doc_id int64 | doc string | target string | arguments string | resps string | filtered_resps string | doc_hash string | prompt_hash string | target_hash string | exact_match int64 | extracted_answers string | source_file string | generation string | info string | evaluation_api_cost string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 13 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the long division equation \\\\( 15 \\\\div 19 \\\\) step by step, follow these steps:\\n\\n1. **Write the numbers vertically**:\\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 15 \\\\\\\\\\n \\\\times & 19 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. **Multiply the ones digit of the di... | ["{'generation': \"To solve the long division equation \\\\( 15 \\\\div 19 \\\\) step by step, follow these steps:\\n\\n1. **Write the numbers vertically**:\\n \\\\[\\n \\\\begin{array}{c@{}c}\\n & 15 \\\\\\\\\\n \\\\times & 19 \\\\\\\\\\n \\\\end{array}\\n \\\\]\\n\\n2. **Multiply the ones digit of the div... | 1fe4a3a3bdceb99acba3870b8820fb7d71d2b128097a35de13101519c94b2714 | 6adf7f5ba7f8982f91ce5cd729a078032176cbdfc8ebc8d4eaebb7f44a3a1fb4 | 3fdba35f04dc8c462986c992bcf875546257113072a909c162f7e470e581e278 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long division equation \\( 15 \\div 19 \\) step by step, follow these steps:\n\n1. **Write the numbers vertically**:\n \\[\n \\begin{array}{c@{}c}\n & 15 \\\\\n \\times & 19 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the ones digit of the dividee with 15**:\n \\[\n 5 \\times 15 = 75\n \... | [{"budget_forced_chunks": ["To solve the long division equation \\( 15 \\div 19 \\) step by step, follow these steps:\n\n1. **Write the numbers vertically**:\n \\[\n \\begin{array}{c@{}c}\n & 15 \\\\\n \\times & 19 \\\\\n \\end{array}\n \\]\n\n2. **Multiply the ones digit of the dividee with 15**:\n \\[\n... | null |
1 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 10 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) step by step, follow these steps:\\n\\n1. **Break down the multiplication into smaller parts:**\\n - First, multiply \\\\( 20 \\\\) by \\\\( 9 \\\\) directly.\\n - Next, break down \\\\( 9 \\\\) into \\\\( 10 - 1 \\\\) and try to make t... | ["{'generation': 'To solve the long division equation \\\\( 20 \\\\div 9 \\\\) step by step, follow these steps:\\n\\n1. **Break down the multiplication into smaller parts:**\\n - First, multiply \\\\( 20 \\\\) by \\\\( 9 \\\\) directly.\\n - Next, break down \\\\( 9 \\\\) into \\\\( 10 - 1 \\\\) and try to make th... | 4e7925e9464d9cd3f15b66d7f0d396c2d208e935db23218e8e12a143a69fdcf5 | bd97db98bf338537ff6865ad3edb32a5afd84e1c203f33f3a520ad9350cff93a | 4a44dc15364204a80fe80e9039455cc1608281820fe2b24f1e5233ade6af1dd5 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long division equation \\( 20 \\div 9 \\) step by step, follow these steps:\n\n1. **Break down the multiplication into smaller parts:**\n - First, multiply \\( 20 \\) by \\( 9 \\) directly.\n - Next, break down \\( 9 \\) into \\( 10 - 1 \\) and try to make the multiplication simpler.\n\n2. **Perform ... | [{"budget_forced_chunks": ["To solve the long division equation \\( 20 \\div 9 \\) step by step, follow these steps:\n\n1. **Break down the multiplication into smaller parts:**\n - First, multiply \\( 20 \\) by \\( 9 \\) directly.\n - Next, break down \\( 9 \\) into \\( 10 - 1 \\) and try to make the multiplication... | null |
