question string | solution string | eval_prompt string | eval_internal_cot string | eval_solution string | raw_eval_prompt string | judge_correct bool | judge_reasoning string |
|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
8152 x 5173
Think step by step. | 42170296 | What is the solution to the long multiplication equation below?
8152 x 5173
Think step by step. | To solve the long multiplication equation \( 8152 \times 5173 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8152 \) by each digit of \( 5173 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | What is the solution to the long multiplication equation below?
8152 x 5173
Think step by step. | true | The solution correctly follows the steps of the long multiplication using the distributive property, accurately breaking down the multiplication into manageable parts, calculating each part correctly, and summing them accurately to arrive at the final result of 42170296, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
8084 x 7418
Think step by step. | 59967112 | What is the solution to the long multiplication equation below?
8084 x 7418
Think step by step. | To solve the long multiplication equation \( 8084 \times 7418 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8084 \) by each digit of \( 7418 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
8084 x 7418
Think step by step. | true | The solution correctly breaks down the multiplication using the distributive property, and all steps performed are accurate. The final computed result (59,967,112) matches the ground truth solution (59967112). The formatting of the numbers did not affect the correctness of the result. | |
What is the solution to the long multiplication equation below?
5072 x 3123
Think step by step. | 15839856 | What is the solution to the long multiplication equation below?
5072 x 3123
Think step by step. | To solve the multiplication problem \(5072 \times 3123\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5072\) by each digit of \(3123\), starting from the rightmost digit, and then sum the results.
\[
\begin{align*}
&5072 \ti... | What is the solution to the long multiplication equation below?
5072 x 3123
Think step by step. | true | The solution correctly applies long multiplication by breaking down the process into manageable steps, correctly multiplying each part and adding the results. The arithmetic is accurate, leading to the final answer of 15839856, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2167 x 1699
Think step by step. | 3681733 | What is the solution to the long multiplication equation below?
2167 x 1699
Think step by step. | To solve the long multiplication equation \( 2167 \times 1699 \), 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 (1699)
We can express \( 1699 \) as \( 1700 - 1 \). This simplifies the multiplication because mu... | What is the solution to the long multiplication equation below?
2167 x 1699
Think step by step. | true | The solution correctly uses the distributive property for multiplication, performs each step accurately, and verifies the final result through long multiplication. Both the computed result and the ground truth solution match, confirming the correctness of the solution. | |
What is the solution to the long multiplication equation below?
3336 x 2850
Think step by step. | 9507600 | What is the solution to the long multiplication equation below?
3336 x 2850
Think step by step. | To solve the multiplication problem \( 3336 \times 2850 \), 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 \( 2850 \) can be expressed as \( 3000 - 150 \). This allows us to rewrite the multiplication as:
\[
3336... | What is the solution to the long multiplication equation below?
3336 x 2850
Think step by step. | true | The provided solution correctly applies the distributive property to break down the multiplication of 3336 and 2850, arrives at the intermediate calculations, and subtracts correctly to reach the final answer of 9,507,600, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5309 x 8938
Think step by step. | 47451842 | What is the solution to the long multiplication equation below?
5309 x 8938
Think step by step. | To solve the long multiplication equation \(5309 \times 8938\), 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, starting from the rightmost digit, and then summing up the partial r... | What is the solution to the long multiplication equation below?
5309 x 8938
Think step by step. | true | The final calculated result of the multiplication, 47,451,842, matches the ground truth solution of 47451842 when considering that they represent the same numeric value. Thus, the solution is correct. | |
What is the solution to the long multiplication equation below?
1910 x 2635
Think step by step. | 5032850 | What is the solution to the long multiplication equation below?
1910 x 2635
Think step by step. | To solve the long multiplication equation \( 1910 \times 2635 \), 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 (2635) by the first number (1910) and then summing the results.
### Step 1: Break down... | What is the solution to the long multiplication equation below?
1910 x 2635
Think step by step. | false | The solution provided indicates that the final result of the multiplication is 5,032,850, but the ground truth solution states it is 5,032,850 (without the trailing zeroes). The correct multiplication result matches the ground truth and does not lead to a mathematically incorrect final answer. However, there is inconsi... | |
What is the solution to the long multiplication equation below?
3408 x 3451
Think step by step. | 11761008 | What is the solution to the long multiplication equation below?
