question string | solution string | model_responses list |
|---|---|---|
What is the solution to the long multiplication equation below?
768 x 947
Think step by step. | 727296 | [
"To solve the long multiplication equation \\(768 \\times 947\\), we can break it down into a series of simpler steps:\n\n1. **Multiply 768 by 7 (the units digit of 947):**\n \\[\n 768 \\times 7 = 532\n \\]\n\n2. **Multiply 768 by 9 (the tens digit of 947, which is also 90):**\n \\[\n 768 \\times 90 = 768... |
What is the solution to the long multiplication equation below?
443 x 301
Think step by step. | 133343 | [
"To solve the long multiplication equation \\(443 \\times 301\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 443 \\\\\n \\times 301 \\\\\n \\end{array}\n \\]\n\n2. **Break down the multiplication into smaller steps:**\n \\[\n 443 \\times 301 = 443 ... |
What is the solution to the long multiplication equation below?
829 x 577
Think step by step. | 478333 | [
"To solve the long multiplication problem \\( 829 \\times 577 \\), we'll follow these steps:\n\n1. **Set up the multiplication:**\n\n \\[\n \\begin{array}{r}\n 829 \\\\\n \\times 577 \\\\\n \\end{array}\n \\]\n\n2. **Break down each number into its tens and units:**\n\n - \\( 829 \\) can be written ... |
What is the solution to the long multiplication equation below?
312 x 571
Think step by step. | 178152 | [
"To solve the long multiplication equation \\( 312 \\times 571 \\), we'll follow the steps of traditional long multiplication. Let’s break it down step by step:\n\n1. **Multiply the units digit of the dividend by the units digit of the multiplier:**\n\n\\[\n312 \\times 1 = 312\n\\]\n\n2. **Multiply the units digit ... |
What is the solution to the long multiplication equation below?
425 x 503
Think step by step. | 213775 | [
"To solve the long multiplication of 425 and 503, follow these steps:\n\n1. **Multiply 425 by 3 (the ones digit of 503):**\n \\[\n 425 \\times 3 = 1275\n \\]\n\n2. **Multiply 425 by 50 (the tens digit of 503, considering it as 5 * 10):**\n \\[\n 425 \\times 50 = 425 \\times (5 \\times 10) = (425 \\times 5... |
What is the solution to the long multiplication equation below?
508 x 466
Think step by step. | 236728 | [
"To solve the long multiplication equation \\(508 \\times 466\\), we'll follow these steps:\n\n1. **Set up the multiplication**: Write down the numbers, aligning the digits by place value.\n ```\n 508\n × 466\n ------\n ```\n\n2. **Multiply the digits**: Multiply 508 by 6 (the units digit of 466)... |
What is the solution to the long multiplication equation below?
202 x 207
Think step by step. | 41814 | [
"To solve the long multiplication of 202 and 207, follow these steps:\n\n1. **Multiply the units digits**: Multiply 2 by 7, which equals 14. Write down 4 and carry over 1.\n2. **Multiply the tens digits and add the carry**: Multiply 2 by 20 (which is the same as multiplying by 2 and then adding a zero at the end), ... |
What is the solution to the long multiplication equation below?
683 x 776
Think step by step. | 530008 | [
"To solve the long multiplication problem \\(683 \\times 776\\), follow these steps:\n\n1. **Set up the multiplication**: Write the numbers 683 and 776 aligned one below the other, like this:\n```\n 683\n × 776\n```\n\n2. **Multiply 683 by 6 (the ones digit of 776)**:\n - Multiply 683 by 6: \n \\[\n ... |
What is the solution to the long multiplication equation below?
566 x 156
Think step by step. | 88296 | [
"To solve the long multiplication of 566 and 156, we'll break it down into simpler steps.\n\nStep 1: Multiply 566 by 6 (the units digit of 156).\n566 x 6 = 3396\n\nStep 2: Multiply 566 by 10 (the tens digit of 156, which is just 1, but we'll count it as 10 for the multiplication).\n566 x 10 = 5660\n\nStep 3: Add th... |
What is the solution to the long multiplication equation below?
948 x 323
Think step by step. | 306204 | [
"To solve the multiplication problem \\(948 \\times 323\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep-by-step solution:\n\n1. **Break down the numbers:**\n - \\(948\\) can be written as \\(900 + 48\\).\n - \\(323\\) can be written as \\(300 ... |
What is the solution to the long multiplication equation below?
623 x 209
Think step by step. | 130207 | [
"To solve the long multiplication problem \\(623 \\times 209\\), we'll follow these steps:\n\n1. **Set up the multiplication**:\n \\[\n \\begin{array}{c@{}c@{}c}\n & 6 & 2 & 3 \\\\\n \\times & 2 & 0 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 623 by 9 (the units digit of 209)**:\n \\[\n 623 \\t... |
What is the solution to the long multiplication equation below?
512 x 562
Think step by step. | 287744 | [
"To solve the multiplication problem \\(512 \\times 562\\), we'll break it down step by step:\n\n1. **Break it into smaller parts**:\n - \\(512 \\times 562 = 512 \\times (500 + 62) = (512 \\times 500) + (512 \\times 62)\\)\n\n2. **Calculate \\(512 \\times 500\\)**:\n - \\(512 \\times 500 = 512 \\times (5 \\time... |
What is the solution to the long multiplication equation below?