2 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 24 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': 'To solve the long division problem \\\\(13 \\\\div 3 = 4\\\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\\\(130\\\\). We add the carried over 1 t... | ["{'generation': 'To solve the long division problem \\\\(13 \\\\div 3 = 4\\\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\\\(130\\\\). We add the carried over 1 to... | 21d37d7882ca656e9c61892eb0e92eb17e6ccb0b44acbf990becc8d10939c8ba | 01fe40f4315157fd51d595d12678270a8d4a97c88098425b3b2c89768f826ed6 | c2356069e9d1e79ca924378153cfbbfb4d4416b1f99d41a2940bfdb66c5319db | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long division problem \\(13 \\div 3 = 4\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\(130\\). We add the carried over 1 to 130, which gives us 131.\... | [{"budget_forced_chunks": ["To solve the long division problem \\(13 \\div 3 = 4\\) with remainder 1, we write down 4 and carry over 1. Then, we multiply 13 by 10 (which is not actually used in this division but can be thought of as multiplying by 10 after carrying), resulting in \\(130\\). We add the carried over 1 to... | null |
3 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 21 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the long multiplication equation \\\\(23 \\\\times 315\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\\n\\n1. Break down 315 into 300 and 15.\\n \\\\[\\n 23 \\\\times 315 = 23 \\\\times (300 + 15)\\n... | ["{'generation': \"To solve the long multiplication equation \\\\(23 \\\\times 315\\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\\n\\n1. Break down 315 into 300 and 15.\\n \\\\[\\n 23 \\\\times 315 = 23 \\\\times (300 + 15)\\n ... | 95ef82ecb05d93a4ee380d4641abaeadd43e6bc9d99c871ce170758b6f305b44 | b74d9dce0967059bc7deb16d7c3ce9ddb7cfb27d70d2987dea642c679674d513 | 6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long multiplication equation \\(23 \\times 315\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Break down 315 into 300 and 15.\n \\[\n 23 \\times 315 = 23 \\times (300 + 15)\n \\]\n\n2. Apply the distributive... | [{"budget_forced_chunks": ["To solve the long multiplication equation \\(23 \\times 315\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Here's how we do it:\n\n1. Break down 315 into 300 and 15.\n \\[\n 23 \\times 315 = 23 \\times (300 + 15)\n \\]\n\... | null |
4 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 17 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the long division equation \\\\(32 \\\\div 4\\\\), we'll follow these steps:\\n\\n1. **Multiply the units digits**: \\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n Write down 8.\\n\\n2. **Multiply the tens digit of the first number with the units digit of the second number**:\\n \\\\[\... | ["{'generation': \"To solve the long division equation \\\\(32 \\\\div 4\\\\), we'll follow these steps:\\n\\n1. **Multiply the units digits**: \\n \\\\[\\n 2 \\\\times 4 = 8\\n \\\\]\\n Write down 8.\\n\\n2. **Multiply the tens digit of the first number with the units digit of the second number**:\\n \\\\[\\... | 37e0958fcc9b1045189fb65b03cc9e071033593787e2f5171ceea9f86e8ebcf4 | ec571e8688c75a5736ce86b7195b61373aaf0be543ff8182bc2cf3a6429e9eab | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long division equation \\(32 \\div 4\\), we'll follow these steps:\n\n1. **Multiply the units digits**: \n \\[\n 2 \\times 4 = 8\n \\]\n Write down 8.\n\n2. **Multiply the tens digit of the first number with the units digit of the second number**:\n \\[\n 3 \\times 4 = 12\n \\]\n Since we... | [{"budget_forced_chunks": ["To solve the long division equation \\(32 \\div 4\\), we'll follow these steps:\n\n1. **Multiply the units digits**: \n \\[\n 2 \\times 4 = 8\n \\]\n Write down 8.\n\n2. **Multiply the tens digit of the first number with the units digit of the second number**:\n \\[\n 3 \\times 4... | null |