3408 x 3451
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3408** and **3451**. 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.
### Breaking Down the Multiplication
One effecti... | What is the solution to the long multiplication equation below?
3408 x 3451
Think step by step. | true | The provided solution calculated the multiplication of 3408 and 3451 correctly. It broke down the problem into manageable parts, verified through standard multiplication methods and careful summation of partial products. The final result of 11,761,008 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1585 x 8512
Think step by step. | 13491520 | What is the solution to the long multiplication equation below?
1585 x 8512
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two large numbers: 1585 and 8512. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down in... | What is the solution to the long multiplication equation below?
1585 x 8512
Think step by step. | true | The provided solution accurately follows the long multiplication process, verifies the result through an alternative method, and arrives at the correct final product of 1585 and 8512, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4042 x 4489
Think step by step. | 18144538 | What is the solution to the long multiplication equation below?
4042 x 4489
Think step by step. | To solve the multiplication \( 4042 \times 4489 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4042 \) by each digit of \( 4489 \), starting from the rightmost digit (units place), and then sum the partial results.
\[
\be... | What is the solution to the long multiplication equation below?
4042 x 4489
Think step by step. | true | The provided solution correctly uses long multiplication and the distributive property to calculate the product of 4042 and 4489. The addition of partial products is also correctly handled, leading to the final result of 18144538, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8922 x 9614
Think step by step. | 85776108 | What is the solution to the long multiplication equation below?
8922 x 9614
Think step by step. | To solve the long multiplication equation \( 8922 \times 9614 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8922) by each digit of the multiplier (9614) and then summing the partial results.
### Step 1: Break... | What is the solution to the long multiplication equation below?
8922 x 9614
Think step by step. | true | The calculated result of 85,776,108 matches the ground truth solution of 85776108 after performing the necessary calculations and verification steps. Hence, the solution is correct. | |
What is the solution to the long multiplication equation below?
7744 x 5963
Think step by step. | 46177472 | What is the solution to the long multiplication equation below?
7744 x 5963
Think step by step. | To solve the multiplication \( 7744 \times 5963 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7744 \) by each digit of \( 5963 \), starting from the rightmost digit (units place), and shift the partial results accordingly.... | What is the solution to the long multiplication equation below?
7744 x 5963
Think step by step. | true | Using the long multiplication method, the solution correctly calculated the product of 7744 and 5963 step-by-step, leading to the final result of 46177472, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1901 x 1425
Think step by step. | 2708925 | What is the solution to the long multiplication equation below?
1901 x 1425
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1901** and **1425**. 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 (1425) by the first ... | What is the solution to the long multiplication equation below?
1901 x 1425
Think step by step. | true | The solution provided follows a clear and structured breakdown of the multiplication process for the numbers 1901 and 1425, leading to the correct final product of 2,708,925. The calculations are verified through various methods, including direct multiplication of each segment, and all partial results have been added c... | |
What is the solution to the long multiplication equation below?
4451 x 5217
Think step by step. | 23220867 | What is the solution to the long multiplication equation below?
4451 x 5217
Think step by step. | To solve the long multiplication equation \(4451 \times 5217\), 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 accordingly, and then adding them toget... | What is the solution to the long multiplication equation below?
4451 x 5217
Think step by step. | true | The solution correctly calculated the product of 4451 and 5217 using the distributive property of multiplication and verified it through a standard long multiplication method. The final result given, \(23220867\), which is equivalent to \(23,220,867\) (the formatting difference with commas does not affect the correctne... | |
What is the solution to the long multiplication equation below?
7324 x 7653
Think step by step. | 56050572 | What is the solution to the long multiplication equation below?
7324 x 7653
Think step by step. | To solve the long multiplication equation \(7324 \times 7653\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7324\) by each digit of \(7653\) (from right to left), shifting the partial results appropriately, and then add them together.... | What is the solution to the long multiplication equation below?
7324 x 7653
Think step by step. | true | The solution provided follows the correct steps of long multiplication using the distributive property. Each multiplication is calculated accurately, and the partial sums are added correctly, leading to the final result of 56050572, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5787 x 1072
Think step by step. | 6203664 | What is the solution to the long multiplication equation below?
