equation below? 2699 x 2608 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 2699 and 2608. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. ### Breaking Down the Multiplication One effect...	What is the solution to the long multiplication equation below? 2699 x 2608 Think step by step.	true	The solution methodically breaks down the multiplication of 2699 and 2608 using the long multiplication method, verifying each step along the way. The intermediate calculations are correct, and the final result of 7,038,992 matches the ground truth solution.
What is the solution to the long multiplication equation below? 7990 x 1250 Think step by step.	9987500	What is the solution to the long multiplication equation below? 7990 x 1250 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 7990 and 1250. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that multiplication can be simplified using the **distributive property of multiplication over add...	What is the solution to the long multiplication equation below? 7990 x 1250 Think step by step.	false	The calculated result in the solution is 9,987,500, but the ground truth solution states that the answer should be 9,987,500 without the extra 0. The ground truth solution is incorrect; both the judge's evaluation and the solution provided result in 9,987,500.
What is the solution to the long multiplication equation below? 8751 x 9132 Think step by step.	79914132	What is the solution to the long multiplication equation below? 8751 x 9132 Think step by step.	To solve the multiplication problem \( 8751 \times 9132 \), we'll use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \( 8751 \) by each digit of \( 9132 \), starting from the rightmost digit, and then sum the partial results. \[ \begin{ali...	What is the solution to the long multiplication equation below? 8751 x 9132 Think step by step.	true	The solution correctly follows the long multiplication method step by step and arrives at the final result, which matches the ground truth solution of 79914132.
What is the solution to the long multiplication equation below? 8906 x 5378 Think step by step.	47896468	What is the solution to the long multiplication equation below? 8906 x 5378 Think step by step.	To solve the long multiplication equation \( 8906 \times 5378 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 8906 \) by each digit of \( 5378 \), starting from the rightmost digit, and then sum all the partial products. ### Step 1:...	What is the solution to the long multiplication equation below? 8906 x 5378 Think step by step.	true	The provided solution accurately calculates the product of 8906 and 5378 using the distributive property of multiplication. Both the breakdown of the multiplication and the final answer match the ground truth solution of 47896468.
What is the solution to the long multiplication equation below? 7525 x 5029 Think step by step.	37843225	What is the solution to the long multiplication equation below? 7525 x 5029 Think step by step.	To solve the long multiplication equation \(7525 \times 5029\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together. ### Step 1...	What is the solution to the long multiplication equation below? 7525 x 5029 Think step by step.	false	The solution concluded with the multiplication result of 37,842,225, while the ground truth solution is 37,843,225. Therefore, the provided solution is incorrect.
What is the solution to the long multiplication equation below? 5668 x 3310 Think step by step.	18761080	What is the solution to the long multiplication equation below? 5668 x 3310 Think step by step.	To solve the long multiplication equation \( 5668 \times 3310 \), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution: ### Step 1: Break down the multiplication We can express \( 3310 \) as \( 3000 + 300 + 10 \). This allows us to multiply \( 5668 \...	What is the solution to the long multiplication equation below? 5668 x 3310 Think step by step.	true	The solution calculated the multiplication of 5668 and 3310 correctly using the distributive property. The step-by-step breakdown adds up the partial results accurately and matches the ground truth solution when formatted, confirming that both are the same value (18761080). Therefore, the solution is correct.
What is the solution to the long multiplication equation below? 9756 x 3998 Think step by step.	39004488	What is the solution to the long multiplication equation below? 9756 x 3998 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 9756 and 3998. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the long multiplication m...	What is the solution to the long multiplication equation below? 9756 x 3998 Think step by step.	true	The solution effectively applies the distributive property to break down the multiplication and verifies the calculations step by step. Both the breakdown using the distributive method and the standard long multiplication yield the same final result of 39,004,488, which matches the ground truth solution.
What is the solution to the long multiplication equation below? 9108 x 7472 Think step by step.	68054976	What is the solution to the long multiplication equation below? 9108 x 7472 Think step by step.	To solve the long multiplication equation \(9108 \times 7472\), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog...	What is the solution to the long multiplication equation below? 9108 x 7472 Think step by step.	true	The solution provided correctly follows the steps of long multiplication using the distributive property and arrives at the correct answer. The formatting of the final answer is only different because of the presence of commas, but the numerical value matches the ground truth solution.
What is the solution to the long multiplication equation below? 9247 x 2916 Think step by step.	26964252	What is the solution to the long multiplication equation below? 9247 x 2916 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 9247 and 2916. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 92...	What is the solution to the long multiplication equation below? 9247 x 2916 Think step by step.	true	The calculated solution matches the ground truth solution when the comma is removed, confirming the multiplication of 9247 and 2916 is correct.
What is the solution to the long multiplication equation below? 3063 x 2473 Think step by step.	7574799	What is the solution to the long multiplication equation below? 3063 x 2473 Think step by step.	To solve the multiplication problem \(3063 \times 2473\), we'll use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \(3063\) by each digit of \(2473\) (from right to left), shifting the partial results appropriately. \[ \begin{align*} &3063...	What is the solution to the long multiplication equation below? 3063 x 2473 Think step by step.	true	The solution accurately applies the long multiplication method and correctly computes the result of multiplying 3063 by 2473. Each step is clearly outlined, and the final summation of partial products leads to the correct answer of 7574799, which matches the ground truth.
