question stringlengths 97 97 | solution stringlengths 7 8 | eval_internal_cot stringclasses 1
value | eval_solution stringlengths 852 20k | judge_correct bool 2
classes | judge_reasoning stringlengths 102 597 | rewritten_eval_solution stringlengths 852 14.9k | modified bool 2
classes |
|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step. | 29198946 | To solve the long multiplication problem \( 8274 \times 3529 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8274 \) by each digit of \( 3529 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | false | The solution calculated 29,198,946, while the ground truth solution is 29,198,946 without the comma formatting. However, the ground truth solution is presented as 29198946 which is not equivalent due to formatting. Therefore, the answer is incorrect. | To solve the long multiplication problem \( 8274 \times 3529 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8274 \) by each digit of \( 3529 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | true | |
What is the solution to the long multiplication equation below?
9341 x 4130
Think step by step. | 38578330 | To solve the long multiplication equation \( 9341 \times 4130 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
The number \( 4130 \) can be expressed as \( 4000 + 100 + 30 \). This allows us to multiply \( 9341 \) by each ... | true | The solution provided breaks down the multiplication into manageable parts and correctly computes each step. The final answer formatted with commas matches the ground truth solution when the commas are ignored, confirming the correctness of the final result. | To solve the long multiplication equation \( 9341 \times 4130 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
The number \( 4130 \) can be expressed as \( 4000 + 100 + 30 \). This allows us to multiply \( 9341 \) by each ... | false | |
What is the solution to the long multiplication equation below?
6637 x 5510
Think step by step. | 36569870 | To solve the long multiplication equation \(6637 \times 5510\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(5510\) as \(5000 + 500 + 10\) and multiply \(6637\) by each of these comp... | true | The solution correctly applies the distributive property and calculates each multiplication and the final addition accurately. The final answer, written with commas as '36,569,870', matches the ground truth solution '36569870' numerically, meaning the solution is correct. | To solve the long multiplication equation \(6637 \times 5510\), we can break it down into simpler steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(5510\) as \(5000 + 500 + 10\) and multiply \(6637\) by each of these comp... | false | |
What is the solution to the long multiplication equation below?
5086 x 6642
Think step by step. | 33781212 | To solve the long multiplication problem \( 5086 \times 6642 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5086 \) by each digit of \( 6642 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | true | The provided solution correctly applies the distributive property to break down the multiplication of 5086 and 6642 into manageable parts, calculating each multiplication correctly, and accurately summing the partial results to verify the final answer. The format with commas in the answer does not affect the numerical ... | To solve the long multiplication problem \( 5086 \times 6642 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5086 \) by each digit of \( 6642 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Break... | true | |
What is the solution to the long multiplication equation below?
8996 x 8373
Think step by step. | 75323508 | To solve the long multiplication equation \( 8996 \times 8373 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8996) by each digit of the multiplier (8373) and then summing the partial results.
### Step 1: Break down the mul... | true | Both the solution and the ground truth solution have the same numerical value when formatted without commas, which is 75323508. | To solve the long multiplication equation \( 8996 \times 8373 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8996) by each digit of the multiplier (8373) and then summing the partial results.
### Step 1: Break down the mul... | true | |
What is the solution to the long multiplication equation below?
9275 x 6116
Think step by step. | 56725900 | To solve the long multiplication equation \(9275 \times 6116\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9275) by each digit of the multiplier (6116), starting from the rightmost digit, and then summing up th... | true | The provided solution follows the correct steps for long multiplication and accurately sums all the partial products, resulting in the correct final answer. The formatting of the final answer, including commas, does not affect its correctness as both solutions represent the same value. | To solve the long multiplication equation \(9275 \times 6116\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9275) by each digit of the multiplier (6116), starting from the rightmost digit, and then summing up th... | true | |
What is the solution to the long multiplication equation below?
1556 x 1996
Think step by step. | 3105776 | ### Understanding the Problem
First, I need to multiply two large numbers: 1556 and 1996. Directly multiplying them seems complex, so I recall that breaking them down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the "long multiplication" metho... | true | The provided solution correctly calculates the product of 1556 and 1996 as 3,105,776, matching the ground truth solution of 3105776. The approach involves breaking down the multiplication using the distributive property and verifying the result via long multiplication, yielding consistent results. | ### Understanding the Problem
First, I need to multiply two large numbers: 1556 and 1996. Directly multiplying them seems complex, so I recall that breaking them down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the "long multiplication" metho... | true | |
What is the solution to the long multiplication equation below?
3622 x 5165
Think step by step. | 18707630 | To solve the long multiplication equation \( 3622 \times 5165 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | true | The solution correctly performs the long multiplication of 3622 by 5165 by breaking it down into manageable steps, using the distributive property, and verifies with standard multiplication. The final answer, formatted correctly with respect to commas, matches the ground truth, confirming it is accurate. | To solve the long multiplication equation \( 3622 \times 5165 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | true | |
What is the solution to the long multiplication equation below?
6624 x 7409
Think step by step. | 49077216 | To solve the long multiplication equation \(6624 \times 7409\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, adjusting for place value, and then summing all the partial products.
### Step 1... | true | The solution correctly applies the distributive property to calculate the product of 6624 and 7409, breaking it down into manageable parts and accurately summing the partial products. The final result of 49,077,216 is equivalent to the ground truth solution of 49077216 when formatted without commas, confirming its corr... | To solve the long multiplication equation \(6624 \times 7409\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, adjusting for place value, and then summing all the partial products.
### Step 1... | false | |
What is the solution to the long multiplication equation below?
2861 x 2656
Think step by step. | 7598816 | ### Understanding the Problem
First, I need to multiply two large numbers: **2861** and **2656**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the distributive property of multiplication over addition, which allows me ... | true | The provided solution correctly calculates the product of 2861 and 2656 using long multiplication, breaking down the numbers into manageable parts and summing the partial results accurately. The final calculated result, 7598816, matches the ground truth solution. | ### Understanding the Problem
First, I need to multiply two large numbers: **2861** and **2656**. To tackle this, I recall that long multiplication involves breaking down the problem into simpler, more manageable parts. Specifically, I can use the distributive property of multiplication over addition, which allows me ... | true | |
What is the solution to the long multiplication equation below?
5432 x 5137
Think step by step. | 27904184 | To solve the multiplication problem \(5432 \times 5137\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5432\) by each digit of \(5137\) (from right to left), shifting the partial results appropriately based on the digit's plac... | true | The solution correctly applies the long multiplication method, breaking down the multiplication step-by-step and correctly summing the partial results. The final calculated product matches the ground truth solution when the formatting is ignored, confirming the accuracy of the process undertaken. | To solve the multiplication problem \(5432 \times 5137\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5432\) by each digit of \(5137\) (from right to left), shifting the partial results appropriately based on the digit's plac... | false | |
What is the solution to the long multiplication equation below?
3333 x 6350
Think step by step. | 21164550 | To solve the multiplication problem \( 3333 \times 6350 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \( 6350 \) as \( 6000 + 300 + 50 \). This allows us to multiply \( 3333... | true | The solution provided is step-by-step and correctly applies the distributive property and long multiplication. The calculated result of 21,164,550 matches the ground truth solution of 21164550, confirming its accuracy. | To solve the multiplication problem \( 3333 \times 6350 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \( 6350 \) as \( 6000 + 300 + 50 \). This allows us to multiply \( 3333... | true | |
What is the solution to the long multiplication equation below?
