Datasets:

TAUR-dev
/

r1_8d_eval

question string	solution string	eval_prompt string	eval_internal_cot string	eval_solution string	raw_eval_prompt string	judge_correct bool	judge_reasoning string
What is the solution to the long multiplication equation below? 97511989 x 29677209 Think step by step.	2893883677558701	What is the solution to the long multiplication equation below? 97511989 x 29677209 Think step by step.	Okay, so I need to multiply 97,511,989 by 29,677,209. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the multiplication easier. Maybe using the distributive property, like splitting each number i...	To solve the long multiplication equation \(97,511,989 \times 29,677,209\), we can break down each number into smaller parts and use the distributive property. Here are the key steps: 1. Break down the numbers: - \(97,511,989 = 97,000,000 + 511,989\) - \(29,677,209 = 29,000,000 + 677,209\) 2. **Use the dist...	What is the solution to the long multiplication equation below? 97511989 x 29677209 Think step by step.	true	The solution provided correctly follows the steps of multiplication using the distributive property, and the final result matches the ground truth solution.
What is the solution to the long multiplication equation below? 39634656 x 65995812 Think step by step.	2615721306060672	What is the solution to the long multiplication equation below? 39634656 x 65995812 Think step by step.	Okay, so I need to multiply these two big numbers: 39,634,656 and 65,995,812. Hmm, that's a huge multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. But doing this manually...	To solve the long multiplication equation \(39,634,656 \times 65,995,812\), we can break down the problem using the distributive property and verify the result through multiple methods. 1. Approximation and Adjustment: - Recognize that \(65,995,812\) is close to \(66,000,000\). - Express \(65,995,812\) as \...	What is the solution to the long multiplication equation below? 39634656 x 65995812 Think step by step.	true	The solution provided accurately follows the steps for long multiplication using the distributive property, and the final result matches the ground truth solution exactly.
What is the solution to the long multiplication equation below? 24755057 x 57601784 Think step by step.	1425935446221688	What is the solution to the long multiplication equation below? 24755057 x 57601784 Think step by step.	Okay, so I need to multiply 24,755,057 by 57,601,784. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might help. Maybe using the distributive property? Like, split each number into parts that are easier t...	To solve the long multiplication equation \(24755057 \times 57601784\), we can break down each number into smaller parts and use the distributive property \((a + b)(c + d) = ac + ad + bc + bd\). 1. Split the numbers: - \(24755057 = 24000000 + 755057\) - \(57601784 = 57000000 + 601784\) 2. **Compute each par...	What is the solution to the long multiplication equation below? 24755057 x 57601784 Think step by step.	true	The provided solution accurately follows the steps of long multiplication, correctly applying the distributive property to break down the numbers into manageable parts. Each calculation of the constituent parts is correct, leading to an accurate final sum that matches the ground truth solution.
What is the solution to the long multiplication equation below? 53563670 x 33752847 Think step by step.	1807926358268490	What is the solution to the long multiplication equation below? 53563670 x 33752847 Think step by step.	Okay, so I need to multiply 53,563,670 by 33,752,847. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. Let me recall: when you have two numbers,...	The solution to the long multiplication equation \(53,\!563,\!670 \times 33,\!752,\!847\) is calculated by breaking down the numbers into manageable parts, using distributive properties, and verifying through multiple methods. Here's the step-by-step breakdown: 1. Breakdown and Multiplication: - Split \(53,\!56...	What is the solution to the long multiplication equation below? 53563670 x 33752847 Think step by step.	true	The solution provided correctly follows a detailed breakdown of the long multiplication process, accurately computes each component, sums them correctly, and confirms the result through multiple methods. The final computed result matches the ground truth solution.