169 x 610
Think step by step. | 103090 | [
"To solve the long multiplication equation \\(169 \\times 610\\), follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 169 \\\\\n \\times 610 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 169 by 0 (the units digit of 610):**\n \\[\n 169 \\times 0 = 0\n \\]\... |
What is the solution to the long multiplication equation below?
171 x 446
Think step by step. | 76266 | [
"To solve the long multiplication equation \\( 171 \\times 446 \\), we will follow the standard method of long multiplication, which involves multiplying each digit of the first number by each digit of the second number, then adding the results.\n\nLet's break it down step by step:\n\n1. **Multiply 171 by 6 (the un... |
What is the solution to the long multiplication equation below?
134 x 928
Think step by step. | 124352 | [
"To solve the long multiplication equation \\(134 \\times 928\\), we can break it down into simpler steps:\n\n1. **Multiply 134 by 8:**\n \\[\n 134 \\times 8 = 1072\n \\]\n\n2. **Multiply 134 by 90 (which is 9 \\times 10):**\n \\[\n 134 \\times 90 = 134 \\times (9 \\times 10) = (134 \\times 9) \\times 10\... |
What is the solution to the long multiplication equation below?
854 x 755
Think step by step. | 644770 | [
"To solve the multiplication problem \\( 854 \\times 755 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep-by-step solution:\n\n1. **Break down the numbers:**\n \\[\n 854 = 800 + 54\n \\]\n \\[\n 755 = 700 + 55\n \\]\n\n2. **Apply the d... |
What is the solution to the long multiplication equation below?
610 x 462
Think step by step. | 281820 | [
"To solve the long multiplication of 610 and 462, we will break it down into simpler steps.\n\n1. **Multiply 610 by 2 (the ones place of 462):**\n \\[\n 610 \\times 2 = 1220\n \\]\n\n2. **Multiply 610 by 40 (the tens place of 462, which is the same as 4 \\times 10 times 10):**\n \\[\n 610 \\times 40 = 244... |
What is the solution to the long multiplication equation below?
154 x 371
Think step by step. | 57134 | [
"To solve the long multiplication equation \\( 154 \\times 371 \\), we'll break it down into a series of steps:\n\n### Step 1: Multiply 154 by 1 (the units digit of 371)\n\\[ 154 \\times 1 = 154 \\]\n\n### Step 2: Multiply 154 by 7 (the tens digit of 371)\n\\[ 154 \\times 7 = 1078 \\]\n(Think: Multiply 154 by 7; it... |
What is the solution to the long multiplication equation below?
797 x 489
Think step by step. | 389733 | [
"To solve the multiplication problem \\( 797 \\times 489 \\), we'll follow these steps:\n\n1. **Break it down into smaller parts**:\n - First, let's split 489 into 400 and 89.\n - This gives us two multiplication problems: \\( 797 \\times 400 \\) and \\( 797 \\times 89 \\).\n\n2. **Calculate each part separatel... |
What is the solution to the long multiplication equation below?
553 x 192
Think step by step. | 106176 | [
"To solve the long multiplication of 553 x 192, we can break it down into smaller steps:\n\n1. Multiply 553 by 2 (the ones place of 192):\n \\boxed{1106}\n\n2. Multiply 553 by 10 (the tens place of 192, which is the same as multiplying by 1 and then adding a zero at the end):\n \\boxed{5530}\n\n3. Add the two r... |
What is the solution to the long multiplication equation below?
576 x 498
Think step by step. | 286848 | [
"To solve the multiplication problem \\(576 \\times 498\\), we will use the standard algorithm for multiplication.\n\nStep-by-step:\n\n1. **Multiply 576 by 8 (the units digit of 498):**\n \\[\n 576 \\times 8 = 4596\n \\]\n\n2. **Multiply 576 by 4 (the tens digit of 498), and place the result two places to the... |
What is the solution to the long multiplication equation below?
793 x 208
Think step by step. | 164944 | [
"To solve the long multiplication equation \\( 793 \\times 208 \\), we'll break it down into a series of simpler steps:\n\n### Step 1: Multiply by the ones place\nFirst, we'll calculate \\( 793 \\times 8 \\).\n\n\\[\n793 \\times 8 = 6344\n\\]\n\n### Step 2: Multiply by the tens place\nNext, multiply \\( 793 \\) by ... |
What is the solution to the long multiplication equation below?
122 x 951
Think step by step. | 116022 | [
"To solve the long multiplication equation \\(122 \\times 951\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 122 \\\\\n \\times 951 \\\\\n \\end{array}\n \\]\n\n2. **Break down each number into its tens and units:**\n - \\(122\\) can be written as \\... |
What is the solution to the long multiplication equation below?
311 x 897
Think step by step. | 278967 | [
"To solve the multiplication problem \\( 311 \\times 897 \\), we will use the standard algorithm for multiplication. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 311 \\\\\n \\times 897 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 311 by 7 (the units di... |
What is the solution to the long multiplication equation below?