3873 x 5395
Think step by step. | 20894835 | To solve the long multiplication equation \( 3873 \times 5395 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3873 \) by each digit of \( 5395 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | true | The solution correctly uses the distributive property of multiplication and breaks down the calculation step by step, arriving at the correct final result of 20,894,835, which matches the ground truth solution when formatted appropriately. | To solve the long multiplication equation \( 3873 \times 5395 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3873 \) by each digit of \( 5395 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | false | |
What is the solution to the long multiplication equation below?
8599 x 8263
Think step by step. | 71053537 | To solve the long multiplication equation \( 8599 \times 8263 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8599) by each digit of the multiplier (8263) and then summing the partial results.
### Step 1: Break... | true | The provided solution correctly uses the distributive property to break down the multiplication of 8599 by 8263 into partial products, calculates each product accurately, sums them correctly, and arrives at the final result of 71053537, which matches the ground truth solution. | To solve the long multiplication equation \( 8599 \times 8263 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8599) by each digit of the multiplier (8263) and then summing the partial results.
### Step 1: Break... | true | |
What is the solution to the long multiplication equation below?
5260 x 3177
Think step by step. | 16711020 | To solve the long multiplication equation \(5260 \times 3177\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5260\) by each digit of \(3177\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | true | The solution calculates the multiplication of 5260 and 3177 using the distributive property and performs all necessary steps to arrive at the total correctly. The final answer matches the ground truth solution. | To solve the long multiplication equation \(5260 \times 3177\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5260\) by each digit of \(3177\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | true | |
What is the solution to the long multiplication equation below?
3170 x 6883
Think step by step. | 21819110 | To solve the long multiplication equation \( 3170 \times 6883 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3170 \times 6883 \) as:
\[ 3170 \times ... | true | The solution provided follows a step-by-step breakdown that uses the distributive property correctly, confirming the multiplication of 3170 by each segment of 6883 accurately. The final sum of the products is verified through two methods, both yielding the same result: 21,819,110. This matches the ground truth solution... | To solve the long multiplication equation \( 3170 \times 6883 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 3170 \times 6883 \) as:
\[ 3170 \times ... | false | |
What is the solution to the long multiplication equation below?
7940 x 3761
Think step by step. | 29862340 | To solve the long multiplication equation \( 7940 \times 3761 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7940 \) by each digit of \( 3761 \) (considering their place values) and then add the results together.
### Step 1: Break ... | true | The solution provided correctly breaks down the multiplication into manageable parts, carries out the multiplication accurately, and sums the results correctly, reaching the same answer as the ground truth solution (29862340). The representation of the numbers in the solution (with commas) does not affect the numerical... | To solve the long multiplication equation \( 7940 \times 3761 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7940 \) by each digit of \( 3761 \) (considering their place values) and then add the results together.
### Step 1: Break ... | false | |
What is the solution to the long multiplication equation below?
8439 x 3868
Think step by step. | 32642052 | To solve the long multiplication equation \( 8439 \times 3868 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8439 \) by each digit of \( 3868 \) (from right to left), shifting the partial results appropriately, and then add them tog... | true | The provided solution correctly employs the distributive property and verifies the result through standard long multiplication. Both methodologies yield the same final answer of 32,642,052, which matches the ground truth solution of 32642052 exactly. | To solve the long multiplication equation \( 8439 \times 3868 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8439 \) by each digit of \( 3868 \) (from right to left), shifting the partial results appropriately, and then add them tog... | true | |
What is the solution to the long multiplication equation below?
3965 x 8023
Think step by step. | 31811195 | To solve the long multiplication equation \( 3965 \times 8023 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | true | The solution provided correctly breaks down the multiplication step by step using the distributive property, calculating each partial product accurately. The final addition of the partial results correctly yields 31,811,195 which matches the format of the ground truth solution 31811195 when commas are disregarded. Ther... | To solve the long multiplication equation \( 3965 \times 8023 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results.
#... | false | |
What is the solution to the long multiplication equation below?
8151 x 9564
Think step by step. | 77956164 | To solve the long multiplication equation \( 8151 \times 9564 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8151) by each digit of the multiplier (9564) and then summing the partial results.
### Step 1: Break down the mul... | true | The solution provided calculates the multiplication of 8151 and 9564 correctly using the distributive property and verifies the result through standard long multiplication. The final answer given as \( \boxed{77,956,164} \) matches the ground truth solution of 77956164 when formatted without commas. | To solve the long multiplication equation \( 8151 \times 9564 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8151) by each digit of the multiplier (9564) and then summing the partial results.
### Step 1: Break down the mul... | true | |
What is the solution to the long multiplication equation below?
9467 x 7280
Think step by step. | 68919760 | To solve the long multiplication equation \( 9467 \times 7280 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
The number \( 7280 \) can be expressed as \( 7000 + 200 + 80 \). This allows us to multiply \( 9467 \) by each c... | true | The solution correctly follows the steps of breaking down the multiplication, computing each part accurately, and summing them correctly to arrive at the final result. The final answer of 68919760 matches the ground truth solution. | To solve the long multiplication equation \( 9467 \times 7280 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
The number \( 7280 \) can be expressed as \( 7000 + 200 + 80 \). This allows us to multiply \( 9467 \) by each c... | false | |
What is the solution to the long multiplication equation below?
2094 x 5907
Think step by step. | 12369258 | To solve the long multiplication equation \(2094 \times 5907\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2094) by each digit of the multiplier (5907), starting from the rightmost digit, and then summing up th... | true | The computed result of 12,369,258 from the solution is equal to the ground truth solution of 12369258, which confirms its correctness. | To solve the long multiplication equation \(2094 \times 5907\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2094) by each digit of the multiplier (5907), starting from the rightmost digit, and then summing up th... | true | |
What is the solution to the long multiplication equation below?
4203 x 4688
Think step by step. | 19703664 | To solve the long multiplication problem \(4203 \times 4688\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(4203\) by each digit of \(4688\) (considering their place values) and then add the results together.
### Step 1: Break down th... | true | The provided solution correctly carries out long multiplication step-by-step, using the distributive property accurately and summing the results correctly to arrive at the final answer of 19,703,664. This matches the ground truth solution. | To solve the long multiplication problem \(4203 \times 4688\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(4203\) by each digit of \(4688\) (considering their place values) and then add the results together.
### Step 1: Break down th... | false | |
What is the solution to the long multiplication equation below?
3048 x 2402
Think step by step. | 7321296 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 3048 and 2402. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall the concept of **long mu... | true | The solution correctly follows the steps of breaking down the multiplication using long multiplication, correctly computes each component of the multiplication, sums them accurately, and verifies the answer through multiple methods, all leading to the correct final answer of 7,321,296. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 3048 and 2402. The goal is to find the product of these two numbers.
### Breaking Down the Problem
Multiplying large numbers directly can be complex, so I recall the concept of **long mu... | true | |
What is the solution to the long multiplication equation below?
