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question stringlengths 97 97	solution stringlengths 7 8	eval_solution stringlengths 852 20k	judge_correct bool 2 classes	judge_reasoning stringlengths 103 892	rewritten_eval_solution stringlengths 954 5.2k	repo stringclasses 1 value	behavior_prompt stringlengths 2.44k 7.32k	behavior_type stringclasses 1 value	behavior_spans listlengths 0 26
What is the solution to the long multiplication equation below? 9341 x 4130 Think step by step.	38578330	To solve the long multiplication equation \( 9341 \times 4130 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution: ### Step 1: Break down the multiplication The number \( 4130 \) can be expressed as \( 4000 + 100 + 30 \). This allows us to multiply \( 9341 \) by each ...	true	The solution correctly breaks down the multiplication into manageable parts, calculates each part accurately, and combines the results with correct addition, ultimately leading to the same result as the ground truth solution (38578330).	To find the product of \( 9341 \) and \( 4130 \) through long multiplication, let's follow a systematic method by breaking it down: ### Step 1: Breakdown of the multiplication We can represent \( 4130 \) as \( 4000 + 100 + 30 \). This allows us to handle each part of the multiplication individually and then sum the re...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9341 x 4130 Think step by step. ## Here is the solution 38578330 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 6637 x 5510 Think step by step.	36569870	To solve the long multiplication equation \(6637 \times 5510\), 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 \(5510\) as \(5000 + 500 + 10\) and multiply \(6637\) by each of these comp...	true	The computed result from the solution, 36,569,870, matches the ground truth solution of 36569870 when presented without a comma. Both forms represent the same numerical value, confirming the correctness of the solution.	To find the result of the multiplication problem \(6637 \times 5510\), we can simplify the process by using the distributive property. Here’s a detailed breakdown: ### Step 1: Decompose the components We can rewrite \(5510\) as the sum of \(5000\), \(500\), and \(10\): \[ 6637 \times 5510 = 6637 \times (5000 + 500 + 1...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 6637 x 5510 Think step by step. ## Here is the solution 36569870 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 6624 x 7409 Think step by step.	49077216	To solve the long multiplication equation \(6624 \times 7409\), 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, adjusting for place value, and then summing all the partial products. ### Step 1...	true	The solution provided follows the correct steps for long multiplication and arrives at the product of 6624 and 7409. The use of the distributive property is applied accurately, and the addition of the partial products is performed correctly. The final result matches the ground truth solution (49077216), confirming that...	To find the product of \(6624\) and \(7409\) using long multiplication, we will apply the distributive property of multiplication. This involves multiplying \(6624\) by every digit of \(7409\), taking into account the place values, and then adding all the resulting products together. ### Step 1: Decompose the mult...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 6624 x 7409 Think step by step. ## Here is the solution 49077216 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 5432 x 5137 Think step by step.	27904184	To solve the multiplication problem \(5432 \times 5137\), we'll use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We'll multiply \(5432\) by each digit of \(5137\) (from right to left), shifting the partial results appropriately based on the digit's plac...	true	The solution correctly calculates the product of 5432 and 5137 step by step using long multiplication. The final answer, 27904184, matches the ground truth solution, confirming its correctness.	To find the product of \(5432\) and \(5137\) using the long multiplication technique, let's go through it step by step. ### Step 1: Breakdown the multiplication We will multiply \(5432\) by each digit of \(5137\) starting from the rightmost digit and move to the left, taking into account the value of each digit's posi...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 5432 x 5137 Think step by step. ## Here is the solution 27904184 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 3873 x 5395 Think step by step.	20894835	To solve the long multiplication equation \( 3873 \times 5395 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 3873 \) by each digit of \( 5395 \), starting from the rightmost digit, and then sum the results. ### Step 1: Break down t...	true	The solution correctly breaks down the multiplication process using the distributive property, calculates each part accurately, sums the partial results correctly, and arrives at the final product which matches the ground truth solution (20894835). Therefore, the judged solution is correct.	To find the product of \( 3873 \) and \( 5395 \), we will perform long multiplication step by step using the distributive property. This approach involves breaking down \( 5395 \) into its individual components: \( 5000 + 300 + 90 + 5 \). We will then multiply \( 3873 \) by each of these parts and sum the results. ###...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3873 x 5395 Think step by step. ## Here is the solution 20894835 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 7940 x 3761 Think step by step.	29862340	To solve the long multiplication equation \( 7940 \times 3761 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 7940 \) by each digit of \( 3761 \) (considering their place values) and then add the results together. ### Step 1: Break ...	