What is the solution to the long multiplication equation below? 81471995 x 26159399 Think step by step.	2131258424531005	What is the solution to the long multiplication equation below? 81471995 x 26159399 Think step by step.	Okay, so I need to multiply 81,471,995 by 26,159,399. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might make it easier. Maybe using the distributive property? Like, splitting each number into parts tha...	The solution to the long multiplication equation \(81471995 \times 26159399\) is calculated by breaking down both numbers into smaller, manageable parts and using the distributive property (FOIL method). Here's the step-by-step breakdown: 1. Split the numbers: - \(81471995 = 80000000 + 1471995\) - \(26159399...	What is the solution to the long multiplication equation below? 81471995 x 26159399 Think step by step.	true	The original solution accurately follows the long multiplication process and performs the arithmetic correctly across each step, leading to a final result that matches the ground truth solution.
What is the solution to the long multiplication equation below? 82669731 x 57977955 Think step by step.	4793021943780105	What is the solution to the long multiplication equation below? 82669731 x 57977955 Think step by step.	Okay, so I need to multiply these two big numbers: 82,669,731 and 57,977,955. Hmm, that's a pretty hefty multiplication. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property or some kind of estimati...	To solve the long multiplication equation \(82669731 \times 57977955\), we can break down the multiplication into smaller, manageable parts and then sum the results. Here are the key steps: 1. Break down the multiplier (57977955) into components: - \(50,000,000\) - \(7,000,000\) - \(900,000\) - \(70,00...	What is the solution to the long multiplication equation below? 82669731 x 57977955 Think step by step.	false	The solution provided for the multiplication of 82669731 by 57977955 is incorrect as it yields a final sum of 4845103874310105, which does not match the ground truth solution of 4793021943780105. There appears to be an error in the calculation during the multiplication or summation of the parts.
What is the solution to the long multiplication equation below? 60460452 x 59942216 Think step by step.	3624133473241632	What is the solution to the long multiplication equation below? 60460452 x 59942216 Think step by step.	Okay, so I need to multiply 60,460,452 by 59,942,216. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the calculation easier. Maybe I can use the distributive property here, like splitting each nu...	To solve the long multiplication equation \(60460452 \times 59942216\), we can break down the numbers and use the distributive property for easier calculation. First, we express each number as a sum of smaller parts: - \(60460452 = 60000000 + 460452\) - \(59942216 = 59000000 + 942216\) Using the distributive property...	What is the solution to the long multiplication equation below? 60460452 x 59942216 Think step by step.	true	The calculated result of the long multiplication of 60460452 and 59942216 as described matches the given ground truth solution, showing that the steps and final answer are correct.
What is the solution to the long multiplication equation below? 78270826 x 89167215 Think step by step.	6979191570169590	What is the solution to the long multiplication equation below? 78270826 x 89167215 Think step by step.	Okay, so I need to multiply 78,270,826 by 89,167,215. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might help. Maybe using the distributive property? Like, split each number into parts that are easier t...	The solution to the long multiplication equation \(78,\!270,\!826 \times 89,\!167,\!215\) is calculated by breaking down the numbers using the distributive property and summing the results of each component. Here's the step-by-step breakdown: 1. Split each number into parts: - \(78,\!270,\!826 = 78,\!000,\!000 ...	What is the solution to the long multiplication equation below? 78270826 x 89167215 Think step by step.	true	The solution provided correctly follows the steps of long multiplication using the distributive property, and the computed result matches the ground truth solution exactly.