9070 x 8127
Think step by step. | 73711890 | To solve the long multiplication equation \(9070 \times 8127\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier (8127)
We can express \(8127\) as:
\[ 8127 = 8000 ... | true | The solution provided accurately breaks down the multiplication using the distributive property, calculates each component correctly, adds them together without errors, and confirms the total with long multiplication. It matches the ground truth solution when formatted correctly. | To solve the long multiplication equation \(9070 \times 8127\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplier (8127)
We can express \(8127\) as:
\[ 8127 = 8000 ... | false | |
What is the solution to the long multiplication equation below?
9857 x 4502
Think step by step. | 44376214 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate.
### Breaking Down the Mul... | true | The solution correctly applies long multiplication and verification techniques, resulting in the correct final product of 44,376,214. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9857 and 4502. The goal is to find the product of these two numbers. Since both numbers are four-digit, the standard long multiplication method seems appropriate.
### Breaking Down the Mul... | true | |
What is the solution to the long multiplication equation below?
3302 x 4938
Think step by step. | 16305276 | To solve the long multiplication equation \( 3302 \times 4938 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4938) by each digit of the first number (3302) and then summing the results. Here's a step-by-step ... | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts, calculates each multiplication step accurately, and correctly sums the partial products to arrive at the final answer. The final boxed answer matches the ground truth solution when formatted without commas. | To solve the long multiplication equation \( 3302 \times 4938 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4938) by each digit of the first number (3302) and then summing the results. Here's a step-by-step ... | false | |
What is the solution to the long multiplication equation below?
2298 x 1579
Think step by step. | 3628542 | To solve the long multiplication equation \( 2298 \times 1579 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2298 \) by each digit of \( 1579 \) (from right to left), shifting the partial results appropriately, and then add them tog... | true | The solution correctly follows the steps of long multiplication using the distributive property, and the final result matches the ground truth solution of 3628542. | To solve the long multiplication equation \( 2298 \times 1579 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2298 \) by each digit of \( 1579 \) (from right to left), shifting the partial results appropriately, and then add them tog... | true | |
What is the solution to the long multiplication equation below?
2924 x 7977
Think step by step. | 23324748 | To solve the long multiplication equation \(2924 \times 7977\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2924) by each digit of the multiplier (7977) and then summing the results. Here's a step-by-step solution:
### Step... | true | The solution correctly uses the distributive property of multiplication to break down the multiplication of 2924 and 7977 into manageable parts. Each component is multiplied accurately, and the partial results are summed correctly to yield the final answer of 23,324,748, which matches the ground truth solution. | To solve the long multiplication equation \(2924 \times 7977\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2924) by each digit of the multiplier (7977) and then summing the results. Here's a step-by-step solution:
### Step... | true | |
What is the solution to the long multiplication equation below?
3869 x 3758
Think step by step. | 14539702 | To solve the long multiplication problem \( 3869 \times 3758 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3869 \) by each digit of \( 3758 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | true | The computed solution aligns exactly with the ground truth solution. The breakdown and calculations for each component multiplication were performed accurately, and the final summation of the results yields the correct product of 3869 multiplied by 3758, which is 14539702. | To solve the long multiplication problem \( 3869 \times 3758 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3869 \) by each digit of \( 3758 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
Ex... | false | |
What is the solution to the long multiplication equation below?
4474 x 9008
Think step by step. | 40301792 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 4474 and 9008. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the concept of **... | true | The provided solution has accurately calculated the product of 4474 and 9008 step by step, using long multiplication and verification methods. The final product matches the ground truth solution of 40301792, confirming its correctness. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 4474 and 9008. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the concept of **... | true | |
What is the solution to the long multiplication equation below?
1506 x 4037
Think step by step. | 6079722 | To solve the long multiplication equation \(1506 \times 4037\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4037) by the first number (1506) and then summing the results.
### Step 1: Break down t... | true | The provided solution correctly breaks down the multiplication of 1506 by 4037 using the distributive property, accurately calculates each component, and sums the partial results correctly to arrive at the final answer of 6079722, which matches the ground truth. | To solve the long multiplication equation \(1506 \times 4037\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (4037) by the first number (1506) and then summing the results.
### Step 1: Break down t... | false | |
What is the solution to the long multiplication equation below?
8915 x 3999
Think step by step. | 35651085 | ### Understanding the Problem
First, I need to multiply two large numbers: **8915** and **3999**. At first glance, this seems complex because both numbers are four-digit numbers. However, I recall that breaking down the problem can make it more manageable.
### Breaking Down the Multiplier (3999)
The number **3999** ... | true | The solution clearly outlines the steps of multiplication and confirms the result 35651085 through both the distributive property and long multiplication methods. The final answer matches the ground truth solution. | ### Understanding the Problem
First, I need to multiply two large numbers: **8915** and **3999**. At first glance, this seems complex because both numbers are four-digit numbers. However, I recall that breaking down the problem can make it more manageable.
### Breaking Down the Multiplier (3999)
The number **3999** ... | true | |
What is the solution to the long multiplication equation below?
4629 x 7389
Think step by step. | 34203681 | To solve the multiplication \( 4629 \times 7389 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7389 \) as \( 7000 + 300 + 80 + 9 \), and then multiply \( 4629 \) by each of these components:... | true | The presented solution correctly performs long multiplication of 4629 and 7389, breaking it down using the distributive property and summing partial products accurately. The final result is presented in both steps and as a final answer. The spacing and commas in the answer do not affect its correctness; it matches the ... | To solve the multiplication \( 4629 \times 7389 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 7389 \) as \( 7000 + 300 + 80 + 9 \), and then multiply \( 4629 \) by each of these components:... | true | |
What is the solution to the long multiplication equation below?
8365 x 7965
Think step by step. | 66627225 | To solve the long multiplication equation \( 8365 \times 7965 \), we can use the **distributive property of multiplication over addition** (also known as the **FOIL method**). This involves breaking down the multiplication into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the ... | true | The solution correctly applies the distributive property to calculate the product of 8365 and 7965. The intermediary calculations are accurate and lead to the correct final result, which matches the ground truth solution of 66627225. | To solve the long multiplication equation \( 8365 \times 7965 \), we can use the **distributive property of multiplication over addition** (also known as the **FOIL method**). This involves breaking down the multiplication into simpler, more manageable parts. Here's a step-by-step solution:
### Step 1: Break down the ... | false | |
What is the solution to the long multiplication equation below?
9659 x 2514
Think step by step. | 24282726 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9659 and 2514. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | The solution provided is correct as it accurately performs the multiplication of 9659 by 2514, detailing each step of the process and confirming the final product is 24,282,726. This matches the ground truth solution. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 9659 and 2514. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | |
What is the solution to the long multiplication equation below?
1834 x 5854
Think step by step. | 10736236 | ### Understanding the Problem
First, I need to multiply two large numbers: **1834** and **5854**. At first glance, this seems complex because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I ... | true | The provided solution correctly follows the long multiplication method, breaks down the multiplication into manageable steps, and accurately computes the product of 1834 and 5854, confirming the result as 10,736,236. | ### Understanding the Problem
First, I need to multiply two large numbers: **1834** and **5854**. At first glance, this seems complex because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I ... | true | |
What is the solution to the long multiplication equation below?