319 x 283
Think step by step. | 90277 | [
"To solve the long multiplication equation \\( 319 \\times 283 \\), follow these steps:\n\n1. **Break down the multiplication**: \n - Multiply 319 by 80 (the tens digit of 283) and then multiply 319 by 3 (the ones digit of 283).\n\n2. **Calculate \\( 319 \\times 80 \\)**:\n - \\( 319 \\times 80 = 319 \\times 8 ... |
What is the solution to the long multiplication equation below?
955 x 312
Think step by step. | 297960 | [
"To solve the long multiplication equation \\(955 \\times 312\\), we can break it down into simpler steps:\n\n1. **Multiply 955 by 1**: \n \\[\n 955 \\times 1 = 955\n \\]\n\n2. **Multiply 955 by 3 (which is the same as multiplying by 3 and then adding a zero at the end)**:\n \\[\n 955 \\times 3 = 2865\n ... |
What is the solution to the long multiplication equation below?
805 x 747
Think step by step. | 601335 | [
"To solve the long multiplication of 805 and 747, follow these steps:\n\n1. **Set up the multiplication:**\n ```\n 805\n x 747\n ```\n\n2. **Multiply 805 by 7 (the ones digit of 747):**\n ```\n 805\n x 7\n ______\n 5635\n ```\n\n3. **Multiply 805 by 4 (the tens digit of 747), and shi... |
What is the solution to the long multiplication equation below?
189 x 937
Think step by step. | 177093 | [
"To solve the long multiplication equation \\(189 \\times 937\\), follow these steps:\n\n1. **Break down the numbers**:\n - 189 can be broken into 100 - 1\n - 937 can be broken into 1000 - 637\n\n2. **Set up the multiplication**:\n \\[\n \\begin{array}{r}\n 100 - 1 \\\\\n \\times 1000 - 637 \\\\\n \\h... |
What is the solution to the long multiplication equation below?
264 x 606
Think step by step. | 159984 | [
"To solve the long multiplication equation \\(264 \\times 606\\), we will follow the standard algorithm for multiplication. Here are the steps:\n\n1. **Set up the multiplication**: Write the numbers side by side, aligning the digits by place value.\n ```\n 264\n × 606\n ------\n ```\n\n2. **Multi... |
What is the solution to the long multiplication equation below?
732 x 520
Think step by step. | 380640 | [
"To solve the long multiplication problem \\(732 \\times 520\\), let's break it down step by step.\n\n### Step 1: Set up the multiplication\nFirst, write the numbers one under the other:\n\\[\n\\begin{array}{r}\n 732 \\\\\n\\times 520 \\\\\n\\hline\n\\end{array}\n\\]\n\n### Step 2: Multiply 732 by 0\nLook at ... |
What is the solution to the long multiplication equation below?
493 x 471
Think step by step. | 232203 | [
"To solve the long multiplication equation \\( 493 \\times 471 \\), we'll follow these steps:\n\n1. **Break it down into simpler steps:**\n \\[\n 493 \\times 471 = 493 \\times (400 + 71)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 493 \\times (400 + 71) = 493 \\times 400 + 493 \\times 71\n ... |
What is the solution to the long multiplication equation below?
866 x 974
Think step by step. | 843484 | [
"To solve the long multiplication of 866 and 974, follow these steps:\n\n1. **Set up the multiplication**:\n ```\n 866\n x 974\n ```\n\n2. **Multiply 866 by 4 (the ones digit of 974)**:\n ```\n 866\n x 4\n ```\n - 4 x 6 = 24 (write down 4 and carry 2)\n - 4 x 8 = 32, plus the carried 2 ... |
What is the solution to the long multiplication equation below?
107 x 536
Think step by step. | 57352 | [
"To solve the long multiplication equation \\(107 \\times 536\\), we can break it down into simpler steps:\n\n1. **Multiply 107 by 6 (the units digit of 536):**\n \\[\n 107 \\times 6 = 642\n \\]\n\n2. **Multiply 107 by 50 (the tens digit of 536, which is 5 with a zero appended):**\n \\[\n 107 \\times 50 =... |
What is the solution to the long multiplication equation below?
677 x 139
Think step by step. | 94103 | [
"To solve the long multiplication equation \\(677 \\times 139\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 6 & 7 & 7 \\\\\n \\times & 1 & 3 & 9 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 677 by 9:**\n \\[\n 677 \\times 9 = 6033\n \\]\... |
What is the solution to the long multiplication equation below?
343 x 656
Think step by step. | 225008 | [
"To solve the long multiplication of 343 and 656, we'll break it down into four steps as follows:\n\n### Step 1: Multiply the units (units are digit values in ones place) \n- The units digit of 343 is 3. \n- The units digit of 656 is 6.\n\nSo, multiply 3 by 6:\n\\[ 3 \\times 6 = 18 \\]\n\n### Step 2: Multiply the t... |
What is the solution to the long multiplication equation below?
394 x 496
Think step by step. | 195424 | [
"To solve the multiplication problem \\(394 \\times 496\\), we can use the standard multiplication method. Let's break it down step by step:\n\n1. **Write down the numbers to be multiplied:**\n \\[\n 394 \\quad \\text{and} \\quad 496\n \\]\n\n2. **Multiply each digit of the first number by each digit of the s... |
What is the solution to the long multiplication equation below?