What is the solution to the long multiplication equation below? 58191452 x 19309974 Think step by step.	1123675425142248	What is the solution to the long multiplication equation below? 58191452 x 19309974 Think step by step.	Okay, so I need to multiply 58,191,452 by 19,309,974. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts might make it easier. Maybe using the distributive property? Like, split each number into parts that ar...	To solve the long multiplication equation \(58,191,452 \times 19,309,974\), we can use the Karatsuba algorithm, which is a divide-and-conquer approach. Here are the key steps: 1. Split the numbers: - \(58,191,452 = 5819 \times 10^4 + 1452\) - \(19,309,974 = 1930 \times 10^4 + 9974\) 2. **Compute the product...	What is the solution to the long multiplication equation below? 58191452 x 19309974 Think step by step.	true	The solution correctly applies the Karatsuba algorithm and correctly calculates the final product, yielding the correct result of 1123675425142248, which matches the ground truth.
What is the solution to the long multiplication equation below? 91914600 x 47919466 Think step by step.	4404498549603600	What is the solution to the long multiplication equation below? 91914600 x 47919466 Think step by step.	Okay, so I need to multiply 91,914,600 by 47,919,466. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done by breaking them down into smaller parts, maybe using the distributive property. Let me recall: a * b = (a1 + a2) * (b1 + ...	To solve the long multiplication equation \(91,914,600 \times 47,919,466\), we can break down the numbers and use the distributive property to simplify the calculation. Here are the key steps: 1. Break down the numbers: - \(91,914,600 = 91,000,000 + 914,600\) - \(47,919,466 = 47,000,000 + 919,466\) 2. **Use...	What is the solution to the long multiplication equation below? 91914600 x 47919466 Think step by step.	true	The solution correctly applies the distributive property and accurately calculates each individual multiplication term. The final summation of all calculated terms also matches the provided ground truth solution, confirming the process and result are correct.
What is the solution to the long multiplication equation below? 74382359 x 99296818 Think step by step.	7385931564033662	What is the solution to the long multiplication equation below? 74382359 x 99296818 Think step by step.	Okay, so I need to multiply 74,382,359 by 99,296,818. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that multiplying large numbers can be done using the standard algorithm, but with numbers this big, it might get really tedious. Maybe there's a smarter way to break...	The solution to the long multiplication equation \(74382359 \times 99296818\) is calculated by breaking down the numbers into more manageable parts. Here's the step-by-step process: 1. Rewrite the multiplier using a round number: \[ 99296818 = 100000000 - 703182 \] Thus, the equation becomes: \[ ...	What is the solution to the long multiplication equation below? 74382359 x 99296818 Think step by step.	true	The provided solution to the multiplication of 74382359 and 99296818 has been calculated step by step with correct breakdowns for both the multiplier and the multiplicand. Each calculation has been verified, and the final result matches the ground truth solution provided, confirming it is correct.
What is the solution to the long multiplication equation below? 51128930 x 65376699 Think step by step.	3342640666802070	What is the solution to the long multiplication equation below? 51128930 x 65376699 Think step by step.	Okay, so I need to multiply these two big numbers: 51,128,930 and 65,376,699. Hmm, that's a pretty large multiplication. Let me think about how to approach this. I remember that for long multiplication, breaking down the numbers into smaller parts might help. Maybe using the distributive property, like splitting each n...	To solve the long multiplication equation \(51,128,930 \times 65,376,699\), we can break down the numbers using the distributive property and standard multiplication techniques. Here is the step-by-step process: 1. Decompose the numbers: - Recognize that \(65,376,699 = 65,376,700 - 1\). - Use the distributiv...	What is the solution to the long multiplication equation below? 51128930 x 65376699 Think step by step.	true	The solution provided has successfully followed the steps of long multiplication, utilized the distributive property correctly, and confirmed the final product matches the ground truth solution. The calculations and verification process were detailed and accurate, leading to the correct final answer.