5 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 18 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': 'To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\\n\\nStep 1: Multiply the first two numbers (12 and 6).\\n12 * 6 = 72\\n\\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are act... | ["{'generation': 'To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\\n\\nStep 1: Multiply the first two numbers (12 and 6).\\n12 * 6 = 72\\n\\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are actu... | a4b2daca5c54b55b15980110f282e22f14fac0971c9652711d3a679e8bd89a3d | 7cfb8ba4d40ba72deb7d7f9cb5b33545b9f643be9e6bb394acaf180179e28cd4 | 4ec9599fc203d176a301536c2e091a19bc852759b255bd6818810a42c5fed14a | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\n\nStep 1: Multiply the first two numbers (12 and 6).\n12 * 6 = 72\n\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are actually multiplying by 1... | [{"budget_forced_chunks": ["To solve the target number 18 using the numbers 12, 6, and 12, we can break it down into the following steps:\n\nStep 1: Multiply the first two numbers (12 and 6).\n12 * 6 = 72\n\nStep 2: Multiply the last two numbers (12 and 6) but place the result in the next place value. This means we are... | null |
6 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 21 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': 'To solve the problem \\\\( 6 \\\\times 15 \\\\times 13 \\\\times 9 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\\\( 10 + 5 \\\\), which allows us to break the multiplication into two parts:\\n\\... | ["{'generation': 'To solve the problem \\\\( 6 \\\\times 15 \\\\times 13 \\\\times 9 \\\\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\\\( 10 + 5 \\\\), which allows us to break the multiplication into two parts:\\n\\n... | a7f237e6a8b37389748df0baa5ea27734734e3277f163e579d92165e4afed893 | ab00774c40567d2e767072fc5936db116736f40a30593069488d7cfe010b27b9 | 6f4b6612125fb3a0daecd2799dfd6c9c299424fd920f9b308110a2c1fbd8f443 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the problem \\( 6 \\times 15 \\times 13 \\times 9 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\( 10 + 5 \\), which allows us to break the multiplication into two parts:\n\n\\[ 6 \\times 15 = 6 \\times (10... | [{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 15 \\times 13 \\times 9 \\), we can break it down into simpler steps by using the distributive property of multiplication over addition. Specifically, we can express 15 as \\( 10 + 5 \\), which allows us to break the multiplication into two parts:\n\n\\[ 6 ... | null |
7 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 17 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the long division equation \\\\( 2 \\\\times 8 = 16 \\\\), add the zero from the intermediate step (16) to get \\\\( 160 \\\\).\\n\\nNext, add the result of the next multiplication step, \\\\( 2 \\\\times 2 = 4 \\\\), to \\\\( 160 \\\\) to get \\\\( 164 \\\\).\\n\\nFinally, add the result o... | ["{'generation': \"To solve the long division equation \\\\( 2 \\\\times 8 = 16 \\\\), add the zero from the intermediate step (16) to get \\\\( 160 \\\\).\\n\\nNext, add the result of the next multiplication step, \\\\( 2 \\\\times 2 = 4 \\\\), to \\\\( 160 \\\\) to get \\\\( 164 \\\\).\\n\\nFinally, add the result of... | 45c1e59b5a1a576b7ae49ac9ab5ee519341b3ff5d15693635b6c69819b16325f | 0e76d7adfecf1d484230f45f4d7e233e3860bce62d005024a9c931e6fe2a8c02 | 4523540f1504cd17100c4835e85b7eefd49911580f8efff0599a8f283be6b9e3 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the long division equation \\( 2 \\times 8 = 16 \\), add the zero from the intermediate step (16) to get \\( 160 \\).\n\nNext, add the result of the next multiplication step, \\( 2 \\times 2 = 4 \\), to \\( 160 \\) to get \\( 164 \\).\n\nFinally, add the result of the final multiplication step, \\( 2 \\times... | [{"budget_forced_chunks": ["To solve the long division equation \\( 2 \\times 8 = 16 \\), add the zero from the intermediate step (16) to get \\( 160 \\).\n\nNext, add the result of the next multiplication step, \\( 2 \\times 2 = 4 \\), to \\( 160 \\) to get \\( 164 \\).\n\nFinally, add the result of the final multipli... | null |