832 x 494
Think step by step. | 411008 | [
"To solve the long multiplication of 832 and 494, we will break it down into smaller steps and then combine the results at the end.\n\nStep 1: Multiply 832 by 4 (the ones digit of 494).\n832 × 4 = 332\n\nStep 2: Multiply 832 by 90 (the tens digit of 494, written as hundreds).\n832 × 90 = 7440\n\nStep 3: Add the res... |
What is the solution to the long multiplication equation below?
926 x 310
Think step by step. | 287060 | [
"To solve the long multiplication equation \\( 926 \\times 310 \\), follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 926 \\\\\n \\times 310 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 926 by 0 (the units digit of 310):**\n \\[\n 926 \\times 0 = 0\n ... |
What is the solution to the long multiplication equation below?
882 x 125
Think step by step. | 110250 | [
"To solve the long multiplication equation \\(882 \\times 125\\), we can break it down into simpler steps:\n\n1. **Multiply 882 by 5**: This is the easiest part because 5 is a simple number. So, \\(882 \\times 5 = 4410\\).\n\n2. **Multiply 882 by 10**: To do this, you can think of it as adding a zero to the end of ... |
What is the solution to the long multiplication equation below?
544 x 260
Think step by step. | 141440 | [
"To solve the long multiplication equation \\(544 \\times 260\\), we will follow the standard method of long multiplication. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 544 \\\\\n \\times 260 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 544 by 0 (the units digit ... |
What is the solution to the long multiplication equation below?
227 x 353
Think step by step. | 80131 | [
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What is the solution to the long multiplication equation below?
462 x 892
Think step by step. | 412104 | [
"To solve the multiplication problem \\( 462 \\times 892 \\), we'll follow these steps:\n\n1. **Break it down into smaller parts**: Instead of multiplying them big numbers at once, which can be risky, we'll break them into smaller parts.\n2. **Use the distributive property**: We can split 892 into 800 + 92.\n3. **M... |
What is the solution to the long multiplication equation below?
472 x 293
Think step by step. | 138296 | [
"To solve the long multiplication equation \\(472 \\times 293\\), we will break it down step by step:\n\n### Step 1: Break down the numbers\nFirst, we break down the numbers into more manageable parts:\n- \\(472\\) can be written as \\(400 + 72\\)\n- \\(293\\) can be written as \\(200 + 93\\)\n\n### Step 2: Multipl... |
What is the solution to the long multiplication equation below?
529 x 999
Think step by step. | 528471 | [
"To solve the multiplication problem \\(529 \\times 999\\), we can use several methods, including the standard algorithm or the partial product method (also called the standard algorithm).\n\n**Method 1: Standard Algorithm**\n\nFirst, we write the numbers vertically and align them:\n\n\\[\n\\begin{array}{r}\n 529 ... |
What is the solution to the long multiplication equation below?
517 x 595
Think step by step. | 307615 | [
"To solve the long multiplication equation \\(517 \\times 595\\), follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 517 \\\\\n \\times 595 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 517 by 5 (the units digit of 595):**\n \\[\n 517 \\times 5 = 2585\n ... |
What is the solution to the long multiplication equation below?
933 x 451
Think step by step. | 420783 | [
"To solve the multiplication problem \\( 933 \\times 451 \\), we will follow these steps:\n\n1. **Break down the numbers:**\n \\[\n 933 = 900 + 33\n \\]\n \\[\n 451 = 400 + 51\n \\]\n\n2. **Use the distributive property of multiplication:**\n \\[\n 933 \\times 451 = (900 + 33) \\times (400 + 51)\n ... |
What is the solution to the long multiplication equation below?
599 x 261
Think step by step. | 156339 | [
"To solve the long multiplication equation \\( 599 \\times 261 \\), we'll follow the steps of standard long multiplication method. Let's break it down step by step:\n\n1. **Multiply the units digit of the dividend by the units digit of the multiplier:**\n\n\\[\n599 \\times 1 = 599\n\\]\n\n2. **Multiply the units di... |
What is the solution to the long multiplication equation below?
199 x 854
Think step by step. | 169946 | [
"To solve the long multiplication equation \\(199 \\times 854\\), follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 199 \\\\\n \\times 854 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 199 by 4 (the units digit of 854):**\n \\[\n 199 \\times 4 = 796\n \\... |
What is the solution to the long multiplication equation below?
776 x 854
Think step by step. | 662704 | [
"To solve the multiplication equation \\( 776 \\times 854 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nFirst, let's expand the multiplication:\n\\[ 776 \\times 854 = 776 \\times (800 + 54) \\]\n\nWe can further expand this to:\n\\[ 776 \\times (800... |
What is the solution to the long multiplication equation below?
130 x 623
Think step by step. | 80990 | [
"To solve the long multiplication equation \\(130 \\times 623\\), we can break it down into simpler steps. Here's a step-by-step solution:\n\n1. **Break down the numbers:**\n - \\(130\\) can be thought of as \\(10 + 30\\).\n - \\(623\\) can be thought of as \\(600 + 23\\).\n\n2. **Multiply each part separately:... |
What is the solution to the long multiplication equation below?