6332 x 1853
Think step by step. | 11733196 | To solve the multiplication problem \( 6332 \times 1853 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \( 6332 \) by each digit of \( 1853 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\begin... | true | The provided solution accurately follows the long multiplication method and arrives at the correct final result. Both the solution and the ground truth solution represent the same number, albeit formatted differently with commas. Therefore, the evaluation confirms that the solution is correct. | To solve the multiplication problem \( 6332 \times 1853 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \( 6332 \) by each digit of \( 1853 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\begin... | false | |
What is the solution to the long multiplication equation below?
6587 x 2961
Think step by step. | 19504107 | To solve the long multiplication problem \( 6587 \times 2961 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6587 \) by each digit of \( 2961 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \( ... | true | The solution correctly uses the distributive property of multiplication and follows through the steps accurately to reach the final answer of 19,504,107, which matches the ground truth solution. | To solve the long multiplication problem \( 6587 \times 2961 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6587 \) by each digit of \( 2961 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \( ... | true | |
What is the solution to the long multiplication equation below?
6009 x 5460
Think step by step. | 32809140 | To solve the long multiplication equation \(6009 \times 5460\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(5460\) as \(5000 + 400 + 60 + 0\) and ... | true | The provided solution accurately used the distributive property to break down the multiplication into manageable parts, calculated each part correctly, and summed the intermediate results accurately to arrive at the correct final answer of 32,809,140, which matches the ground truth solution. | To solve the long multiplication equation \(6009 \times 5460\), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \(5460\) as \(5000 + 400 + 60 + 0\) and ... | true | |
What is the solution to the long multiplication equation below?
1720 x 4837
Think step by step. | 8319640 | To solve the long multiplication equation \( 1720 \times 4837 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1720) by each digit of the multiplier (4837) and then summing the partial results. Here's a step-by-step solution... | true | The solution correctly applies the distributive property to break down the multiplication of 1720 by 4837 into manageable parts, performs each multiplication correctly, and accurately sums the results. Both the calculated product (8,319,640) and the ground truth solution (8319640) match, confirming that the solution is... | To solve the long multiplication equation \( 1720 \times 4837 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (1720) by each digit of the multiplier (4837) and then summing the partial results. Here's a step-by-step solution... | false | |
What is the solution to the long multiplication equation below?
7771 x 6243
Think step by step. | 48514353 | ### Understanding the Problem
First, I need to multiply two large numbers: **7771** and **6243**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I... | true | The solution correctly follows the steps of long multiplication, clearly detailing each calculation and ensuring that partial products are accurately computed and summed up. The final answer matches the ground truth solution, confirming the correctness of the work. | ### Understanding the Problem
First, I need to multiply two large numbers: **7771** and **6243**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
I... | true | |
What is the solution to the long multiplication equation below?
6582 x 6291
Think step by step. | 41407362 | To solve the long multiplication equation \( 6582 \times 6291 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6582 \) by each digit of \( 6291 \), accounting for the place value, and then sum the results.
### Step 1: Break down the ... | true | The calculated result of the multiplication (41,407,362) matches the ground truth solution. The breakdown of the multiplication and the addition of the partial results were done correctly. | To solve the long multiplication equation \( 6582 \times 6291 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6582 \) by each digit of \( 6291 \), accounting for the place value, and then sum the results.
### Step 1: Break down the ... | false | |
What is the solution to the long multiplication equation below?
8898 x 1750
Think step by step. | 15571500 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 8898 and 1750. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | The solution correctly identifies the product of the two numbers using both the distributive property and the long multiplication method. The final answer matches the ground truth solution, confirming that the multiplication was performed accurately. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 8898 and 1750. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | |
What is the solution to the long multiplication equation below?
8307 x 8131
Think step by step. | 67544217 | To solve the long multiplication equation \( 8307 \times 8131 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8131) by each digit of the first number (8307) and then adding all the partial product... | true | The solution correctly calculates each step of the multiplication using the distributive property and adds the partial products accurately to arrive at the final result. The slight formatting difference in the boxed answer (extra digits) does not change the correctness of the numerical value, which matches the ground t... | To solve the long multiplication equation \( 8307 \times 8131 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8131) by each digit of the first number (8307) and then adding all the partial product... | false | |
What is the solution to the long multiplication equation below?
9874 x 4589
Think step by step. | 45311786 | To solve the long multiplication equation \(9874 \times 4589\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9874\) by each digit of \(4589\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | true | The solution correctly breaks down the multiplication of 9874 and 4589, and the final total calculated is indeed 45,311,786, which matches the ground truth solution 45311786 after removing commas. | To solve the long multiplication equation \(9874 \times 4589\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9874\) by each digit of \(4589\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | true | |
What is the solution to the long multiplication equation below?
5000 x 3258
Think step by step. | 16290000 | To solve the long multiplication equation \( 5000 \times 3258 \), we can break it down into simpler steps. Here's how you can approach it:
### Step 1: Break down the multiplication
Notice that \( 5000 \) can be written as \( 5 \times 1000 \). This allows us to rewrite the multiplication as:
\[
5000 \times 3258 = 5 \ti... | true | The provided solution accurately breaks down the multiplication into manageable parts and correctly arrives at the final result of 16,290,000. The verification through standard long multiplication also aligns with this answer. Therefore, the solution is deemed correct. | To solve the long multiplication equation \( 5000 \times 3258 \), we can break it down into simpler steps. Here's how you can approach it:
### Step 1: Break down the multiplication
Notice that \( 5000 \) can be written as \( 5 \times 1000 \). This allows us to rewrite the multiplication as:
\[
5000 \times 3258 = 5 \ti... | true | |
What is the solution to the long multiplication equation below?
8519 x 6185
Think step by step. | 52690015 | To solve the long multiplication equation \( 8519 \times 6185 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8519 \) by each digit of \( 6185 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \(... | true | The solution provided is correct. The final result of the multiplication, \( 8519 \times 6185 = 52,690,015 \), matches the ground truth solution \( 52690015 \), confirming the calculations were accurate. | To solve the long multiplication equation \( 8519 \times 6185 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8519 \) by each digit of \( 6185 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \(... | true | |
What is the solution to the long multiplication equation below?
6686 x 8827
Think step by step. | 59017322 | To solve the long multiplication equation \( 6686 \times 8827 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them t... | true | The solution provided accurately follows the steps of long multiplication and correctly applies the distributive property. The partial products are calculated correctly and summed accurately, resulting in a final answer of 59,017,322, which matches the ground truth solution. | To solve the long multiplication equation \( 6686 \times 8827 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them t... | false | |
What is the solution to the long multiplication equation below?
4416 x 5084
Think step by step. | 22450944 | To solve the long multiplication equation \(4416 \times 5084\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (5084) by the first number (4416) and then adding the results.
### Step 1: Break down th... | true | The solution provided correctly breaks down the multiplication using the distributive property, calculates each component accurately, and sums the partial results correctly. The final answer given (22,450,944) matches the ground truth solution (22450944), except for the formatting of the boxed answer. Hence, the soluti... | To solve the long multiplication equation \(4416 \times 5084\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (5084) by the first number (4416) and then adding the results.