What is the solution to the long multiplication equation below? 3872 x 9462 Think step by step.	36636864	What is the solution to the long multiplication equation below? 3872 x 9462 Think step by step.	To solve the long multiplication equation \( 3872 \times 9462 \), we'll break it down step by step using the long multiplication method. Here's how it works: ### Step 1: Break down the multiplication We'll multiply \( 3872 \) by each digit of \( 9462 \), starting from the rightmost digit (units place) and moving l...	What is the solution to the long multiplication equation below? 3872 x 9462 Think step by step.	true	The provided solution accurately follows the steps of long multiplication, correctly breaks down the multiplication into partial products, and sums those products accurately. The final answer matches the ground truth of 36636864.
What is the solution to the long multiplication equation below? 7589 x 4308 Think step by step.	32693412	What is the solution to the long multiplication equation below? 7589 x 4308 Think step by step.	To solve the long multiplication equation \( 7589 \times 4308 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 7589 \) by each digit of \( 4308 \), starting from the rightmost digit, and then sum the results. ### Step 1: Break down t...	What is the solution to the long multiplication equation below? 7589 x 4308 Think step by step.	true	The solution provided correctly demonstrates the step-by-step long multiplication process, accurately computes the intermediate results, and arrives at the correct final answer of 32,693,412, which matches the ground truth solution when formatted properly.
What is the solution to the long multiplication equation below? 2409 x 2084 Think step by step.	5020356	What is the solution to the long multiplication equation below? 2409 x 2084 Think step by step.	To solve the long multiplication equation \( 2409 \times 2084 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 2409 \) by each digit of \( 2084 \) (considering their place values) and then add the results together. ### Step 1: Break ...	What is the solution to the long multiplication equation below? 2409 x 2084 Think step by step.	true	The solution provided correctly breaks down the multiplication of 2409 and 2084 using the distributive property and combines the results accurately, resulting in the final answer of 5,020,356, which matches the ground truth solution.
What is the solution to the long multiplication equation below? 5127 x 3393 Think step by step.	17395911	What is the solution to the long multiplication equation below? 5127 x 3393 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 5127 and 3393. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) ...	What is the solution to the long multiplication equation below? 5127 x 3393 Think step by step.	true	The given solution accurately breaks down the multiplication of 5127 and 3393 using long multiplication, calculates all partial products correctly, and sums them up to arrive at the correct final answer of 17395911, which matches the ground truth solution.
What is the solution to the long multiplication equation below? 2618 x 3358 Think step by step.	8791244	What is the solution to the long multiplication equation below? 2618 x 3358 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 2618 and 3358. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number by the entire fir...	What is the solution to the long multiplication equation below? 2618 x 3358 Think step by step.	true	The solution provided thoroughly details the steps to multiply the two numbers (2618 and 3358) using long multiplication, breaking down each part correctly and combining the results accurately. The final product matches the ground truth solution of 8791244.
What is the solution to the long multiplication equation below? 6819 x 9738 Think step by step.	66403422	What is the solution to the long multiplication equation below? 6819 x 9738 Think step by step.	To solve the long multiplication equation \( 6819 \times 9738 \), we'll break it down step by step using the long multiplication method. Here's how it works: ### Step 1: Break down the multiplication using the distributive property We can express \( 9738 \) as \( 9000 + 700 + 30 + 8 \), and then multiply \( 6819 \...	What is the solution to the long multiplication equation below? 6819 x 9738 Think step by step.	true	The solution presents a detailed breakdown of the long multiplication process and arrives at the correct final answer of 66,403,422, which matches the ground truth solution of 66403422. Hence, the solution is correct.
What is the solution to the long multiplication equation below? 3507 x 6774 Think step by step.	23756418	What is the solution to the long multiplication equation below? 3507 x 6774 Think step by step.	To solve the long multiplication equation \( 3507 \times 6774 \), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results togethe...	What is the solution to the long multiplication equation below? 3507 x 6774 Think step by step.	true	The solution correctly uses the distributive property of multiplication to break down the multiplication problem, computes each step correctly, and sums all partial results accurately to arrive at the final answer. The final result matches the ground truth solution.
What is the solution to the long multiplication equation below? 2439 x 2497 Think step by step.	6090183	What is the solution to the long multiplication equation below? 2439 x 2497 Think step by step.	To solve the long multiplication equation \(2439 \times 2497\), we'll use the standard multiplication method, breaking it down into simpler, more manageable steps. Here's how it works: ### Step 1: Break down the multiplication using the distributive property We can express \(2497\) as \(2000 + 400 + 90 + 7\) and m...	What is the solution to the long multiplication equation below? 2439 x 2497 Think step by step.	true	The provided solution correctly calculates the product of 2439 and 2497 using the standard multiplication method, correctly breaking down the components and summing the partial results. The final answer is presented in the boxed format and matches the ground truth solution.
What is the solution to the long multiplication equation below? 2173 x 6346 Think step by step.	13789858	What is the solution to the long multiplication equation below? 2173 x 6346 Think step by step.	To solve the long multiplication equation \(2173 \times 6346\), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \(2173\) by each digit of \(6346\), starting from the rightmost digit, and then sum the results, taking care to align the number...	What is the solution to the long multiplication equation below? 2173 x 6346 Think step by step.	true	The solution correctly applies the distributive property of multiplication and provides accurate intermediate results for each multiplication, leading to an accurate final addition of these results. The final answer matches the ground truth solution.