636 x 733
Think step by step. | 466188 | [
"To solve the long multiplication problem \\(636 \\times 733\\), follow these steps:\n\n1. **Set up the multiplication**: Write the numbers side by side, aligning the digits by place value.\n ```\n 636\n × 733\n ------\n ```\n\n2. **Multiply the numbers (ignore the decimal points for now)**:\n ... |
What is the solution to the long multiplication equation below?
155 x 268
Think step by step. | 41540 | [
"To solve the long multiplication equation \\(155 \\times 268\\), we will follow the standard long multiplication method.\n\nStep 1: Set up the multiplication as follows:\n```\n 155\n × 268\n ----\n```\nStep 2: Multiply 155 by 8 (the units digit of 268).\n```\n 155\n × 268\n ----\n 1240 (155 × 8)... |
What is the solution to the long multiplication equation below?
608 x 722
Think step by step. | 438976 | [
"To solve the long multiplication equation \\(608 \\times 722\\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 608 \\\\\n \\times & 722 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 608 by 2 (the units digit of 722):**\n \\[\n 608 \\times 2 = ... |
What is the solution to the long multiplication equation below?
548 x 803
Think step by step. | 440044 | [
"To solve the long multiplication equation \\(548 \\times 803\\), we can break it down into a series of simpler steps:\n\n1. **Multiply 548 by 3:**\n \\[\n 548 \\times 3 = 1644\n \\]\n\n2. **Multiply 548 by 80 (which is the same as multiplying by 8 and then adding a zero):**\n \\[\n 548 \\times 8 = 4320\n... |
What is the solution to the long multiplication equation below?
339 x 101
Think step by step. | 34239 | [
"To solve the long multiplication equation \\(339 \\times 101\\), we will break it down into simpler steps.\n\n1. **Multiply 339 by 1:**\n \\[\n 339 \\times 1 = 339\n \\]\n\n2. **Multiply 339 by 0 (systematic error):**\n \\[\n 339 \\times 0 = 0\n \\]\n\n3. **Add the results from steps 1 and 2:**\n \\[... |
What is the solution to the long multiplication equation below?
305 x 298
Think step by step. | 90890 | [
"To solve the long multiplication problem \\(305 \\times 298\\), we'll follow these steps:\n\n1. **Set up the multiplication**: Write the numbers one under the other, aligning the digits by place value.\n ```\n 305\n x 298\n ----\n ```\n\n2. **Multiply 305 by 8 (the units digit of 298)**:\n \\[\n ... |
What is the solution to the long multiplication equation below?
472 x 303
Think step by step. | 143016 | [
"To solve the long multiplication equation \\(472 \\times 303\\), let's break it down step by step:\n\n1. First, let's multiply the numbers individually:\n - \\(472 \\times 3 = 1416\\)\n - \\(472 \\times 0 = 0\\)\n - \\(472 \\times 30 = 14160\\)\n\n2. Now, add these results together:\n \\[\n 1416 + 0 + 14... |
What is the solution to the long multiplication equation below?
322 x 398
Think step by step. | 128156 | [
"To solve the multiplication problem \\(322 \\times 398\\), we can use the distributive property of multiplication over addition, which is a common method for solving this kind of problem. Here are the steps:\n\n1. Write out the original problem: \\(322 \\times 398\\).\n\n2. Break it down into simpler parts:\n - ... |
What is the solution to the long multiplication equation below?
984 x 103
Think step by step. | 101352 | [
"To solve the long multiplication problem \\(984 \\times 103\\), we can break it down into simpler steps:\n\n1. **Multiply 984 by 3 (the units digit of 103):**\n \\[\n 984 \\times 3 = 2952\n \\]\n\n2. **Multiply 984 by 10 (the tens digit of 103, which is the same as multiplying by 1 and then adding a zero at ... |
What is the solution to the long multiplication equation below?
931 x 484
Think step by step. | 450604 | [
"To solve the long multiplication equation \\( 931 \\times 484 \\), we'll follow the standard cordinate method of long multiplication. Here are the steps:\n\n1. **Break down the numbers:**\n - \\( 931 \\) can be broken down into \\( 900 + 31 \\).\n - \\( 484 \\) can be broken down into \\( 400 + 84 \\).\n\n2. *... |
What is the solution to the long multiplication equation below?
250 x 549
Think step by step. | 137250 | [
"To solve the long multiplication equation \\( 250 \\times 549 \\), we will break it down step by step. \n\n### Step 1: Break down 250 into its component values.\n- \\( 250 = 200 + 50 \\)\n\n### Step 2: Multiplying 200 by 549.\n- First, find 200 and 549:\n - \\( 200 \\times 549 \\)\n \n To make this easier, you ... |
What is the solution to the long multiplication equation below?
948 x 412
Think step by step. | 390576 | [
"To solve the multiplication problem \\( 948 \\times 412 \\), we will follow the standard method of long multiplication. Here are the steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 948 \\\\\n \\times 412 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 948 by 2 (the ones... |
What is the solution to the long multiplication equation below?
948 x 146
Think step by step. | 138408 | [
"To solve the long multiplication equation \\( 948 \\times 146 \\), we'll follow the standard long multiplication method step by step. Here's the process:\n\n1. **Set up the problem:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 4 & 8 \\\\\n \\times & 1 & 4 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Multiply... |
What is the solution to the long multiplication equation below?