true	The final answer provided in the solution, 29,862,340, is correct and matches the ground truth solution of 29862340 when formatted without the comma.	To solve the multiplication problem \( 7940 \times 3761 \), we'll approach it step-by-step by applying the distributive property. This involves multiplying \( 7940 \) by each digit of \( 3761 \), taking into account their positional values, and then summing the results. ### Step 1: Decompose the number First, we c...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 7940 x 3761 Think step by step. ## Here is the solution 29862340 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 3965 x 8023 Think step by step.	31811195	To solve the long multiplication equation \( 3965 \times 8023 \), 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. #...	true	The provided solution correctly applies the distributive property to multiply the two numbers, and the calculated final result matches the ground truth value of 31811195. Thus, the solution is correct.	To solve the multiplication problem \( 3965 \times 8023 \), we'll follow a step-by-step approach using the distributive property, which allows us to break the second number into manageable parts, multiply each part by the first number, and then combine those results. ### Step 1: Decompose the multiplication We can...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3965 x 8023 Think step by step. ## Here is the solution 31811195 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 9467 x 7280 Think step by step.	68919760	To solve the long multiplication equation \( 9467 \times 7280 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution: ### Step 1: Break down the multiplication The number \( 7280 \) can be expressed as \( 7000 + 200 + 80 \). This allows us to multiply \( 9467 \) by each c...	true	The solution correctly applies long multiplication by breaking down the number 7280 into its constituent parts (7000, 200, and 80), performing the multiplications correctly, and accurately summing the results. The final result matches the ground truth solution.	To find the product of \( 9467 \times 7280 \) using long multiplication, we can simplify the process by breaking it down into smaller parts. Here’s how we can approach it step by step: ### Step 1: Simplify the Multiplication We can separate \( 7280 \) into its component parts: \( 7000 + 200 + 80 \). This way, we can m...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9467 x 7280 Think step by step. ## Here is the solution 68919760 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 4203 x 4688 Think step by step.	19703664	To solve the long multiplication problem \(4203 \times 4688\), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \(4203\) by each digit of \(4688\) (considering their place values) and then add the results together. ### Step 1: Break down th...	true	The solution correctly calculates the product of 4203 and 4688 using long multiplication, breaking it down into parts and summing the results accurately. The final answer of 19,703,664 matches the ground truth solution.	To find the product of \(4203\) and \(4688\), we will use long multiplication by breaking down the number \(4688\) into its components. This approach allows us to multiply \(4203\) by each part of \(4688\) separately and then combine the results. ### Step 1: Decompose \(4688\) We can represent \(4688\) as: \[ 4000 + 6...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4203 x 4688 Think step by step. ## Here is the solution 19703664 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 3302 x 4938 Think step by step.	16305276	To solve the long multiplication equation \( 3302 \times 4938 \), we'll break it down using the distributive property of multiplication over addition. This method involves multiplying each digit of the second number (4938) by each digit of the first number (3302) and then summing the results. Here's a step-by-step ...	true	The solution accurately computes the product of 3302 and 4938 using the distributive property of multiplication, breaking it down into manageable parts and summing them correctly. The final answer matches the ground truth provided, which confirms its correctness.	To find the product of \( 3302 \) and \( 4938 \), we can use the distributive property of multiplication. This approach involves expanding the second number and multiplying each part by the first number, then adding the results together. Let’s go through the process step-by-step: ### Step 1: Break Down the Multipl...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3302 x 4938 Think step by step. ## Here is the solution 16305276 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 3869 x 3758 Think step by step.	14539702	To solve the long multiplication problem \( 3869 \times 3758 \), we'll break it down using the distributive property of multiplication over addition. This means we'll multiply \( 3869 \) by each digit of \( 3758 \), accounting for place values, and then sum the results. ### Step 1: Break down the multiplication Ex...	true	The calculated result of the multiplication is 14,539,702, which matches the ground truth solution of 14539702 when formatted without commas.	## Solution Steps Recap To compute the long multiplication of \( 3869 \times 3758 \), we'll utilize the distributive property to simplify the process. We will break \( 3758 \) down into its place value components before performing the individual multiplications. ### Step 1: Breakdown the numbers We can express \( ...