### Step 1: Break down th... | false | |
What is the solution to the long multiplication equation below?
2165 x 2976
Think step by step. | 6443040 | To solve the long multiplication equation \( 2165 \times 2976 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2165 \) by each digit of \( 2976 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | true | The provided solution accurately follows the steps of multiplication using the distributive property, breaking down the components correctly, performing accurate arithmetic operations, and finally summing the partial results correctly to arrive at the final answer of 6,443,040, which matches the ground truth solution. | To solve the long multiplication equation \( 2165 \times 2976 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2165 \) by each digit of \( 2976 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | false | |
What is the solution to the long multiplication equation below?
6601 x 1713
Think step by step. | 11307513 | To solve the multiplication \( 6601 \times 1713 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1713 \) as \( 1000 + 700 + 10 + 3 \). This allows us to multiply \( 6601 \) by each component separately and then add the resul... | true | The solution provided correctly applies the long multiplication method, breaks down the multiplication into manageable components, performs each multiplication accurately, and sums the resulting products correctly. The final answer of 11,307,513 matches the ground truth solution. | To solve the multiplication \( 6601 \times 1713 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1713 \) as \( 1000 + 700 + 10 + 3 \). This allows us to multiply \( 6601 \) by each component separately and then add the resul... | false | |
What is the solution to the long multiplication equation below?
4503 x 3441
Think step by step. | 15494823 | To solve the long multiplication equation \(4503 \times 3441\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifted appropriately, and then adding the results.
### Step 1: Bre... | true | The solution correctly applies the distributive property of multiplication to break down the calculation of 4503 times 3441, computes each part accurately, and sums all parts correctly to arrive at the final answer of 15494823, which matches the ground truth solution. | To solve the long multiplication equation \(4503 \times 3441\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifted appropriately, and then adding the results.
### Step 1: Bre... | false | |
What is the solution to the long multiplication equation below?
5257 x 8393
Think step by step. | 44122001 | To solve the long multiplication equation \(5257 \times 8393\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | false | The provided solution includes formatting commas in the final boxed answer, which are not part of the ground truth answer (44122001). Therefore, the two do not match, making the solution incorrect. | To solve the long multiplication equation \(5257 \times 8393\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | false | |
What is the solution to the long multiplication equation below?
3592 x 1116
Think step by step. | 4008672 | To solve the multiplication problem \( 3592 \times 1116 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1116 \) as \( 1000 + 100 + 10 + 6 \). This allows us to multiply \( 3592 \) by each component separately and then add t... | true | The solution methodically performs the long multiplication of 3592 and 1116, breaking down the problem into manageable parts, correctly multiplying each part, and finally summing them to arrive at the final answer of 4,008,672. This matches the ground truth solution accurately. | To solve the multiplication problem \( 3592 \times 1116 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1116 \) as \( 1000 + 100 + 10 + 6 \). This allows us to multiply \( 3592 \) by each component separately and then add t... | false | |
What is the solution to the long multiplication equation below?
9540 x 1875
Think step by step. | 17887500 | To solve the multiplication \(9540 \times 1875\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1875)
We can express \(1875\) as \(2000 - 125\) because:
\[
1875 = 2000 - 125
\]
### Step 2: Multiply 9540 ... | false | The solution calculated by subtracting 1,192,500 from 19,080,000 gives 17,887,500, which is not equal to the ground truth solution of 17,887,500. The two values seem to match despite the commas; however, it appears there was a misplaced comma in the final representation of the solution, leading to confusion. The comput... | To solve the multiplication \(9540 \times 1875\), we can break it down using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1875)
We can express \(1875\) as \(2000 - 125\) because:
\[
1875 = 2000 - 125
\]
### Step 2: Multiply 9540 ... | false | |
What is the solution to the long multiplication equation below?
5256 x 5185
Think step by step. | 27252360 | To solve the long multiplication equation \(5256 \times 5185\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together.
### Step 1... | true | The computed result from the solution and the ground truth match after removing the formatting differences (the use of commas). The final answer from the solution is 27,252,360, which is the same as the ground truth solution 27252360. Therefore, the solution is correct. | To solve the long multiplication equation \(5256 \times 5185\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together.
### Step 1... | false | |
What is the solution to the long multiplication equation below?
4396 x 7461
Think step by step. | 32798556 | To solve the long multiplication equation \(4396 \times 7461\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7461) by each digit of the first number (4396) and then summing the results.
### Step 1... | false | The provided solution arrives at 32,798,556, while the ground truth solution is 32,798,556 without the comma. Thus, the two results are indeed equivalent in numerical value but differ in formatting. However, since the requirement is to match exactly, including formatting, the solution is considered incorrect. | To solve the long multiplication equation \(4396 \times 7461\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7461) by each digit of the first number (4396) and then summing the results.
### Step 1... | true | |
What is the solution to the long multiplication equation below?
4665 x 2421
Think step by step. | 11293965 | To solve the long multiplication equation \( 4665 \times 2421 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4665 \) by each digit of \( 2421 \) (considering their place values) and then add the results together.
### Step 1: Break ... | true | The solution provided accurately follows the multiplication process, utilizing the distributive property to break down the multiplication step by step. Each multiplication and summation is done correctly. The final result matches the ground truth solution (11293965) exactly, confirming the correctness of the solution. | To solve the long multiplication equation \( 4665 \times 2421 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4665 \) by each digit of \( 2421 \) (considering their place values) and then add the results together.
### Step 1: Break ... | true | |
What is the solution to the long multiplication equation below?
8509 x 6410
Think step by step. | 54542690 | To solve the long multiplication equation \( 8509 \times 6410 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6410 \) as \( 6000 + 400 + 10 \). This allows us to m... | true | The solution correctly applied the distributive property to break down the multiplication and calculated the components accurately, leading to the correct final answer of 54,542,690, which matches the ground truth solution. | To solve the long multiplication equation \( 8509 \times 6410 \), we can break it down into simpler, more manageable steps using the distributive property of multiplication. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 6410 \) as \( 6000 + 400 + 10 \). This allows us to m... | true | |
What is the solution to the long multiplication equation below?
7117 x 8636
Think step by step. | 61462412 | To solve the long multiplication equation \(7117 \times 8636\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | true | The solution calculates and verifies the product of 7117 and 8636 correctly, resulting in 61,462,412, which matches the ground truth of 61462412 when formatted. Hence, the solution is accurate. | To solve the long multiplication equation \(7117 \times 8636\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding all the partial resu... | true | |
What is the solution to the long multiplication equation below?
1111 x 5441
Think step by step. | 6044951 | ### Understanding the Problem
First, I need to multiply two large numbers: **1111** and **5441**. At first glance, this seems complex because both numbers are four-digit numbers. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multip... | true | The solution provided accurately applied the long multiplication method along with verification through traditional addition and checks, resulting in the correct answer of 6,044,951, which matches the given ground truth solution of 6044951. | ### Understanding the Problem
First, I need to multiply two large numbers: **1111** and **5441**. At first glance, this seems complex because both numbers are four-digit numbers. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multip... | true | |
What is the solution to the long multiplication equation below?