148 x 472
Think step by step. | 69856 | [
"To solve the multiplication equation \\(148 \\times 472\\), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's the step-by-step process:\n\n1. **Write out the original problem:** \\(148 \\times 472\\).\n\n2. **Break down the numbers into parts:** We can ... |
What is the solution to the long multiplication equation below?
237 x 202
Think step by step. | 47874 | [
"To solve the long multiplication equation \\(237 \\times 202\\), we can follow these steps:\n\n1. **Set up the multiplication as a standard example:**\n \\[\n \\begin{array}{r}\n 237 \\\\\n \\times 202 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 237 by 2 (the units digit of 202):**\n \\[... |
What is the solution to the long multiplication equation below?
602 x 453
Think step by step. | 272706 | [
"To solve the long multiplication equation \\(602 \\times 453\\), we will follow the standard method of long multiplication, which involves multiplying each digit of the first number (602) by each digit of the second number (453), from right to left, and then adding the results.\n\nLet's break it down step by step:... |
What is the solution to the long multiplication equation below?
935 x 253
Think step by step. | 236555 | [
"To solve the multiplication equation \\(935 \\times 253\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep by step:\n\n1. **Write out the numbers:**\n \\[\n 935 \\times 253 = 935 \\times (200 + 3)\n \\]\n \n2. **Distribute** the multiplicati... |
What is the solution to the long multiplication equation below?
924 x 368
Think step by step. | 340032 | [
"To solve the long multiplication problem \\(924 \\times 368\\), we'll follow these steps:\n\n1. **Set up the multiplication**: We'll break it into smaller parts, which makes it easier to manage.\n\n\\[\n\\begin{array}{r}\n 924 \\\\\n\\times 368 \\\\\n\\hline\n\\end{array}\n\\]\n\n2. **Multiply 924 by 8 (the units... |
What is the solution to the long multiplication equation below?
804 x 854
Think step by step. | 686616 | [
"To solve the multiplication problem \\( 804 \\times 854 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep-by-step solution:\n\n1. **Break down the numbers:**\n - \\( 804 \\) can be written as \\( 800 + 4 \\).\n - \\( 854 \\) can be written as ... |
What is the solution to the long multiplication equation below?
967 x 666
Think step by step. | 644022 | [
"To solve the long multiplication problem \\( 967 \\times 666 \\), we will follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{c@{}c@{}c}\n & 9 & 6 & 7 \\\\\n \\times & 6 & 6 & 6 \\\\\n \\end{array}\n \\]\n\n2. **Multiply 967 by 666:**\n - First, multiply 967 by the ones ... |
What is the solution to the long multiplication equation below?
178 x 180
Think step by step. | 32040 | [
"To solve the multiplication problem \\(178 \\times 180\\), we can use the standard multiplication method. Let's break it down step by step:\n\n1. First, note that when multiplying by 180, we can use the distributive property of multiplication over addition:\n \\[\n 178 \\times 180 = 178 \\times (10 + 80)\n \... |
What is the solution to the long multiplication equation below?
626 x 503
Think step by step. | 314878 | [
"To solve the long multiplication problem \\(626 \\times 503\\), we'll follow these steps:\n\n1. **Set up the multiplication**: We'll break it into smaller parts, which makes it easier to handle.\n\n\\[\n626 \\times 503 = 626 \\times (500 + 3)\n\\]\n\n2. **Use the distributive property**: Distribute the multiplicat... |
What is the solution to the long multiplication equation below?
356 x 893
Think step by step. | 317908 | [
"To solve the long multiplication equation \\( 356 \\times 893 \\), we'll follow the steps of multiplication algorithm, focusing on each digit of both numbers.\n\n### Step-by-Step Solution:\n\n1. **Multiply 356 by 3 (the units digit of 893):**\n \\[\n 356 \\times 3 = 106\n \\]\n\n2. **Multiply 356 by 8 (the t... |
What is the solution to the long multiplication equation below?
445 x 414
Think step by step. | 184230 | [
"To solve the long multiplication equation \\(445 \\times 414\\), follow these steps:\n\n1. **Break down the numbers**: \n - 445 can be written as \\(400 + 45\\).\n - 414 can be written as \\(400 + 14\\).\n\n2. **Multiply each part of the first number by each part of the second number**:\n - \\(400 \\times 40... |
What is the solution to the long multiplication equation below?
756 x 305
Think step by step. | 230580 | [
"To solve the long multiplication equation \\( 756 \\times 305 \\), we'll follow the steps of multiplication and then carry over any results:\n\n1. **Multiply 756 by 5 (the units digit of 305):**\n \\[\n 756 \\times 5 = 3780\n \\]\n\n2. **Multiply 756 by 3 (the tens digit of 305) and shift one place to the le... |
What is the solution to the long multiplication equation below?
422 x 557
Think step by step. | 235054 | [
"To solve the multiplication problem \\( 422 \\times 557 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep-by-step solution:\n\n1. **Break down the numbers:**\n - \\( 422 \\) can be written as \\( 400 + 22 \\).\n - \\( 557 \\) can be written as... |
What is the solution to the long multiplication equation below?