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Dataset card for evals__r1_8d_eval

This dataset was made with Curator.

Dataset details

A sample from the dataset:

{
    "question": "What is the solution to the long multiplication equation below?\n\n97511989 x 29677209\n\nThink step by step.",
    "solution": "2893883677558701",
    "eval_prompt": "What is the solution to the long multiplication equation below?\n\n97511989 x 29677209\n\nThink step by step.",
    "eval_internal_cot": "Okay, so I need to multiply 97,511,989 by 29,677,209. Hmm, that's a pretty big multiplication problem. Let me think about how to approach this. I remember that for large numbers, breaking them down into smaller parts can make the multiplication easier. Maybe using the distributive property, like splitting each number into parts that are easier to handle. Let me try that.\n\nFirst, let me write down both numbers:\n\n97,511,989 and 29,677,209.\n\nHmm, maybe I can break each number into two parts. For example, split them into millions and the rest. Let's see:\n\n97,511,989 can be written as 97,000,000 + 511,989.\n\nSimilarly, 29,677,209 can be written as 29,000,000 + 677,209.\n\nThen, using the distributive property: (a + b)(c + d) = ac + ad + bc + bd.\n\nSo, multiplying these two numbers would be:\n\n(97,000,000)(29,000,000) + (97,000,000)(677,209) + (511,989)(29,000,000) + (511,989)(677,209).\n\nOkay, let's compute each part step by step.\n\nFirst part: 97,000,000 x 29,000,000.\n\nThat's 97 x 29 followed by 12 zeros (since each number has 6 zeros, so 6 + 6 = 12). Let me compute 97 x 29.\n\n97 x 29: 97 x 30 = 2,910, subtract 97, so 2,910 - 97 = 2,813. So, 2,813 followed by 12 zeros: 2,813,000,000,000,000.\n\nWait, 97,000,000 is 97 million, which is 97 x 10^6, and 29,000,000 is 29 x 10^6. So multiplying them gives (97 x 29) x 10^12. Which is 2,813 x 10^12, so 2,813,000,000,000,000. That seems right.\n\nSecond part: 97,000,000 x 677,209.\n\nSo, 97,000,000 is 97 x 10^6, and 677,209 is approximately 677,209. Let me compute 97 x 677,209 first, then multiply by 10^6.\n\nWait, actually, 97,000,000 x 677,209 = 97,000,000 x 677,209. Let me compute 97 x 677,209 first.\n\nHmm, 97 x 677,209. Let's break that down. 100 x 677,209 = 67,720,900. Subtract 3 x 677,209: 3 x 677,209 = 2,031,627. So, 67,720,900 - 2,031,627 = 65,689,273. Then, multiply by 10^6 (since 97,000,000 is 97 x 10^6). So, 65,689,273 x 10^6 = 65,689,273,000,000.\n\nWait, let me check that again. If 97,000,000 is 97 x 10^6, then multiplying by 677,209 gives (97 x 677,209) x 10^6. Which is 65,689,273 x 10^6, which is 65,689,273,000,000. Yes, that seems correct.\n\nThird part: 511,989 x 29,000,000.\n\nSimilarly, 29,000,000 is 29 x 10^6. So, 511,989 x 29 x 10^6.\n\nFirst compute 511,989 x 29. Let's do that.\n\n511,989 x 30 = 15,359,670. Subtract 511,989: 15,359,670 - 511,989 = 14,847,681. Then multiply by 10^6: 14,847,681 x 10^6 = 14,847,681,000,000.\n\nFourth part: 511,989 x 677,209.\n\nThis is the trickiest part because both numbers are in the hundred thousands. Let me see. Maybe I can use the same method, breaking them down.\n\nAlternatively, maybe use the standard multiplication algorithm, but that might take time. Let me see if there's a smarter way.\n\nAlternatively, note that 511,989 x 677,209. Let me approximate first to check later.\n\nBut let's compute it step by step.\n\nFirst, write 511,989 as 500,000 + 11,989.