5787 x 1072
Think step by step. | To solve the multiplication problem \( 5787 \times 1072 \), we'll break it down using the **long multiplication method**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 1072 \) as \( 1000 + 70 + 2 \). This allows us to multiply \( 5787 \) by each component separately and th... | What is the solution to the long multiplication equation below?
5787 x 1072
Think step by step. | true | The solution provided is correct. The calculations for each component of the multiplication were done accurately, and the final result of 6203664 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3430 x 5437
Think step by step. | 18648910 | What is the solution to the long multiplication equation below?
3430 x 5437
Think step by step. | To solve the long multiplication equation \(3430 \times 5437\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (3430) by each digit of the multiplier (5437), starting from the rightmost digit, and then summing all t... | What is the solution to the long multiplication equation below?
3430 x 5437
Think step by step. | true | The solution provided correctly breaks down the multiplication of 3430 by 5437 using the distributive property and subsequently adds all the partial products accurately. The final answer reported, 18,648,910, matches the ground truth solution of 18648910 (ignoring the formatting of commas). Therefore, the given solutio... | |
What is the solution to the long multiplication equation below?
1528 x 6001
Think step by step. | 9169528 | What is the solution to the long multiplication equation below?
1528 x 6001
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1528** and **6001**. At first glance, this seems like a standard long multiplication problem, but I wonder if there's a smarter way to approach it, perhaps by breaking it down into simpler parts.
### Breaking Down the Multiplier
The number ... | What is the solution to the long multiplication equation below?
1528 x 6001
Think step by step. | true | The solution has correctly calculated the product of 1528 and 6001 and verified the answer through multiple methods including long multiplication and a calculator. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4709 x 2008
Think step by step. | 9455672 | What is the solution to the long multiplication equation below?
4709 x 2008
Think step by step. | To solve the multiplication problem \( 4709 \times 2008 \), 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 (2008)
The number \( 2008 \) can be expressed as:
\[ 2008 = 2000 + 8 \]
### Step 2: Multiply 4709 ... | What is the solution to the long multiplication equation below?
4709 x 2008
Think step by step. | true | The solution correctly applies the distributive property of multiplication and reaches the correct final result of \( 9,455,672 \), which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2170 x 3515
Think step by step. | 7627550 | What is the solution to the long multiplication equation below?
2170 x 3515
Think step by step. | To solve the long multiplication equation \(2170 \times 3515\), 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 values, and then adding the results together.
... | What is the solution to the long multiplication equation below?
2170 x 3515
Think step by step. | false | The solution provided incorrectly calculated the final sum of the partial products. The final answer should be 7627550, but the solution states it as 7627550. Thus, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
5256 x 8961
Think step by step. | 47099016 | What is the solution to the long multiplication equation below?
5256 x 8961
Think step by step. | To solve the multiplication problem \(5256 \times 8961\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5256\) by each digit of \(8961\) (from right to left), shifting the partial results appropriately to account for place valu... | What is the solution to the long multiplication equation below?
5256 x 8961
Think step by step. | true | The solution provided utilizes the long multiplication method correctly and performs each multiplication and addition step accurately. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3260 x 6373
Think step by step. | 20775980 | What is the solution to the long multiplication equation below?
3260 x 6373
Think step by step. | To solve the multiplication problem \(3260 \times 6373\), 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 (6373)
Express \(6373\) as \(6000 + 300 + 70 + 3\). This allows us to multiply \(3260\) by each compo... | What is the solution to the long multiplication equation below?
3260 x 6373
Think step by step. | false | The solution provided calculates the product of 3260 and 6373 step-by-step, but in the final addition, the partial sums were added incorrectly. The correct partial sum should yield 20775980, which matches the ground truth solution. The final answer given in the solution is incorrectly stated as 20775980 instead of 2077... | |
What is the solution to the long multiplication equation below?
1124 x 5917
Think step by step. | 6650708 | What is the solution to the long multiplication equation below?
1124 x 5917
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1124** and **5917**. 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... | What is the solution to the long multiplication equation below?
1124 x 5917
Think step by step. | true | The provided solution correctly outlines the multiplication of 1124 and 5917, and the final calculated product matches the ground truth solution, which is 6650708. | |
What is the solution to the long multiplication equation below?
7747 x 7621
Think step by step. | 59039887 | What is the solution to the long multiplication equation below?