489 x 535
Think step by step. | 261615 | [
"To solve the long multiplication equation \\(489 \\times 535\\), follow these steps:\n\n1. **Break down the multiplication**: \n - Multiply 489 by 5 (the first digit of 535), and then multiply 489 by 30 (the tens digit of 535, multiplied by 10).\n\n2. **First multiplication**:\n - \\(489 \\times 5 = 2445\\).\n... |
What is the solution to the long multiplication equation below?
373 x 936
Think step by step. | 349128 | [
"To solve the multiplication problem \\(373 \\times 936\\), we can break it down into simpler steps:\n\n1. **Multiply 373 by 6 (the units digit of 936):**\n \\[\n 373 \\times 6 = 2238\n \\]\n\n2. **Multiply 373 by 90 (the tens digit of 936, which is 9 times 10):**\n \\[\n 373 \\times 90 = 3357\n \\]\n\n... |
What is the solution to the long multiplication equation below?
503 x 824
Think step by step. | 414472 | [
"To solve the multiplication problem \\( 503 \\times 824 \\), we'll break it down step by step:\n\n1. **Break it into smaller parts**:\n - Let's start with the tens digit of 503 and the tens digit of 824.\n - The tens digit of 503 is 5, and the tens digit of 824 is 8.\n\n2. **Multiply 5 by 8**:\n - This is:\n... |
What is the solution to the long multiplication equation below?
602 x 635
Think step by step. | 382270 | [
"To solve the long multiplication equation \\(602 \\times 635\\), we can break it down into simpler steps:\n\n1. **Multiply 602 by 35:**\n - First, multiply 602 by 5:\n \\[\n 602 \\times 5 = 3010\n \\]\n - Next, multiply 602 by 30 (which is the same as multiplying by 3 and then adding a zero):\n ... |
What is the solution to the long multiplication equation below?
369 x 631
Think step by step. | 232839 | [
"To solve the long multiplication equation \\(369 \\times 631\\), we will follow these steps:\n\n1. **Break down the problem using the distributive property of multiplication:**\n \\[\n 369 \\times 631 = 369 \\times (600 + 31)\n \\]\n\n2. **Apply the distributive property:**\n \\[\n 369 \\times 600 + 369 ... |
What is the solution to the long multiplication equation below?
245 x 950
Think step by step. | 232750 | [
"To solve the long multiplication equation \\(245 \\times 950\\), we can break it down into simpler steps.\n\n1. **Break down the numbers:**\n - \\(245\\) can be thought of as \\(200 + 45\\).\n - \\(950\\) can be thought of as \\(1000 - 50\\).\n\n2. **Multiply the numbers in the tens place:**\n - Multiply \\(... |
What is the solution to the long multiplication equation below?
495 x 890
Think step by step. | 440550 | [
"To solve the long multiplication equation \\(495 \\times 890\\), follow these steps:\n\n1. **Set up the multiplication:**\n \\[\n \\begin{array}{r}\n 495 \\\\\n \\times 890 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 495 by 0 (the units digit of 890):**\n \\[\n 495 \\times 0 = 0\n \\... |
What is the solution to the long multiplication equation below?
964 x 550
Think step by step. | 530200 | [
"To solve the long multiplication problem \\( 964 \\times 550 \\), follow these steps:\n\n1. **Write the numbers in a column format**:\n ```\n 964\n x 550\n ```\n\n2. **Multiply each digit of the bottom number by the top number**:\n - Multiply 5 by 4:\n \\[\n 5 \\times 4 = 20\n \\]\n W... |
What is the solution to the long multiplication equation below?
351 x 562
Think step by step. | 197262 | [
"To solve the long multiplication equation \\(351 \\times 562\\), we will break it down into a series of simpler multiplications. Here's the step-by-step process:\n\n1. Multiply 351 by 2 (the units digit of 562):\n \\[\n 351 \\times 2 = 702\n \\]\n\n2. Multiply 351 by 50 (the tens digit of 562, which is the s... |
What is the solution to the long multiplication equation below?
428 x 478
Think step by step. | 204584 | [
"To solve the multiplication problem \\(428 \\times 478\\), we will use the standard algorithm for multiplication. Here are the steps:\n\n1. **Multiply 428 by 8 (the units digit of 478):**\n \\[\n 428 \\times 8 = 3424\n \\]\n\n2. **Multiply 428 by 4 (the tens digit of 478), and remember to shift one place to ... |
What is the solution to the long multiplication equation below?
963 x 403
Think step by step. | 388089 | [
"To solve the multiplication \\( 963 \\times 403 \\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep-by-step solution:\n\n1. **Write the numbers in a convenient format**:\n \\[\n 963 \\times 403 = 963 \\times (4 \\times 101)\n \\]\n\n2. **Break... |
What is the solution to the long multiplication equation below?
668 x 371
Think step by step. | 247828 | [
"To solve the long multiplication equation \\( 668 \\times 371 \\), we'll follow the standard method of long multiplication, which involves multiplying each digit of the first number by each digit of the second number, then adding the results.\n\nLet's break it down step by step:\n\n1. **Multiply 668 by 1 (the unit... |
What is the solution to the long multiplication equation below?