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3869 x 3758 Think step by step. ## Here is the solution 14539702 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 1506 x 4037 Think step by step.	6079722	To solve the long multiplication equation \(1506 \times 4037\), 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 (4037) by the first number (1506) and then summing the results. ### Step 1: Break down t...	true	The solution correctly applies long multiplication and the distributive property, breaking down the multiplication into manageable parts. The individual calculations for each segment of the first number multiplied by the parts of the second number are accurate, and the final aggregated sum matches the ground truth resu...	To find the product of \(1506\) and \(4037\) using long multiplication, we'll break it down into steps, applying the distributive property of multiplication. This method involves calculating the product of each digit of the number \(4037\) with \(1506\) and then adding up these results. ### Step 1: Breakdown of multip...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 1506 x 4037 Think step by step. ## Here is the solution 6079722 ## Here are the current task instructions Count h...	verification	[]
What is the solution to the long multiplication equation below? 8365 x 7965 Think step by step.	66627225	To solve the long multiplication equation \( 8365 \times 7965 \), we can use the distributive property of multiplication over addition (also known as the FOIL method). This involves breaking down the multiplication into simpler, more manageable parts. Here's a step-by-step solution: ### Step 1: Break down the ...	true	The calculated result of 8365 multiplied by 7965 is indeed 66,627,225, which matches the ground truth solution of 66627225. The correct formatting of the answer, ensuring no typing discrepancies, confirms that both solutions are equivalent despite different representations (including leading zeros). Therefore, the solu...	To find the result of the multiplication \( 8365 \times 7965 \), we will utilize the distributive property, which helps simplify the calculation. Here’s how to approach the problem step by step: ### Step 1: Decompose the second number We can express \( 7965 \) as \( 8000 - 35 \). Thus, we can rewrite the multiplic...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 8365 x 7965 Think step by step. ## Here is the solution 66627225 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 6332 x 1853 Think step by step.	11733196	To solve the multiplication problem \( 6332 \times 1853 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication Multiply \( 6332 \) by each digit of \( 1853 \), starting from the rightmost digit, and shift the partial results accordingly. \[ \begin...	true	The solution correctly calculates the product of 6332 and 1853 using long multiplication and accurately sums the partial products to arrive at the final result of 11733196, which matches the ground truth solution.	To find the product of \( 6332 \times 1853 \), we will utilize the long multiplication technique and break down the procedure step by step. ### Step 1: Decompose the Multiplication We can express \( 1853 \) as the sum of its components, which allows us to multiply \( 6332 \) by each digit separately: \[ \begin{al...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 6332 x 1853 Think step by step. ## Here is the solution 11733196 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 1720 x 4837 Think step by step.	8319640	To solve the long multiplication equation \( 1720 \times 4837 \), we can break it down using the distributive property of multiplication over addition. This method involves multiplying the multiplicand (1720) by each digit of the multiplier (4837) and then summing the partial results. Here's a step-by-step solution...	true	The solution correctly follows the long multiplication method using the distributive property. Each part of the multiplication is computed accurately, and the final sum is also correct. The calculated result (8,319,640) matches the ground truth solution (8319640). Therefore, the solution is correct.	To find the product of 1720 and 4837 through long multiplication, we can utilize the distributive property to simplify the calculation. This approach involves multiplying 1720 by each digit of 4837 separately and then combining the results. Below are the steps clearly laid out: ### Step 1: Decompose the Multiplier...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 1720 x 4837 Think step by step. ## Here is the solution 8319640 ## Here are the current task instructions Count h...	verification	[]
What is the solution to the long multiplication equation below? 8307 x 8131 Think step by step.	67544217	To solve the long multiplication equation \( 8307 \times 8131 \), 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 (8131) by each digit of the first number (8307) and then adding all the partial product...	true	The solution correctly calculates the product of 8307 and 8131 using the long multiplication method, and the final summed result matches the ground truth solution, which is 67544217.	To find the product of \( 8307 \) and \( 8131 \) through long multiplication, we'll proceed step by step by utilizing the distributive property, which allows us to simplify the multiplication process. ### Step 1: Express the multiplication We can rewrite \( 8307 \times 8131 \) as: \[ 8307 \times 8131 = 8307 \times...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 8307 x 8131 Think step by step. ## Here is the solution 67544217 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 6686 x 8827 Think step by step.	59017322	To solve the long multiplication equation \( 6686 \times 8827 \), 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...	