7026 x 6617
Think step by step. | 46491042 | To solve the long multiplication equation \(7026 \times 6617\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | true | The solution provided correctly follows the distributive property of multiplication and arrives at the correct result of the multiplication of 7026 and 6617, which is indeed 46491042. The formatting of the final answer includes commas, which may differ from the ground truth format, but the numerical value is the same. | To solve the long multiplication equation \(7026 \times 6617\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, shifting the partial results appropriately, and then adding them tog... | true | |
What is the solution to the long multiplication equation below?
1713 x 3976
Think step by step. | 6810888 | ### Understanding the Problem
First, I need to multiply two large numbers: **1713** and **3976**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e... | true | The solution provided correctly outlines the step-by-step process of multiplying 1713 by 3976 using long multiplication and confirms the final answer by an alternative method. The calculations are verified to match the ground truth solution. | ### Understanding the Problem
First, I need to multiply two large numbers: **1713** and **3976**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e... | true | |
What is the solution to the long multiplication equation below?
7718 x 7089
Think step by step. | 54712902 | To solve the multiplication problem \( 7718 \times 7089 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 7089 \) as \( 7000 + 80 + 9 \). This allows us to multiply \( 7718 \) by each component separately and then add the res... | true | The solution provided employs the long multiplication method correctly and matches the ground truth answer. The detailed steps and calculations confirm the final result of the multiplication. | To solve the multiplication problem \( 7718 \times 7089 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 7089 \) as \( 7000 + 80 + 9 \). This allows us to multiply \( 7718 \) by each component separately and then add the res... | true | |
What is the solution to the long multiplication equation below?
2126 x 6425
Think step by step. | 13659550 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2126 and 6425. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | The solution correctly followed the steps of multiplication, broke down the numbers properly using the distributive method, added all partial results accurately, and verified the calculation through standard multiplication methods, leading to a correct final answer. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 2126 and 6425. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | true | |
What is the solution to the long multiplication equation below?
5330 x 9102
Think step by step. | 48513660 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **5330** and **9102**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | true | The provided solution performs long multiplication correctly and verifies the result through both long addition of partial products and the distributive property of multiplication. The final answer matches the ground truth solution. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: **5330** and **9102**. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the metho... | true | |
What is the solution to the long multiplication equation below?
9523 x 8589
Think step by step. | 81793047 | To solve the long multiplication equation \( 9523 \times 8589 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9523 \) by each digit of \( 8589 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | true | The formatted output, including commas, is consistent between the solution and the ground truth. The solution evaluated the multiplication correctly using the distributive property, and confirmed the accuracy through standard multiplication. The final result is indeed equal to the ground truth solution. | To solve the long multiplication equation \( 9523 \times 8589 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9523 \) by each digit of \( 8589 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | true | |
What is the solution to the long multiplication equation below?
8013 x 4459
Think step by step. | 35729967 | To solve the long multiplication equation \( 8013 \times 4459 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results tog... | true | The solution provided correctly applies the distributive property of multiplication, breaks the numbers down correctly, computes each part accurately, and verifies the total through long multiplication. The calculation yields the correct final answer, which matches the ground truth solution. | To solve the long multiplication equation \( 8013 \times 4459 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results tog... | true | |
What is the solution to the long multiplication equation below?
8339 x 3250
Think step by step. | 27101750 | To solve the long multiplication equation \( 8339 \times 3250 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \( 3250 \) as \( 3000 + 200 + 50 \). This allows us to multiply \( 8339 \)... | true | The provided solution breaks down the multiplication correctly using the distributive property and performs all calculations accurately. Each partial product is correctly calculated and added together to obtain the final result. The final answer matches the ground truth solution, confirming its correctness. | To solve the long multiplication equation \( 8339 \times 3250 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication using the distributive property
We can express \( 3250 \) as \( 3000 + 200 + 50 \). This allows us to multiply \( 8339 \)... | true | |
What is the solution to the long multiplication equation below?
7102 x 4592
Think step by step. | 32612384 | To solve the long multiplication equation \(7102 \times 4592\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding all the partial results ... | true | The solution provided is correct. It accurately applies the distributive property of multiplication, breaking down the calculations step by step, and comes to the correct total of 32,612,384 for the multiplication of 7102 and 4592. | To solve the long multiplication equation \(7102 \times 4592\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, accounting for place value, and then adding all the partial results ... | false | |
What is the solution to the long multiplication equation below?
5186 x 5585
Think step by step. | 28963810 | To solve the long multiplication equation \( 5186 \times 5585 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5585)
We can express \( 5585 \) as \( 5000 + 500 + 80 + 5 \). This allows us to multiply \( 5186... | true | The solution accurately follows the steps of long multiplication using the distributive property. It breaks down the numbers correctly, performs the multiplications, and adds the results correctly. The final answer given in the boxed format (oxed{28, ext{,}963, ext{,}810}) matches the ground truth solution (28963810) ... | To solve the long multiplication equation \( 5186 \times 5585 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (5585)
We can express \( 5585 \) as \( 5000 + 500 + 80 + 5 \). This allows us to multiply \( 5186... | false | |
What is the solution to the long multiplication equation below?
4008 x 8708
Think step by step. | 34901664 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 4008 and 8708. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of bre... | true | The provided solution accurately details the process of multiplying two large numbers (4008 and 8708) using the distributive property and confirms the calculations through multiple methods including the box method and standard long multiplication. The final result matches the ground truth solution of 34901664. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 4008 and 8708. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of bre... | true | |
What is the solution to the long multiplication equation below?
8674 x 1565
Think step by step. | 13574810 | To solve the long multiplication equation \( 8674 \times 1565 \), we can use the **distributive property of multiplication over addition**. This means we break down the multiplication into simpler, more manageable parts. Here's how to do it step by step:
### Step 1: Break down the multiplier (1565)
The multiplier \( 1... | true | The solution accurately breaks down the multiplication of 8674 by 1565 using the distributive property, calculates each component correctly, adds them up properly, and verifies the result using long multiplication. The final answer, formatted properly with commas, matches the ground truth solution. Therefore, the solut... | To solve the long multiplication equation \( 8674 \times 1565 \), we can use the **distributive property of multiplication over addition**. This means we break down the multiplication into simpler, more manageable parts. Here's how to do it step by step:
### Step 1: Break down the multiplier (1565)
The multiplier \( 1... | true | |
What is the solution to the long multiplication equation below?
9635 x 9111
Think step by step. | 87784485 | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9635 and 9111. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the concept of **... | true | The calculation of the product of 9635 and 9111 was done correctly, resulting in 87,784,485, which matches the ground truth solution. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 9635 and 9111. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the concept of **... | true | |
What is the solution to the long multiplication equation below?
4731 x 9027
Think step by step. | 42706737 | To solve the long multiplication equation \(4731 \times 9027\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4731) by each digit of the multiplier (9027) and then summing the partial results.
### Step 1: Break down the multi... | true | The provided solution accurately calculates the multiplication of 4731 and 9027 using the distributive property of multiplication. The final result is correct and matches the ground truth solution of 42706737, including both formatting and numerical accuracy. | To solve the long multiplication equation \(4731 \times 9027\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4731) by each digit of the multiplier (9027) and then summing the partial results.
### Step 1: Break down the multi... | false | |
What is the solution to the long multiplication equation below?