7747 x 7621
Think step by step. | To solve the long multiplication equation \( 7747 \times 7621 \), 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... | What is the solution to the long multiplication equation below?
7747 x 7621
Think step by step. | true | The solution correctly followed the steps of long multiplication and accurately calculated the product of 7747 and 7621, yielding the final result of 59,039,887. While the formatting includes commas, the numerical values match exactly. | |
What is the solution to the long multiplication equation below?
7321 x 3351
Think step by step. | 24532671 | What is the solution to the long multiplication equation below?
7321 x 3351
Think step by step. | To solve the multiplication problem \( 7321 \times 3351 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 7321 \) by each digit of \( 3351 \), starting from the rightmost digit, and then sum the results.
\[
\begin{align*}
&7... | What is the solution to the long multiplication equation below?
7321 x 3351
Think step by step. | true | The solution provided uses correct long multiplication steps and the result matches with the ground truth solution when ignoring formatting differences. Both represent the same number 24532671. | |
What is the solution to the long multiplication equation below?
6128 x 1672
Think step by step. | 10246016 | What is the solution to the long multiplication equation below?
6128 x 1672
Think step by step. | To solve the long multiplication equation \(6128 \times 1672\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6128) by each digit of the multiplier (1672), starting from the rightmost digit, and then summing up th... | What is the solution to the long multiplication equation below?
6128 x 1672
Think step by step. | true | The provided solution correctly calculates the product of 6128 and 1672 using the distributive property and verifies it with standard long multiplication. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6701 x 4090
Think step by step. | 27407090 | What is the solution to the long multiplication equation below?
6701 x 4090
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two large numbers: 6701 and 4090. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down into simpler, mor... | What is the solution to the long multiplication equation below?
6701 x 4090
Think step by step. | true | The solution provided correctly calculates the product of 6701 and 4090 step by step, confirming the final answer of 27,407,090 using multiple methods, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3339 x 7948
Think step by step. | 26538372 | What is the solution to the long multiplication equation below?
3339 x 7948
Think step by step. | To solve the long multiplication equation \( 3339 \times 7948 \), 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... | What is the solution to the long multiplication equation below?
3339 x 7948
Think step by step. | true | The solution calculates the product of 3339 and 7948 correctly using the distributive property and verifies it with the standard long multiplication method, both resulting in the same final answer. While the formatting of the final answer differs (with commas in the solution and none in the ground truth), the numerical... | |
What is the solution to the long multiplication equation below?
3372 x 5233
Think step by step. | 17645676 | What is the solution to the long multiplication equation below?
3372 x 5233
Think step by step. | To solve the multiplication problem \( 3372 \times 5233 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3372 \) by each digit of \( 5233 \), starting from the rightmost digit (units place), and shift the partial results acc... | What is the solution to the long multiplication equation below?
3372 x 5233
Think step by step. | true | The solution provided accurately follows the long multiplication method step-by-step and confirms the correct final product of the multiplication operation, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7372 x 8816
Think step by step. | 64991552 | What is the solution to the long multiplication equation below?
7372 x 8816
Think step by step. | To solve the multiplication problem \(7372 \times 8816\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7372\) by each digit of \(8816\) (from right to left), keeping track of the place values by adding zeros as needed.
\[
\be... | What is the solution to the long multiplication equation below?
7372 x 8816
Think step by step. | true | The solution accurately follows the long multiplication procedure to compute the product of 7372 and 8816 step-by-step, with correct calculations for each partial product and their proper summation. The final boxed answer matches the ground truth solution when formatted appropriately (including commas). Therefore, the ... | |
What is the solution to the long multiplication equation below?
9095 x 6874
Think step by step. | 62519030 | What is the solution to the long multiplication equation below?
9095 x 6874
Think step by step. | To solve the long multiplication equation \( 9095 \times 6874 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9095 \) by each digit of \( 6874 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplicatio... | What is the solution to the long multiplication equation below?
9095 x 6874
Think step by step. | true | The solution correctly applies the distributive property of multiplication and accurately computes the partial products. The final sum of the partial products is correctly calculated as \( 62,519,030 \) which matches the ground truth solution of \( 62519030 \). Thus, the solution is deemed correct. | |
What is the solution to the long multiplication equation below?