true	The solution correctly applies the distributive property to break down the multiplication into manageable parts, accurately calculates each multiplication, and correctly sums the results to arrive at the final answer of 59017322, which matches the ground truth solution.	To solve the multiplication \(6686 \times 8827\), we will approach it by using the distributive property. This technique entails breaking down the second number into its components, multiplying each part by the first number, and then combining the results. ### Step 1: Decompose the multiplication We can rewrite \(...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 6686 x 8827 Think step by step. ## Here is the solution 59017322 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 4416 x 5084 Think step by step.	22450944	To solve the long multiplication equation \(4416 \times 5084\), 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 (5084) by the first number (4416) and then adding the results. ### Step 1: Break down th...	true	The calculated product of 4416 and 5084 is correctly computed from its components using the distributive property and matches the ground truth solution.	To find the product of \(4416\) and \(5084\) using long multiplication, we will go through the process methodically, applying the distributive property. This involves breaking down \(5084\) into its components and multiplying each by \(4416\), then summing the results. ### Step 1: Breakdown of the Second Number Fi...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4416 x 5084 Think step by step. ## Here is the solution 22450944 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 2165 x 2976 Think step by step.	6443040	To solve the long multiplication equation \( 2165 \times 2976 \), we'll break it down step by step using the distributive property of multiplication over addition. This means we'll multiply \( 2165 \) by each digit of \( 2976 \), accounting for place values, and then sum the results. ### Step 1: Break down the mul...	true	The provided solution correctly follows the steps of long multiplication using the distributive property, breaking down the multiplication into manageable parts and accurately calculating the individual products, ultimately adding them correctly to produce the final result. The calculated final product of 6,443,040 mat...	To find the product of \( 2165 \) and \( 2976 \) using long multiplication, we will systematically apply the distributive property, which involves multiplying \( 2165 \) by each digit of \( 2976 \) separately and then combining the results based on their place values. ### Step 1: Decompose the second number We can...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 2165 x 2976 Think step by step. ## Here is the solution 6443040 ## Here are the current task instructions Count h...	verification	[]
What is the solution to the long multiplication equation below? 6601 x 1713 Think step by step.	11307513	To solve the multiplication \( 6601 \times 1713 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We can express \( 1713 \) as \( 1000 + 700 + 10 + 3 \). This allows us to multiply \( 6601 \) by each component separately and then add the resul...	true	The solution correctly applies the long multiplication technique by breaking down the number 1713 into its components and accurately calculating each partial product. After summing the results, the final answer matches the ground truth solution (11307513). Therefore, the solution is correct.	To calculate \( 6601 \times 1713 \), we can apply the long multiplication technique. Let's go through the steps carefully. ### Step 1: Decompose the multiplication We can rewrite \( 1713 \) as the sum of its components: \( 1000 + 700 + 10 + 3 \). This way, we multiply \( 6601 \) by each part individually and then ...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 6601 x 1713 Think step by step. ## Here is the solution 11307513 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 4503 x 3441 Think step by step.	15494823	To solve the long multiplication equation \(4503 \times 3441\), 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, shifted appropriately, and then adding the results. ### Step 1: Bre...	true	The computed product of 4503 and 3441 is correct as it matches the ground truth solution, 15494823, when leading zeros are disregarded.	To find the product of \(4503\) and \(3441\), we'll utilize a systematic approach by applying the distributive property. This involves breaking down the second number into its individual components and multiplying each part by the first number. Here’s how we can do this step-by-step: ### Step 1: Break down the sec...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 4503 x 3441 Think step by step. ## Here is the solution 15494823 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 5257 x 8393 Think step by step.	44122001	To solve the long multiplication equation \(5257 \times 8393\), 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...	false	The solution arrived at 44,122,001, but the ground truth solution provided is 44122001, which matches the raw number without formatting. This indicates a formatting discrepancy rather than a calculation error. The two values are numerically equivalent, so while the numeric value is correct, the outputs are not identica...	To solve the multiplication problem \(5257 \times 8393\), we'll approach it by utilizing the distributive property, which involves breaking down the second number and multiplying each part by the first number, then summing the results. ### Step 1: Decompose \(8393\) We can rewrite \(8393\) as \(8000 + 300 + 90 + 3...