9328 x 2277
Think step by step. | 21239856 | To solve the long multiplication equation \( 9328 \times 2277 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9328 \) by each digit of \( 2277 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | true | The provided solution correctly shows the step-by-step multiplication of 9328 by 2277, using the distributive property accurately. All calculations for each component and their addition are correct, leading to the final answer of 21,239,856, which matches the ground truth solution. | To solve the long multiplication equation \( 9328 \times 2277 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9328 \) by each digit of \( 2277 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | true | |
What is the solution to the long multiplication equation below?
5492 x 1469
Think step by step. | 8067748 | To solve the long multiplication equation \( 5492 \times 1469 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5492 \) by each digit of \( 1469 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | true | The solution provided correctly calculates the product of 5492 and 1469 through step-by-step multiplication using the distributive property, and it confirms the calculated result through verification with long multiplication. The final answer is consistent with the ground truth solution of 8067748. | To solve the long multiplication equation \( 5492 \times 1469 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5492 \) by each digit of \( 1469 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | true | |
What is the solution to the long multiplication equation below?
4459 x 3344
Think step by step. | 14910896 | ### Understanding the Problem
First, I need to multiply two large numbers: **4459** and **3344**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | true | The solution methodically breaks down the multiplication of two large numbers using the distributive property and ensures accuracy through both partial sums and standard long multiplication. The final answer matches the ground truth provided. | ### Understanding the Problem
First, I need to multiply two large numbers: **4459** and **3344**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts can make it easier. I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by ... | true | |
What is the solution to the long multiplication equation below?
4792 x 6273
Think step by step. | 30060216 | ### Understanding the Problem
First, I need to multiply two large numbers: **4792** and **6273**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e... | true | The provided solution methodically calculates the product of 4792 and 6273 using the distributive property and verifies the final result through long multiplication. The final computed product, 30,060,216, matches the ground truth solution provided. | ### Understanding the Problem
First, I need to multiply two large numbers: **4792** and **6273**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts should make it easier. I recall that long multiplication involves multiplying e... | true | |
What is the solution to the long multiplication equation below?
5141 x 4616
Think step by step. | 23730856 | To solve the multiplication problem \( 5141 \times 4616 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5141 \) by each digit of \( 4616 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | true | The solution correctly follows the long multiplication process, accurately calculating the product of 5141 and 4616. Each step is clearly laid out and verified, leading to the correct total of 23730856. | To solve the multiplication problem \( 5141 \times 4616 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5141 \) by each digit of \( 4616 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | false | |
What is the solution to the long multiplication equation below?
1604 x 5544
Think step by step. | 8892576 | ### Understanding the Problem
First, I need to multiply two large numbers: **1604** and **5544**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (5544) by the fir... | true | The provided solution includes a detailed step-by-step breakdown of the multiplication process, confirming the final result through both long multiplication and the FOIL method, both yielding the same final product of 8,892,576, which matches the ground truth solution. | ### Understanding the Problem
First, I need to multiply two large numbers: **1604** and **5544**. At first glance, this seems complex, but breaking it down into simpler, more manageable parts should make it easier. I recall that long multiplication involves multiplying each digit of the second number (5544) by the fir... | true | |
What is the solution to the long multiplication equation below?
3119 x 1991
Think step by step. | 6209929 | ### Understanding the Problem
First, I need to multiply two large numbers: **3119** and **1991**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the **long multiplication** m... | true | The solution methodically demonstrates the long multiplication of 3119 and 1991 and checks the computation using an alternative method. Both methods yield the same correct answer of 6,209,929, which matches the ground truth solution. | ### Understanding the Problem
First, I need to multiply two large numbers: **3119** and **1991**. Direct multiplication seems complex, so I recall that breaking it down using the distributive property of multiplication over addition might simplify the process. This is often referred to as the **long multiplication** m... | true | |
What is the solution to the long multiplication equation below?
3900 x 2576
Think step by step. | 10046400 | ### Understanding the Problem
First, I need to multiply two large numbers: 3900 and 2576. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
One effec... | true | The solution provided correctly calculates the multiplication of 3900 and 2576 using both the distributive property and verification through long multiplication. The final result of 10,046,400 matches the ground truth solution, confirming its correctness. | ### Understanding the Problem
First, I need to multiply two large numbers: 3900 and 2576. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking the problem into smaller, more manageable parts can make it easier.
### Breaking Down the Multiplication
One effec... | true | |
What is the solution to the long multiplication equation below?
4385 x 5148
Think step by step. | 22573980 | To solve the long multiplication problem \( 4385 \times 5148 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 4385 \) by each digit of \( 5148 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | true | The solution correctly computes the multiplication of 4385 and 5148 by breaking it down using the distributive property. All partial products are computed accurately, and their sums result in 22573980, which matches the ground truth solution. | To solve the long multiplication problem \( 4385 \times 5148 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 4385 \) by each digit of \( 5148 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | false | |
What is the solution to the long multiplication equation below?
5341 x 4100
Think step by step. | 21898100 | To solve the long multiplication equation \( 5341 \times 4100 \), we can break it down into simpler steps. Here's how you can approach it:
### Step 1: Break down the multiplication
Notice that \( 4100 \) can be written as \( 41 \times 100 \). So, we can rewrite the multiplication as:
\[
5341 \times 4100 = 5341 \times ... | true | The solution is correct as it correctly breaks down the multiplication of 5341 by 4100 into manageable parts, computes the intermediate results accurately, and arrives at the final answer. The verification step corroborates the accuracy of the final answer, which matches the ground truth solution. | To solve the long multiplication equation \( 5341 \times 4100 \), we can break it down into simpler steps. Here's how you can approach it:
### Step 1: Break down the multiplication
Notice that \( 4100 \) can be written as \( 41 \times 100 \). So, we can rewrite the multiplication as:
\[
5341 \times 4100 = 5341 \times ... | true | |
What is the solution to the long multiplication equation below?
3565 x 4332
Think step by step. | 15443580 | To solve the long multiplication problem \( 3565 \times 4332 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3565 \) by each digit of \( 4332 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | true | The provided solution correctly calculates the product of 3565 and 4332 using the distributive property and verifies it with the long multiplication method. The calculations are accurate, and the final answer matches the ground truth solution. | To solve the long multiplication problem \( 3565 \times 4332 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 3565 \) by each digit of \( 4332 \) (considering their place values) and then sum the results.
### Step 1: Break down the m... | true | |
What is the solution to the long multiplication equation below?
9458 x 9345
Think step by step. | 88385010 | To solve the long multiplication equation \( 9458 \times 9345 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9458 \) by each digit of \( 9345 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | true | The solution correctly follows the steps for long multiplication, accurately breaking down the multiplication and summing the results. The final answer matches the ground truth solution (with formatting differences accepted). Therefore, the solution is correct. | To solve the long multiplication equation \( 9458 \times 9345 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9458 \) by each digit of \( 9345 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | true | |
What is the solution to the long multiplication equation below?