7647 x 5248
Think step by step. | 40131456 | What is the solution to the long multiplication equation below?
7647 x 5248
Think step by step. | To solve the long multiplication problem \(7647 \times 5248\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7647\) by each digit of \(5248\) (from right to left), shift the partial results appropriately, and then add them together.
Here's the step... | What is the solution to the long multiplication equation below?
7647 x 5248
Think step by step. | true | The solution correctly performs the multiplication of 7647 and 5248 using the distributive property, breaking down the numbers and correctly calculating the partial products and their sum. The final answer matches the ground truth solution when formatted properly (40,131,456 is equivalent to 40131456). | |
What is the solution to the long multiplication equation below?
9770 x 7644
Think step by step. | 74681880 | What is the solution to the long multiplication equation below?
9770 x 7644
Think step by step. | To solve the long multiplication equation \( 9770 \times 7644 \), 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 (7644)
We can express \( 7644 \) as \( 8000 - 356 \). This allows us to rewrite the multiplic... | What is the solution to the long multiplication equation below?
9770 x 7644
Think step by step. | false | The provided solution includes unnecessary commas in the final result, which are not present in the ground truth solution. The correct arithmetic calculation was performed, as evidenced by the resulting number calculation; however, the formatting with commas does not match the ground truth output. | |
What is the solution to the long multiplication equation below?
3323 x 2089
Think step by step. | 6941747 | What is the solution to the long multiplication equation below?
3323 x 2089
Think step by step. | To solve the multiplication problem \( 3323 \times 2089 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 2089 \) as \( 2000 + 80 + 9 \). This allows us to multiply \( 3323 \) by each component separately and then add the res... | What is the solution to the long multiplication equation below?
3323 x 2089
Think step by step. | true | The solution follows a correct methodology of breaking down the multiplication into smaller components, performing each multiplication accurately, and then correctly summing the results. The final answer presented matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
9238 x 7442
Think step by step. | 68749196 | What is the solution to the long multiplication equation below?
9238 x 7442
Think step by step. | To solve the long multiplication problem \( 9238 \times 7442 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 9238 \) by each digit of \( 7442 \), starting from the rightmost digit, and shift the partial resu... | What is the solution to the long multiplication equation below?
9238 x 7442
Think step by step. | true | The solution presents a step-by-step breakdown of the long multiplication process, accurately multiplying each digit of the second number (7442) by the first number (9238) and correctly shifting the results. The final addition of the partial products leads to the correct total of 68,749,196. Therefore, the given soluti... | |
What is the solution to the long multiplication equation below?
5215 x 9235
Think step by step. | 48160525 | What is the solution to the long multiplication equation below?
5215 x 9235
Think step by step. | To solve the long multiplication equation \(5215 \times 9235\), 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... | What is the solution to the long multiplication equation below?
5215 x 9235
Think step by step. | true | The provided solution correctly breaks down the multiplication using the distributive property, accurately computes the individual products, and sums them correctly to arrive at the final answer of 48,160,525, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6769 x 5635
Think step by step. | 38143315 | What is the solution to the long multiplication equation below?
6769 x 5635
Think step by step. | To solve the multiplication problem \( 6769 \times 5635 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 6769 \) by each digit of \( 5635 \), starting from the rightmost digit (units place) and moving left. Remember to add p... | What is the solution to the long multiplication equation below?
6769 x 5635
Think step by step. | true | The solution provided correctly follows the long multiplication method step-by-step, and the final calculated result matches the ground truth solution of 38143315. | |
What is the solution to the long multiplication equation below?
2996 x 8312
Think step by step. | 24902752 | What is the solution to the long multiplication equation below?
2996 x 8312
Think step by step. | To solve the long multiplication equation \( 2996 \times 8312 \), 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 (8312) by each digit of the first number (2996) and then summing up the partial results... | What is the solution to the long multiplication equation below?
2996 x 8312
Think step by step. | true | The presented solution correctly breaks down the multiplication of 2996 by 8312 using the distributive property, calculates each partial product accurately, and sums them correctly. The final result obtained, 24,902,752, matches the ground truth solution perfectly (24902752), confirming the correctness. | |
What is the solution to the long multiplication equation below?
7691 x 9402
Think step by step. | 72310782 | What is the solution to the long multiplication equation below?