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 5257 x 8393 Think step by step. ## Here is the solution 44122001 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 3592 x 1116 Think step by step.	4008672	To solve the multiplication problem \( 3592 \times 1116 \), we can use the long multiplication method. Here's a step-by-step breakdown: ### Step 1: Break down the multiplication We can express \( 1116 \) as \( 1000 + 100 + 10 + 6 \). This allows us to multiply \( 3592 \) by each component separately and then add t...	true	The solution correctly follows the long multiplication method and accurately computes each part, summing the results correctly to arrive at the final product of 4,008,672, which matches the ground truth.	To calculate the multiplication \( 3592 \times 1116 \), we can utilize the long multiplication method by breaking it down into manageable parts. Here’s how we can approach it step by step: ### Step 1: Decompose the multiplier We can represent \( 1116 \) as the sum \( 1000 + 100 + 10 + 6 \). This allows us to calcu...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 3592 x 1116 Think step by step. ## Here is the solution 4008672 ## Here are the current task instructions Count h...	verification	[]
What is the solution to the long multiplication equation below? 9540 x 1875 Think step by step.	17887500	To solve the multiplication \(9540 \times 1875\), 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 (1875) We can express \(1875\) as \(2000 - 125\) because: \[ 1875 = 2000 - 125 \] ### Step 2: Multiply 9540 ...	true	The solution follows a correct application of the distributive property and accurately calculates each component of the multiplication step by step. The final result matches the ground truth solution of 17887500.	To compute \(9540 \times 1875\), we can use the distributive property to simplify the calculation step by step. ### Step 1: Decompose the multiplier (1875) We can break down \(1875\) into \(2000 - 125\). This means: \[ 1875 = 2000 - 125 \] ### Step 2: Perform the multiplications Next, we will multiply \(9540\) wi...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 9540 x 1875 Think step by step. ## Here is the solution 17887500 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 5256 x 5185 Think step by step.	27252360	To solve the long multiplication equation \(5256 \times 5185\), 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...	true	The solution correctly applies the distributive property to calculate the product of 5256 and 5185. All intermediate multiplications and the final addition are performed accurately, leading to the correct final answer of 27,252,360, which matches the ground truth solution.	To solve the multiplication problem \(5256 \times 5185\), we can use the distributive property of multiplication. This involves breaking down the second number into its individual components based on place value and multiplying each part by the first number before summing all the results. ### Step 1: Break down \(...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 5256 x 5185 Think step by step. ## Here is the solution 27252360 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 7102 x 4592 Think step by step.	32612384	To solve the long multiplication equation \(7102 \times 4592\), we'll break it down step by step using the distributive property of multiplication over addition. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding all the partial results ...	true	The solution correctly applies the distributive property of multiplication to break down the numbers into manageable parts. Each partial multiplication is accurate, and the summation of those parts has been performed correctly. The final result matches the ground truth solution when formatted appropriately.	To find the product of \(7102\) and \(4592\) using long multiplication, we can apply the distributive property, which allows us to break the problem into simpler parts. Here’s how we can approach it step by step. ### Step 1: Decompose \(4592\) First, we can express \(4592\) as the sum of its place values, specific...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 7102 x 4592 Think step by step. ## Here is the solution 32612384 ## Here are the current task instructions Count ...	verification	[]
What is the solution to the long multiplication equation below? 5186 x 5585 Think step by step.	28963810	To solve the long multiplication equation \( 5186 \times 5585 \), 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 (5585) We can express \( 5585 \) as \( 5000 + 500 + 80 + 5 \). This allows us to multiply \( 5186...	true	The solution accurately follows the long multiplication method, using the distributive property effectively to break down the multiplication into simpler parts. All calculations are correctly executed, and the final total matches the ground truth solution when formatted appropriately.	To find the product of \( 5186 \) and \( 5585 \) through long multiplication, we can break down the process using the distributive property. Here's how: ### Step 1: Decompose the number (5585) We can view \( 5585 \) as \( 5000 + 500 + 80 + 5 \). This allows us to multiply \( 5186 \) by each part separately and then su...	TAUR-dev/lmfd__rewritten_v3_to_4omini__train	An LLM was asked a question and we want to see if it used self verification as a reasoning strategy to solve it. ## Here is the question What is the solution to the long multiplication equation below? 5186 x 5585 Think step by step. ## Here is the solution 28963810 ## Here are the current task instructions Count ...	verification	[]

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