TAUR-dev/lmfd__hinted_method_w_verification__gpt4omini

{
    "question": "What is the solution to the long multiplication equation below?\n\n8274 x 3529\n\nThink step by step.",
    "solution": "29198946",
    "eval_prompt": "What is the solution to the long multiplication equation below?\n\n8274 x 3529\n\nThink step by step.\n\nBreak this question 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 together. Verify complex operations like long addition by one doing it step by step but also redoing your calculations to make sure you can rederive the right answer.",
    "eval_internal_cot": "",
    "eval_solution": "To solve \\( 8274 \\times 3529 \\) using the distributive property of multiplication over addition, we break down the multiplication based on each digit of the second number \\( 3529\\) and account for its place value.\n\nWe can rewrite \\( 3529\\) as \\( 3000 + 500 + 20 + 9 \\).\n\nNow we will multiply \\( 8274\\) by each of these components:\n\n### Step 1: Multiply \\( 8274\\) by each digit\n\n1. **Multiply by 3000**:\n   \\[\n   8274 \\times 3000 = 24822000\n   \\]\n\n2. **Multiply by 500**:\n   \\[\n   8274 \\times 500 = 4137000\n   \\]\n\n3. **Multiply by 20**:\n   \\[\n   8274 \\times 20 = 165480\n   \\]\n\n4. **Multiply by 9**:\n   \\[\n   8274 \\times 9 = 74466\n   \\]\n\n### Step 2: Add all the partial results\n\nNow we will add the results from each step together:\n\n- \\( 24822000\\)\n- \\( 4137000\\)\n- \\( 165480\\)\n- \\( 74466\\)\n\n### Let's add these step by step:\n\n1. **First add \\( 24822000\\) and \\( 4137000\\)**:\n   \\[\n   24822000 + 4137000 = 28959000\n   \\]\n\n2. **Now add \\( 165480\\)**:\n   \\[\n   28959000 + 165480 = 29124480\n   \\]\n\n3. **Finally, add \\( 74466\\)**:\n   \\[\n   29124480 + 74466 = 29198946\n   \\]\n\n### Final Result\nThus, the result of \\( 8274 \\times 3529 \\) is:\n\n\\[\n\\boxed{29198946}\n\\] \n\n### Verification of the addition:\n\nTo ensure the accuracy of our addition, let's break it down.\n\n1. **Add \\( 28959000\\) and \\( 165480\\)**:\n   - Align the numbers:\n   ```\n     28959000\n   +    165480\n   ------------\n     29124480  (Confirming this one)\n   ```\n\n2. **Now, add \\( 29124480\\) and \\( 74466\\)**:\n   - Align the numbers:\n   ```\n     29124480\n   +      74466\n   ------------\n     29198946  (Confirming this final result)\n   ```\n\nThus, the calculations hold firm as \\( 8274 \\times 3529 = 29198946\\).",
    "raw_eval_prompt": "What is the solution to the long multiplication equation below?\n\n8274 x 3529\n\nThink step by step.\n\nBreak this question 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 together. Verify complex operations like long addition by one doing it step by step but also redoing your calculations to make sure you can rederive the right answer.",
    "judge_correct": true,
    "judge_reasoning": "The provided solution correctly utilizes the distributive property of multiplication and accurately adds the results of each step. The final computed product of \\( 8274 \\times 3529 \\) matches the ground truth solution of \\( 29198946 \\) precisely."
}

from datasets import load_dataset

dataset = load_dataset("TAUR-dev/lmfd__hinted_method_w_verification__gpt4omini", split="default")