What is the solution to the long multiplication equation below? 3419 x 9827 Think step by step.	33598513	What is the solution to the long multiplication equation below? 3419 x 9827 Think step by step.	To solve the long multiplication problem \( 3419 \times 9827 \), we'll break it down using the distributive property of multiplication over addition. This means we'll multiply \( 3419 \) by each digit of \( 9827 \), accounting for place values, and then sum the results. ### Step 1: Break down the multiplication Ex...	What is the solution to the long multiplication equation below? 3419 x 9827 Think step by step.	false	The computed total of 33,666,893 does not match the ground truth solution of 33,598,513. Therefore, the solution is incorrect.
What is the solution to the long multiplication equation below? 2703 x 5036 Think step by step.	13612308	What is the solution to the long multiplication equation below? 2703 x 5036 Think step by step.	To solve the long multiplication equation \( 2703 \times 5036 \), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (5036) by each digit of the first number (2703) and then adding all the partial product...	What is the solution to the long multiplication equation below? 2703 x 5036 Think step by step.	true	The solution provided is correct. The calculated result of the multiplication is accurately derived step by step, and matches the ground truth solution when expressed in a standard numerical format.
What is the solution to the long multiplication equation below? 9531 x 7373 Think step by step.	70272063	What is the solution to the long multiplication equation below? 9531 x 7373 Think step by step.	To solve the long multiplication equation \(9531 \times 7373\), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying the multiplicand (9531) by each digit of the multiplier (7373), considering their place values, and then summing the part...	What is the solution to the long multiplication equation below? 9531 x 7373 Think step by step.	true	The final answer provided in the solution matches the ground truth solution of 70272063. The solution correctly applied the distributive property of multiplication, broke down the numbers accurately, and confirmed the result through standard long multiplication, resulting in consistent and correct computation.
What is the solution to the long multiplication equation below? 5443 x 4753 Think step by step.	25870579	What is the solution to the long multiplication equation below? 5443 x 4753 Think step by step.	To solve the long multiplication equation \(5443 \times 4753\), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu...	What is the solution to the long multiplication equation below? 5443 x 4753 Think step by step.	true	The provided solution accurately follows the steps for long multiplication, properly breaks down the multiplication into manageable parts, and sums these parts correctly to arrive at the final product of 5443 and 4753, which matches the ground truth solution.
What is the solution to the long multiplication equation below? 6448 x 4737 Think step by step.	30544176	What is the solution to the long multiplication equation below? 6448 x 4737 Think step by step.	To solve the long multiplication equation \(6448 \times 4737\), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial results together....	What is the solution to the long multiplication equation below? 6448 x 4737 Think step by step.	true	The solution provided uses the distributive property correctly and accurately calculates the products of each component and the sums of the partial results. The final answer matches the ground truth solution.
What is the solution to the long multiplication equation below? 2428 x 2498 Think step by step.	6065144	What is the solution to the long multiplication equation below? 2428 x 2498 Think step by step.	### Understanding the Problem First, I need to multiply two large numbers: 2428 and 2498. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. ### Breaking Down the Multiplication One effecti...	What is the solution to the long multiplication equation below? 2428 x 2498 Think step by step.	true	The given solution provides a detailed step-by-step calculation of the product of 2428 and 2498, using various methods including the distributive property, standard long multiplication, and an alternative method. Each step has been checked for accuracy, and the final result matches the ground truth solution of 6065144.
What is the solution to the long multiplication equation below? 1950 x 9500 Think step by step.	18525000	What is the solution to the long multiplication equation below? 1950 x 9500 Think step by step.	To solve the multiplication \( 1950 \times 9500 \), we can break it down into simpler steps. Here's a detailed, step-by-step solution: ### Step 1: Break down the multiplication We can use the distributive property of multiplication to simplify the calculation. Notice that \( 9500 \) can be written as \( 10,000 - 500 \...	What is the solution to the long multiplication equation below? 1950 x 9500 Think step by step.	true	The solution calculates the multiplication of 1950 and 9500 correctly and arrives at the same result as the ground truth solution, which is 18525000. The methods used to verify the calculations confirm that the answer is indeed correct.
What is the solution to the long multiplication equation below? 9213 x 2411 Think step by step.	22212543	What is the solution to the long multiplication equation below? 9213 x 2411 Think step by step.	To solve the long multiplication problem \( 9213 \times 2411 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 9213 \) by each digit of \( 2411 \), accounting for place values, and then sum the results. ### Step 1: Break down the mult...	What is the solution to the long multiplication equation below? 9213 x 2411 Think step by step.	false	The solution arrived at a total of 22,212,543, but this is incorrect. The ground truth solution is 22,212,543, which is simply the number 2212543 with an additional placeholder for a million. The thousands digit is incorrectly calculated in the summation. Therefore, the provided solution has an arithmetic error.
What is the solution to the long multiplication equation below? 1129 x 9352 Think step by step.	10558408	What is the solution to the long multiplication equation below? 1129 x 9352 Think step by step.	To solve the multiplication problem \(1129 \times 9352\), we'll use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \(1129\) by each digit of \(9352\) (from right to left), keeping track of the place values by adding zeros as we move left. ...	What is the solution to the long multiplication equation below? 1129 x 9352 Think step by step.	true	The solution provided uses the long multiplication method correctly and arrives at the final answer, which matches the ground truth solution when formatted appropriately (ignoring comma placement). Therefore, the solution is correct.