127 x 374
Think step by step. | 47498 | [
"To solve the long multiplication equation \\(127 \\times 374\\), we can break it down into simpler steps:\n\n1. **Multiply 127 by 4 (the units digit of 374):**\n \\[\n 127 \\times 4 = 508\n \\]\n\n2. **Multiply 127 by 30 (the tens digit of 374, which is 30):**\n \\[\n 127 \\times 30 = 3810\n \\]\n\n3. ... |
What is the solution to the long multiplication equation below?
829 x 416
Think step by step. | 344864 | [
"To solve the long multiplication of 829 and 416, follow these steps:\n\n1. **Multiply the ones place of 829 by each digit in 416:**\n\n - \\( 9 \\times 6 = 54 \\)\n - \\( 9 \\times 1 = 9 \\)\n\n2. **Write the results vertically:**\n\n \\[\n \\begin{array}{r}\n 829 \\\\\n \\times \\ 416 \\\\\n \\hli... |
What is the solution to the long multiplication equation below?
776 x 205
Think step by step. | 159080 | [
"To solve the long multiplication problem \\( 776 \\times 205 \\), we will follow the standard method of long multiplication:\n\n1. **Set up the multiplication:**\n ```\n 776\n × 205\n ```\n\n2. **Multiply 776 by 5:**\n ```\n 776\n × 205\n ------\n 3830 (776 × 5)\n ```\n\n3. **M... |
What is the solution to the long multiplication equation below?
636 x 360
Think step by step. | 228960 | [
"To solve the long multiplication problem \\(636 \\times 360\\), let's break it down step by step:\n\n1. First, let's write the numbers in a column format, aligning the digits by their place values.\n \n \\[\n \\begin{array}{r}\n 636 \\\\\n \\times 360 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. Now, ... |
What is the solution to the long multiplication equation below?
883 x 970
Think step by step. | 856510 | [
"To solve the long multiplication equation \\(883 \\times 970\\), follow these steps:\n\n1. **Break down the numbers:**\n - \\(883\\) can be broken down into \\(800 + 83\\).\n - \\(970\\) can be broken down into \\(900 + 70\\).\n\n2. **Multiply each part of \\(883\\) by each part of \\(970\\):**\n - \\(800 \\... |
What is the solution to the long multiplication equation below?
682 x 458
Think step by step. | 312356 | [
"To solve the multiplication problem \\(682 \\times 458\\), we can break it down into simpler steps.\n\n### Step 1: Break down the multiplication\nWe can think of \\(682\\) as \\(600 + 82\\) and \\(458\\) as \\(400 + 58\\). This is called the distributive property of multiplication over addition.\n\n### Step 2: Mul... |
What is the solution to the long multiplication equation below?
967 x 333
Think step by step. | 322011 | [
"To solve the multiplication equation \\(967 \\times 333\\), we can break it down into simpler steps using the distributive property of multiplication over addition.\n\nStep by step:\n\n1. **Write out the multiplication:**\n \\[\n 967 \\times 333\n \\]\n\n2. **Break it into parts:**\n We can split 333 into ... |
What is the solution to the long multiplication equation below?
234 x 392
Think step by step. | 91728 | [
"To solve the multiplication equation 234 x 392, we will follow the standard long multiplication method. \n\nStep 1: Multiply 234 by 2 (the ones place of 392).\n234 x 2 = 468\n\nStep 2: Multiply 234 by 30 (the tens place of 392, before the 2).\n234 x 30 = 7020\n\nStep 3: Add the two results from Step 1 and Step 2.\... |
What is the solution to the long multiplication equation below?
547 x 293
Think step by step. | 160271 | [
"To solve the long multiplication equation \\(547 \\times 293\\), we will follow the standard method of long multiplication, which involves multiplying each digit of the first number by each digit of the second number, then adding the results.\n\nHere are the steps:\n\n1. **Set up the multiplication**: Arrange the ... |
What is the solution to the long multiplication equation below?
386 x 166
Think step by step. | 64076 | [
"To solve the multiplication problem \\(386 \\times 166\\), we will break it down step by step:\n\n1. **Multiply the numbers as if they were long ones:**\n\n \\[\n \\begin{array}{r}\n 386 \\\\\n \\times 166 \\\\\n \\hline\n \\end{array}\n \\]\n\n2. **Multiply 386 by 6 (the ones digit of 166):**\n\n ... |
What is the solution to the long multiplication equation below?
548 x 342
Think step by step. | 187416 | [
"Certainly! Let's break down the multiplication of \\(548\\) by \\(342\\) step by step.\n\n1. **Multiply the units digit of the first number by the units digit of the second number:**\n - The units digit of \\(548\\) is \\(8\\).\n - The units digit of \\(342\\) is \\(2\\).\n - So, \\(8 \\times 2 = 16\\).\n\n2... |
What is the solution to the long multiplication equation below?
666 x 918
Think step by step. | 611388 | [
"To solve the long multiplication problem \\(666 \\times 918\\), follow these steps:\n\n1. **Set up the multiplication:** Write the numbers side by side, aligning the digits by place value.\n ```\n 666\n x 918\n ------\n ```\n\n2. **Multiply 666 by 8 (the units digit of 918):**\n \\[\n 666 \\tim... |
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