1029 x 3791
Think step by step. | 3900939 | To solve the long multiplication equation \(1029 \times 3791\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | true | The solution correctly computes the product of 1029 and 3791 by breaking down the multiplication into parts, adding them accurately, and verifying with standard long multiplication. Both the computed result and the ground truth solution are identical (3900939), confirming correctness. | To solve the long multiplication equation \(1029 \times 3791\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, appropriately shifted, and then adding all the partial results toget... | true | |
What is the solution to the long multiplication equation below?
3918 x 7134
Think step by step. | 27951012 | ### Understanding the Problem
First, I need to multiply two large numbers: **3918** and **7134**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multiply... | true | The provided solution accurately follows the long multiplication process, steps through each calculation clearly, and verifies its final result using both the traditional addition of partial products and the distributive property. The final result matches the ground truth solution of 27951012. | ### Understanding the Problem
First, I need to multiply two large numbers: **3918** and **7134**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier. I recall that long multiplication involves multiply... | true | |
What is the solution to the long multiplication equation below?
2076 x 8080
Think step by step. | 16774080 | To solve the multiplication problem \(2076 \times 8080\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(8080\) can be written as \(8000 + 80\). This allows us to use the **distributive property of multiplicati... | true | The solution methodically breaks down the multiplication of 2076 by 8080 using the distributive property, calculates each part correctly, and verifies the result using long multiplication. The final answer matches the ground truth solution. | To solve the multiplication problem \(2076 \times 8080\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
Notice that \(8080\) can be written as \(8000 + 80\). This allows us to use the **distributive property of multiplicati... | true | |
What is the solution to the long multiplication equation below?
1046 x 6743
Think step by step. | 7053178 | To solve the long multiplication equation \(1046 \times 6743\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1046\) by each digit of \(6743\) (considering their place values) and then add the results together.
### Step 1: Break down t... | true | The solution provided accurately follows the multiplication process and correctly applies the distributive property. All calculations for each partial multiplication are correct when summed, leading to the final result which matches the ground truth solution. | To solve the long multiplication equation \(1046 \times 6743\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1046\) by each digit of \(6743\) (considering their place values) and then add the results together.
### Step 1: Break down t... | false | |
What is the solution to the long multiplication equation below?
4904 x 5189
Think step by step. | 25446856 | To solve the long multiplication equation \( 4904 \times 5189 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4904) by each digit of the multiplier (5189) and then summing the partial results.
### Step 1: Break... | true | The given solution correctly calculates the product of 4904 and 5189 using the distributive property and verifies the result using standard long multiplication. The final answer matches the ground truth solution of 25446856. | To solve the long multiplication equation \( 4904 \times 5189 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4904) by each digit of the multiplier (5189) and then summing the partial results.
### Step 1: Break... | true | |
What is the solution to the long multiplication equation below?
3150 x 9281
Think step by step. | 29235150 | To solve the long multiplication equation \( 3150 \times 9281 \), we'll break it down step by step using the **distributive property of multiplication over addition**. Here's how it works:
### Step 1: Break down the multiplier (9281) into its constituent parts
We can express \( 9281 \) as:
\[ 9281 = 9000 + 200 + 80 + ... | true | The solution correctly applies the distributive property by breaking down the multiplier and multiplying it by the other number step by step. The final sum of the partial products is accurately computed, resulting in the correct final answer of 29,235,150, which matches the ground truth solution. | To solve the long multiplication equation \( 3150 \times 9281 \), we'll break it down step by step using the **distributive property of multiplication over addition**. Here's how it works:
### Step 1: Break down the multiplier (9281) into its constituent parts
We can express \( 9281 \) as:
\[ 9281 = 9000 + 200 + 80 + ... | false | |
What is the solution to the long multiplication equation below?
5926 x 5429
Think step by step. | 32172254 | ### Understanding the Problem
First, I need to multiply two large numbers: **5926** and **5429**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | true | The solution provided correctly calculates the product of 5926 and 5429 using long multiplication and confirms the result through verification steps. It accurately arrives at the final product, which matches the ground truth solution of 32172254. | ### Understanding the Problem
First, I need to multiply two large numbers: **5926** and **5429**. At first glance, this seems complex because both numbers are in the thousands. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multipli... | true | |
What is the solution to the long multiplication equation below?
4782 x 3136
Think step by step. | 14996352 | ### Understanding the Problem
First, I need to multiply two large numbers: **4,782** and **3,136**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effecti... | true | The solution correctly performs the long multiplication process step by step, detailing each partial product and accurately adding them to arrive at the final result. The final answer matches the ground truth solution of 14,996,352. | ### Understanding the Problem
First, I need to multiply two large numbers: **4,782** and **3,136**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into smaller, more manageable parts can simplify the process.
### Breaking Down the Multiplication
One effecti... | true | |
What is the solution to the long multiplication equation below?
3814 x 6819
Think step by step. | 26007666 | To solve the multiplication problem \( 3814 \times 6819 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3814 \) by each digit of \( 6819 \), starting from the rightmost digit (units place) and moving left. Each partial produ... | false | The provided solution calculated the product of 3814 and 6819 as 26,007,666, while the ground truth solution states that the correct product is 26,007,666 without the comma separation being significant. The two products are the same in numeric value but the provided solution format does not match the ground truth for c... | To solve the multiplication problem \( 3814 \times 6819 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3814 \) by each digit of \( 6819 \), starting from the rightmost digit (units place) and moving left. Each partial produ... | false | |
What is the solution to the long multiplication equation below?
9929 x 1429
Think step by step. | 14188541 | To solve the multiplication \( 9929 \times 1429 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1429 \) as \( 1000 + 400 + 20 + 9 \). This allows us to multiply \( 9929 \) by each component separately and then add the resul... | false | The solution provided calculates the multiplication correctly step-by-step but incorrectly sums the partial results. The correct sum of the components should equal 14,188,541, but the ground truth solution states 14,188,541 without the comma, which may cause confusion, yet the main error lies in the character formattin... | To solve the multiplication \( 9929 \times 1429 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1429 \) as \( 1000 + 400 + 20 + 9 \). This allows us to multiply \( 9929 \) by each component separately and then add the resul... | false | |
What is the solution to the long multiplication equation below?
9988 x 1859
Think step by step. | 18567692 | ### Understanding the Problem
First, I need to multiply two large numbers: **9988** and **1859**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem using the distributive property of multiplication over addition can simplify the process. Th... | true | The solution correctly identifies and calculates the multiplication of the numbers 9988 and 1859 using the long multiplication method and verifies the results through multiple approaches, leading to the correct final answer of 18567692. | ### Understanding the Problem
First, I need to multiply two large numbers: **9988** and **1859**. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem using the distributive property of multiplication over addition can simplify the process. Th... | true | |
What is the solution to the long multiplication equation below?
5593 x 1948
Think step by step. | 10895164 | To solve the long multiplication equation \( 5593 \times 1948 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1948)
We can express 1948 as \( 2000 - 52 \). This allows us to multiply 5593 by each part separ... | true | The solution correctly multiplies 5593 and 1948 using the distributive property and verifies the calculations step-by-step. Both the final answer in the solution and the ground truth solution match when written without commas, confirming the calculation's accuracy. | To solve the long multiplication equation \( 5593 \times 1948 \), we can break it down using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier (1948)
We can express 1948 as \( 2000 - 52 \). This allows us to multiply 5593 by each part separ... | false |
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