7691 x 9402
Think step by step. | To solve the long multiplication equation \(7691 \times 9402\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7691\) by each digit of \(9402\) (from right to left), shifting the partial results appropriately, and then add them together.
### Step 1:... | What is the solution to the long multiplication equation below?
7691 x 9402
Think step by step. | true | The solution correctly breaks down the multiplication of 7691 by each digit of 9402 using the distributive property and adds the results correctly. The final result, represented as 72,310,782 (with commas added for clarity), is indeed correct as it matches the ground truth solution 72310782 when formatted without comma... | |
What is the solution to the long multiplication equation below?
5055 x 4857
Think step by step. | 24552135 | What is the solution to the long multiplication equation below?
5055 x 4857
Think step by step. | To solve the long multiplication equation \(5055 \times 4857\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5055) by each digit of the multiplier (4857), considering their place values, and then summing all the partial produ... | What is the solution to the long multiplication equation below?
5055 x 4857
Think step by step. | false | The solution calculated 24,552,135, while the ground truth solution indicates the correct answer is 24,552,135 (24552135 without any commas). The discrepancy in formatting does not affect the numeric value, but in terms of correctness, the two values are indeed the same in number, yet there is an inconsistency in how t... | |
What is the solution to the long multiplication equation below?
5090 x 1645
Think step by step. | 8373050 | What is the solution to the long multiplication equation below?
5090 x 1645
Think step by step. | To solve the long multiplication equation \( 5090 \times 1645 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 5090 \) by each digit of \( 1645 \), accounting for place values, and then sum the results.
### Step 1: Break down the mul... | What is the solution to the long multiplication equation below?
5090 x 1645
Think step by step. | true | The calculated product of 5090 and 1645 is indeed 8373050 as shown through detailed step-by-step multiplication and summation. The solution matches the ground truth. | |
What is the solution to the long multiplication equation below?
6696 x 4153
Think step by step. | 27808488 | What is the solution to the long multiplication equation below?
6696 x 4153
Think step by step. | To solve the long multiplication equation \( 6696 \times 4153 \), 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 summing all the partial produ... | What is the solution to the long multiplication equation below?
6696 x 4153
Think step by step. | true | The solution correctly follows the steps of long multiplication using the distributive property and accurately sums the partial products. The final calculated result of 27,808,488 matches the ground truth solution. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
9328 x 3621
Think step by step. | 33776688 | What is the solution to the long multiplication equation below?
9328 x 3621
Think step by step. | To solve the long multiplication problem \( 9328 \times 3621 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9328 \) by each digit of \( 3621 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication... | What is the solution to the long multiplication equation below?
9328 x 3621
Think step by step. | true | The solution correctly follows the distributive property and accurately computes the product of 9328 and 3621. The final answer derived from the summation of individual components matches the ground truth solution (33776688). Thus, the solution is deemed correct. | |
What is the solution to the long multiplication equation below?
9652 x 3026
Think step by step. | 29206952 | What is the solution to the long multiplication equation below?
9652 x 3026
Think step by step. | To solve the long multiplication equation \(9652 \times 3026\), 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 products... | What is the solution to the long multiplication equation below?
9652 x 3026
Think step by step. | true | The calculation of the multiplication was done step by step using the distributive property, yielding the correct final result of 29,206,952. Both the detailed breakdown and the verification through traditional long multiplication confirm the correctness of the answer. | |
What is the solution to the long multiplication equation below?
5218 x 2392
Think step by step. | 12481456 | What is the solution to the long multiplication equation below?
5218 x 2392
Think step by step. | To solve the long multiplication equation \(5218 \times 2392\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5218) by each digit of the multiplier (2392), accounting for place values, and then summing the partial... | What is the solution to the long multiplication equation below?
5218 x 2392
Think step by step. | true | The solution provided correctly applies the distributive property for the multiplication of 5218 by each component of 2392, leading to the correct final sum of 12,481,456. The verification step with traditional long multiplication confirms the accuracy, as both methods result in the same product. The final boxed answer... | |
What is the solution to the long multiplication equation below?
3564 x 5714
Think step by step. | 20364696 | What is the solution to the long multiplication equation below?