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Dataset card for v3_4d_eval__mini_all

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Dataset details

A sample from the dataset:

{
    "question": "What is the solution to the long multiplication equation below?\n\n5761 x 7525\n\nThink step by step.",
    "solution": "43351525",
    "eval_prompt": "What is the solution to the long multiplication equation below?\n\n5761 x 7525\n\nThink step by step.",
    "eval_internal_cot": "",
    "eval_solution": "To solve the long multiplication equation  $5761 \\times 7525$ , we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:\n\n### Step 1: Break down the multiplier (7525)\nWe can express  $7525$  as  $8000 - 475$ . This allows us to rewrite the multiplication as:\n\\[\n5761 \\times 7525 = 5761 \\times (8000 - 475)\n\\]\n\n### Step 2: Multiply 5761 by 8000\n\\[\n5761 \\times 8000 = 5761 \\times 8 \\times 1000 = 46,088 \\times 1000 = 46,088,000\n\\]\n\n### Step 3: Multiply 5761 by 475\nNow, break down  $475$  into  $500 - 25$ :\n\\[\n5761 \\times 475 = 5761 \\times (500 - 25)\n\\]\n\\[\n= 5761 \\times 500 - 5761 \\times 25\n\\]\n\n#### Multiply 5761 by 500:\n\\[\n5761 \\times 500 = 5761 \\times 5 \\times 100 = 28,805 \\times 100 = 2,880,500\n\\]\n\n#### Multiply 5761 by 25:\n\\[\n5761 \\times 25 = 5761 \\times \\left(20 + 5\\right) = 5761 \\times 20 + 5761 \\times 5\n\\]\n\\[\n= 115,220 + 28,805 = 144,025\n\\]\n\n#### Subtract the two results:\n\\[\n5761 \\times 475 = 2,880,500 - 144,025 = 2,736,475\n\\]\n\n### Step 4: Subtract the results from Step 2 and Step 3\n\\[\n5761 \\times 7525 = 46,088,000 - 2,736,475 = 43,351,525\n\\]\n\n### Final Answer:\n\\[\n\\boxed{43,\\!351,\\!525}\n\\]",
    "raw_eval_prompt": "What is the solution to the long multiplication equation below?\n\n5761 x 7525\n\nThink step by step.",
    "judge_correct": true,
    "judge_reasoning": "The solution accurately followed the steps of breaking down the multiplication using the distributive property, calculated the intermediate products correctly, and performed the final subtraction accurately. The format of the answer is consistent with the ground truth solution, confirming its correctness."
}

Loading the dataset

You can load this dataset using the following code:

from datasets import load_dataset

dataset = load_dataset("TAUR-dev/v3_4d_eval__mini_all")

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