8 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 22 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\\n\\nFirst, we can break down the problem into simpler steps:\\n\\n1. Multiply the numbers in pairs:\\n - 21 * 15 = 315\\n - 21 * 9 = 189\\n\\n2. Add the result... | ["{'generation': \"To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\\n\\nFirst, we can break down the problem into simpler steps:\\n\\n1. Multiply the numbers in pairs:\\n - 21 * 15 = 315\\n - 21 * 9 = 189\\n\\n2. Add the results... | 167220307e1ef076a95de3ecc155ceac76542c67d9bfe7f28083afac878049e0 | 15b1e41847c3fd678b61f9e016eda0d418836829766dc3d9e8d8e1b5133c1d3a | 785f3ec7eb32f30b90cd0fcf3657d388b5ff4297f2f9716ff66e9b69c05ddd09 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\n\nFirst, we can break down the problem into simpler steps:\n\n1. Multiply the numbers in pairs:\n - 21 * 15 = 315\n - 21 * 9 = 189\n\n2. Add the results of these multiplications... | [{"budget_forced_chunks": ["To solve the problem of creating an equation with the numbers[21, 15, 5, 9] that equals 22, we can use the basic arithmetic operations.\n\nFirst, we can break down the problem into simpler steps:\n\n1. Multiply the numbers in pairs:\n - 21 * 15 = 315\n - 21 * 9 = 189\n\n2. Add the result... | null |
9 | {"query": [{"role": "system", "content": "Solve the problem step by step. Write your thoughts in <think> </think> tags.\nThe answer is a series of arithmetic operations (+, -, *, /) that results in the target number.\n\nWrite the final answer in <final_answer> </final_answer> tags.\nFor the final answer, make sure that... | 14 | {"gen_args_0": {"arg_0": "<|im_start|>system\nYou are Qwen, created by Alibaba Cloud. You are a helpful assistant.<|im_end|>\n<|im_start|>user\n[{'role': 'system', 'content': 'Solve the problem step by step. Write your thoughts in <think> </think> tags.\\nThe answer is a series of arithmetic operations (+, -, *, /) tha... | [["{'generation': \"To solve the problem \\\\( 6 \\\\times 22 \\\\) using step-by-step reasoning, we can break it down into simpler steps:\\n\\n1. **Break down the multiplication:**\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive property:**\\n \\\\[\\n 6 \\\\times ... | ["{'generation': \"To solve the problem \\\\( 6 \\\\times 22 \\\\) using step-by-step reasoning, we can break it down into simpler steps:\\n\\n1. **Break down the multiplication:**\\n \\\\[\\n 6 \\\\times 22 = 6 \\\\times (20 + 2)\\n \\\\]\\n\\n2. **Apply the distributive property:**\\n \\\\[\\n 6 \\\\times (... | 9177efbdceb2c6d3585fa1de81c78225fbf88132fb0ae87fe539a216301a3389 | a3d20e36b20880d64b880d4378e3aea9de8a3687a302888a392e88997a29b20f | 8527a891e224136950ff32ca212b45bc93f69fbb801c3b1ebedac52775f99e61 | 0 | [false] | samples_countdown_2025-06-06T02-10-35.135228.jsonl | ["To solve the problem \\( 6 \\times 22 \\) using step-by-step reasoning, we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 6 \\times (20 + 2) = 6 \\times 20 + 6 \\times 2\n \\]... | [{"budget_forced_chunks": ["To solve the problem \\( 6 \\times 22 \\) using step-by-step reasoning, we can break it down into simpler steps:\n\n1. **Break down the multiplication:**\n \\[\n 6 \\times 22 = 6 \\times (20 + 2)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 6 \\times (20 + 2) = 6 \\time... | null |
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