\n\nAnd 677,209 as 600,000 + 77,209.\n\nThen, using distributive property again:\n\n(500,000 + 11,989)(600,000 + 77,209) = 500,000*600,000 + 500,000*77,209 + 11,989*600,000 + 11,989*77,209.\n\nCompute each term:\n\nFirst term: 500,000 x 600,000 = 300,000,000,000.\n\nSecond term: 500,000 x 77,209 = 38,604,500,000.\n\nThird term: 11,989 x 600,000 = 7,193,400,000.\n\nFourth term: 11,989 x 77,209. Hmm, this is still a bit complex. Let's compute 11,989 x 77,209.\n\nLet me break this down further. Let's write 77,209 as 70,000 + 7,209.\n\nSo, 11,989 x 70,000 = 11,989 x 7 x 10,000 = 83,923 x 10,000 = 839,230,000.\n\nThen, 11,989 x 7,209. Let's compute that.\n\n11,989 x 7,000 = 83,923,000.\n\n11,989 x 209 = ?\n\nCompute 11,989 x 200 = 2,397,800.\n\n11,989 x 9 = 107,901.\n\nSo, total is 2,397,800 + 107,901 = 2,505,701.\n\nTherefore, 11,989 x 7,209 = 83,923,000 + 2,505,701 = 86,428,701.\n\nTherefore, the fourth term is 839,230,000 + 86,428,701 = 925,658,701.\n\nSo, adding all four terms for the fourth part:\n\n300,000,000,000 + 38,604,500,000 + 7,193,400,000 + 925,658,701.\n\nLet's add them step by step.\n\nFirst, 300,000,000,000 + 38,604,500,000 = 338,604,500,000.\n\nThen, 338,604,500,000 + 7,193,400,000 = 345,797,900,000.\n\nThen, 345,797,900,000 + 925,658,701 = 346,723,558,701.\n\nSo, the fourth part is 346,723,558,701.\n\nNow, let's sum up all four parts:\n\nFirst part: 2,813,000,000,000,000\n\nSecond part: 65,689,273,000,000\n\nThird part: 14,847,681,000,000\n\nFourth part: 346,723,558,701\n\nSo, adding them all together:\n\nStart with the largest term: 2,813,000,000,000,000\n\nAdd the second part: 2,813,000,000,000,000 + 65,689,273,000,000 = 2,878,689,273,000,000\n\nAdd the third part: 2,878,689,273,000,000 + 14,847,681,000,000 = 2,893,536,954,000,000\n\nAdd the fourth part: 2,893,536,954,000,000 + 346,723,558,701 = 2,893,883,677,558,701\n\nWait, let me check that addition again. Let's convert all numbers to the same units for clarity.\n\nFirst part: 2,813,000,000,000,000\n\nSecond part: 65,689,273,000,000\n\nThird part: 14,847,681,000,000\n\nFourth part: 346,723,558,701\n\nSo, adding the second and third parts first: 65,689,273,000,000 + 14,847,681,000,000 = 80,536,954,000,000\n\nThen add that to the first part: 2,813,000,000,000,000 + 80,536,954,000,000 = 2,893,536,954,000,000\n\nThen add the fourth part: 2,893,536,954,000,000 + 346,723,558,701 = 2,893,883,677,558,701\n\nSo, the total is 2,893,883,677,558,701.\n\nBut wait, let me verify this with another method to ensure I didn't make a mistake. Maybe using estimation.\n\nOriginal numbers: 97,511,989 and 29,677,209.\n\nApproximately, 97.5 million and 29.7 million.\n\nMultiplying 97.5 million x 29.7 million.\n\nBut wait, 97.5 million is 97.5 x 10^6, and 29.7 million is 29.7 x 10^6.\n\nMultiplying them gives (97.5 x 29.7) x 10^12.\n\nCompute 97.5 x 29.7:\n\nFirst, 100 x 29.7 = 2,970\n\nSubtract 2.5 x 29.7: 2.5 x 29.7 = 74.25\n\nSo, 2,970 - 74.25 = 2,895.75\n\nTherefore, approximately 2,895.75 x 10^12, which is 2,895,750,000,000,000.\n\nOur calculated answer was 2,893,883,677,558,701, which is slightly lower. The difference is about 1.867 billion, which might be due to the approximation. But since we did exact calculations, maybe the exact answer is correct. Let me check the individual parts again.\n\nFirst part: 97,000,000 x 29,000,000 = 2,813,000,000,000,000. Correct.\n\nSecond part: 97,000,000 x 677,209 = 65,689,273,000,000. Let me verify 97,000,000 x 677,209.