3564 x 5714
Think step by step. | To solve the long multiplication equation \( 3564 \times 5714 \), 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... | What is the solution to the long multiplication equation below?
3564 x 5714
Think step by step. | true | The given solution correctly uses the distributive property of multiplication over addition and verifies the result using long multiplication, yielding the correct final answer of 20364696. | |
What is the solution to the long multiplication equation below?
7014 x 3286
Think step by step. | 23048004 | What is the solution to the long multiplication equation below?
7014 x 3286
Think step by step. | To solve the long multiplication equation \(7014 \times 3286\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7014\) by each digit of \(3286\) (from right to left), shift the partial results appropriately, and then add them together.
#... | What is the solution to the long multiplication equation below?
7014 x 3286
Think step by step. | true | The solution correctly applies the distributive property of multiplication, breaks down the multiplication into smaller parts, calculates each part accurately, and adds them together correctly. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7536 x 2187
Think step by step. | 16481232 | What is the solution to the long multiplication equation below?
7536 x 2187
Think step by step. | To solve the multiplication problem \(7536 \times 2187\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(7536\) by each digit of \(2187\) (from right to left), shifting the partial results appropriately based on the digit's plac... | What is the solution to the long multiplication equation below?
7536 x 2187
Think step by step. | true | The solution correctly uses the long multiplication method to compute the product of 7536 and 2187. Each individual multiplication and the subsequent additions are accurately performed, leading to the correct final answer. | |
What is the solution to the long multiplication equation below?
3976 x 8951
Think step by step. | 35589176 | What is the solution to the long multiplication equation below?
3976 x 8951
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3976** and **8951**. 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: T... | What is the solution to the long multiplication equation below?
3976 x 8951
Think step by step. | true | The solution correctly follows the distributive property of multiplication, accurately computes each partial product, sums them correctly, and verifies with an alternative method, ultimately arriving at the correct final result of 35,589,176. | |
What is the solution to the long multiplication equation below?
4103 x 3218
Think step by step. | 13203454 | What is the solution to the long multiplication equation below?
4103 x 3218
Think step by step. | To solve the long multiplication equation \( 4103 \times 3218 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4103 \) by each digit of \( 3218 \) (considering their place values) and then add the results together.
### Step 1: Break ... | What is the solution to the long multiplication equation below?
4103 x 3218
Think step by step. | false | The solution's final answer provided as '13,203,454' (formatted with a comma) is not the same value as the ground truth solution '13203454' (without a comma). The numeric value is correct, but the formatting leads to a misunderstanding in the comparison for correctness. | |
What is the solution to the long multiplication equation below?
2793 x 9199
Think step by step. | 25692807 | What is the solution to the long multiplication equation below?
2793 x 9199
Think step by step. | To solve the long multiplication equation \( 2793 \times 9199 \), 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 (9199)
Notice that \( 9199 \) is very close to \( 10,000 \). Specifically:
\[ 9199 = 10,000 - 801... | What is the solution to the long multiplication equation below?
2793 x 9199
Think step by step. | true | The solution provided correctly calculates the product of 2793 and 9199 using both the distributive property and a verification via long multiplication. The final computed value (25,692,807) matches the ground truth despite the difference in formatting. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
6418 x 3649
Think step by step. | 23419282 | What is the solution to the long multiplication equation below?
6418 x 3649
Think step by step. | To solve the long multiplication equation \( 6418 \times 3649 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 6418 \) by each digit of \( 3649 \) (starting from the rightmost digit) and then sum the results, taking care to align the ... | What is the solution to the long multiplication equation below?
6418 x 3649
Think step by step. | true | The solution correctly uses the distributive property of multiplication and aligns the calculations accurately. After summing all the partial products, the final result obtained is 23,419,282, which matches the ground truth solution of 23419282 (ignoring the formatting with commas), confirming the correctness of the so... | |
What is the solution to the long multiplication equation below?
4463 x 3496
Think step by step. | 15602648 | What is the solution to the long multiplication equation below?
4463 x 3496
Think step by step. | Alright, let's tackle the multiplication problem: **4463 × 3496**. Multiplying large numbers can seem daunting, but breaking it down into smaller, more manageable steps makes it much easier. Here's how I'll approach it:
### Understanding the Problem
We need to multiply two four-digit numbers: 4,463 and 3,496. One eff... | What is the solution to the long multiplication equation below?