\n\n97,000,000 x 677,209 = 97,000,000 x 600,000 + 97,000,000 x 77,209.\n\nWait, 97,000,000 x 600,000 = 58,200,000,000,000\n\n97,000,000 x 77,209 = ?\n\nCompute 97,000,000 x 70,000 = 6,790,000,000,000\n\n97,000,000 x 7,209 = ?\n\n97,000,000 x 7,000 = 679,000,000,000\n\n97,000,000 x 209 = 97,000,000 x 200 + 97,000,000 x 9 = 19,400,000,000 + 873,000,000 = 20,273,000,000\n\nSo, total 679,000,000,000 + 20,273,000,000 = 699,273,000,000\n\nTherefore, 97,000,000 x 77,209 = 6,790,000,000,000 + 699,273,000,000 = 7,489,273,000,000\n\nTherefore, total second part: 58,200,000,000,000 + 7,489,273,000,000 = 65,689,273,000,000. Which matches the previous calculation. So that's correct.\n\nThird part: 511,989 x 29,000,000 = 14,847,681,000,000. Let's verify.\n\n511,989 x 29,000,000 = 511,989 x 29 x 1,000,000.\n\nWe calculated 511,989 x 29 = 14,847,681. Then multiplied by 1,000,000 gives 14,847,681,000,000. Correct.\n\nFourth part: 511,989 x 677,209 = 346,723,558,701. Let's check this again.\n\nEarlier, we broke it down into:\n\n(500,000 + 11,989)(600,000 + 77,209) = 300,000,000,000 + 38,604,500,000 + 7,193,400,000 + 925,658,701 = 346,723,558,701.\n\nWait, adding those four numbers:\n\n300,000,000,000\n\n+38,604,500,000 = 338,604,500,000\n\n+7,193,400,000 = 345,797,900,000\n\n+925,658,701 = 346,723,558,701. Correct.\n\nSo all parts are correct. Therefore, the total sum is 2,813,000,000,000,000 + 65,689,273,000,000 + 14,847,681,000,000 + 346,723,558,701 = 2,893,883,677,558,701.\n\nBut let me check once more with another approach. Maybe using the standard algorithm for multiplication, but given the size, it's impractical to do manually. Alternatively, use another breakdown.\n\nAlternatively, note that 97,511,989 is close to 100,000,000, and 29,677,209 is close to 30,000,000. So, 100 million x 30 million = 3,000,000,000,000,000. But our answer is 2,893,883,677,558,701, which is about 2.894 quadrillion, which is slightly less than 3 quadrillion, which makes sense because both numbers are slightly less than 100 million and 30 million. So the approximation checks out.\n\nAlternatively, maybe use another method: (a - b)(c - d) = ac - ad - bc + bd, where a and c are the larger approximations.\n\nBut since both numbers are less than 100 million and 30 million, maybe not necessary.\n\nAlternatively, use the calculator to verify, but since I can't use a calculator, I have to rely on my step-by-step breakdown.\n\nAlternatively, check the individual components again.\n\nWait, let's check the fourth part again: 511,989 x 677,209 = 346,723,558,701.\n\nLet me compute 511,989 x 677,209 using another method.\n\nLet me write 511,989 as 500,000 + 11,989.\n\nMultiply 500,000 x 677,209 = 338,604,500,000.\n\nThen, 11,989 x 677,209.\n\nCompute 10,000 x 677,209 = 6,772,090,000.\n\n1,989 x 677,209.\n\nCompute 1,000 x 677,209 = 677,209,000.\n\n989 x 677,209.\n\nCompute 900 x 677,209 = 609,488,100.\n\n89 x 677,209.\n\nCompute 80 x 677,209 = 54,176,720.\n\n9 x 677,209 = 6,094,881.\n\nSo, 80 x 677,209 + 9 x 677,209 = 54,176,720 + 6,094,881 = 60,271,601.\n\nTherefore, 989 x 677,209 = 609,488,100 + 60,271,601 = 669,759,701.\n\nTherefore, 1,989 x 677,209 = 677,209,000 + 669,759,701 = 1,346,968,701.\n\nTherefore, 11,989 x 677,209 = 6,772,090,000 + 1,346,968,701 = 8,119,058,701.\n\nTherefore, total 511,989 x 677,209 = 338,604,500,000 + 8,119,058,701 = 346,723,558,701. Correct.\n\nSo, all parts are confirmed. Therefore, the total is indeed 2,893,883,677,558,701.\n\nBut let me check once more the addition of all four parts:\n\nFirst part: 2,813,000,000,000,000\n\nSecond part: 65,689,273,000,000\n\nThird part: 14,847,681,000,000\n\nFourth part: 346,723,558,701\n\nAdding second and third parts: 65,689,273,000,000 + 14,847,681,000,000 = 80,536,954,000,000\n\nAdding to first part: 2,813,000,000,000,000 + 80,536,954,000,000 = 2,893,536,954,000,000\n\nAdding fourth part: 2,893,536,954,000,000 + 346,723,558,701 = 2,893,883,677,558,701\n\nYes, that's correct. So the final answer is 2,893,883,677,558,701.\n\nBut wait, let me check if there's a possibility of a miscalculation in the addition steps.\n\nFirst part: 2,813,000,000,000,000\n\nSecond part: 65,689,273,000,000\n\nThird part: 14,847,681,000,000\n\nFourth part: 346,723,558,701\n\nLet me add them in a different order. Let's add all parts step by step.\n\nStart with 2,813,000,000,000,000\n\nAdd 65,689,273,000,000: 2,813,000,000,000,000 + 65,689,273,000,000 = 2,878,689,273,000,000\n\nThen add 14,847,681,000,000: 2,878,689,273,000,000 + 14,847,681,000,000 = 2,893,536,954,000,000\n\nThen add 346,723,558,701: 2,893,536,954,000,000 + 346,723,558,701 = 2,893,883,677,558,701\n\nYes, same result. So I think this is correct.\n\nTherefore, the solution to 97,511,989 multiplied by 29,677,209 is 2,893,883,677,558,701.\n\n**Final Answer**\nThe solution to the long multiplication equation is \\boxed{2893883677558701}.",
    "eval_solution": "To solve the long multiplication equation  $97,511,989 \\times 29,677,209$ , we can break down each number into smaller parts and use the distributive property. Here are the key steps:\n\n1. **Break down the numbers:**\n   -  $97, 511, 989 = 97, 000, 000 + 511, 989$ \n   -  $29, 677, 209 = 29, 000, 000 + 677, 209$ \n\n2. **Use the distributive property  $(a + b) (c + d) = a c + a d + b c + b d$ :**\n   - Compute each part separately:\n     -  $97,000,000 \\times 29,000,000$ \n     -  $97,000,000 \\times 677,209$ \n     -  $511,989 \\times 29,000,000$ \n     -  $511,989 \\times 677,209$ \n\n3. **Calculate each part:**\n   -  $97,000,000 \\times 29,000,000 = 2,813,000,000,000,000$ \n   -  $97,000,000 \\times 677,209 = 65,689,273,000,000$ \n   -  $511,989 \\times 29,000,000 = 14,847,681,000,000$ \n   -  $511,989 \\times 677,209 = 346,723,558,701$ \n\n4. **Sum all parts:**\n   - Add the results of each part:\n     -  $2, 813, 000, 000, 000, 000 + 65, 689, 273, 000, 000 = 2, 878, 689, 273, 000, 000$ \n     -  $2, 878, 689, 273, 000, 000 + 14, 847, 681, 000, 000 = 2, 893, 536, 954, 000, 000$ \n     -  $2, 893, 536, 954, 000, 000 + 346, 723, 558, 701 = 2, 893, 883, 677, 558, 701$ \n\nThus, the solution to the long multiplication equation  $97,511,989 \\times 29,677,209$  is  $\\boxed{2893883677558701}$ .",
    "raw_eval_prompt": "What is the solution to the long multiplication equation below?\n\n97511989 x 29677209\n\nThink step by step.",
    "judge_correct": true,
    "judge_reasoning": "The solution provided correctly follows the steps of multiplication using the distributive property, and the final result matches the ground truth solution."
}

Loading the dataset

You can load this dataset using the following code:

from datasets import load_dataset

dataset = load_dataset("TAUR-dev/evals__r1_8d_eval", split="default")

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