4463 x 3496
Think step by step. | true | The provided solution correctly details the steps of long multiplication and accurately computes the final product of 4,463 × 3,496, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
3606 x 1808
Think step by step. | 6519648 | What is the solution to the long multiplication equation below?
3606 x 1808
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two four-digit numbers: 3606 and 1808. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it down using the **di... | What is the solution to the long multiplication equation below?
3606 x 1808
Think step by step. | true | The solution correctly breaks down the multiplication of 3606 and 1808 using the distributive property and steps for long multiplication. All calculations are accurate, leading to the correct final answer of 6,519,648, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6432 x 5744
Think step by step. | 36945408 | What is the solution to the long multiplication equation below?
6432 x 5744
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6432** and **5744**. 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 (5744) by the fir... | What is the solution to the long multiplication equation below?
6432 x 5744
Think step by step. | true | The solution correctly follows the process of long multiplication, breaking down each step and verifying the calculations through multiple methods. The final result of 36945408 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
9775 x 6950
Think step by step. | 67936250 | What is the solution to the long multiplication equation below?
9775 x 6950
Think step by step. | To solve the long multiplication equation \( 9775 \times 6950 \), 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 \( 6950 \) as \( 7000 - 50 \). This allows us to multiply \( 977... | What is the solution to the long multiplication equation below?
9775 x 6950
Think step by step. | true | The solution correctly calculates the product of 9775 and 6950 using the distributive property, and confirms the result using standard long multiplication. Both methods yield the final answer of 67936250, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
7520 x 6403
Think step by step. | 48150560 | What is the solution to the long multiplication equation below?
7520 x 6403
Think step by step. | To solve the multiplication problem \( 7520 \times 6403 \), 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
The multiplier \( 6403 \) can be expressed as:
\[ 6403 = 6000 + 400 + 0 + 3 \]
### Step 2: Multipl... | What is the solution to the long multiplication equation below?
7520 x 6403
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication and accurately calculates each component before summing them up. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3184 x 4238
Think step by step. | 13493792 | What is the solution to the long multiplication equation below?
3184 x 4238
Think step by step. | To solve the long multiplication equation \( 3184 \times 4238 \), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 3184 \) by each digit of \( 4238 \), starting from the rightmost digit (units place), and shift t... | What is the solution to the long multiplication equation below?
3184 x 4238
Think step by step. | true | The provided solution correctly follows the long multiplication method step by step, accurately computing each partial product and summing them to arrive at the final answer. The final answer, formatted with commas, matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7052 x 2233
Think step by step. | 15747116 | What is the solution to the long multiplication equation below?
7052 x 2233
Think step by step. | To solve the long multiplication equation \(7052 \times 2233\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7052) by each digit of the multiplier (2233), starting from the rightmost digit, and then summing the p... | What is the solution to the long multiplication equation below?
7052 x 2233
Think step by step. | true | The solution correctly computes the product of 7052 and 2233 using the distributive property of multiplication and confirms the result with standard long multiplication, arriving at the same total of 15747116. | |
What is the solution to the long multiplication equation below?
1190 x 8334
Think step by step. | 9917460 | What is the solution to the long multiplication equation below?
1190 x 8334
Think step by step. | To solve the long multiplication equation \( 1190 \times 8334 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's how to do it step by step:
### Step 1: Break down the multiplication
We can express \( 8334 \) as \( 8000 + 300 + 30 + 4... | What is the solution to the long multiplication equation below?
1190 x 8334
Think step by step. | true | The solution correctly applies the distributive property of multiplication and carefully breaks down the operations into manageable parts, verifying them step by step. The final addition steps are calculated accurately, confirming that the result matches the ground truth solution of 9917460. | |
What is the solution to the long multiplication equation below?
7140 x 7579
Think step by step. | 54114060 | What is the solution to the long multiplication equation below?
7140 x 7579
Think step by step. | To solve the multiplication problem \(7140 \times 7579\), 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 (7579)
Express \(7579\) as \(8000 - 421\) (since \(8000 - 421 = 7579\)).
### Step 2: Multiply 7140 b... | What is the solution to the long multiplication equation below?
7140 x 7579
Think step by step. | true | The provided solution correctly applies the distributive property of multiplication and accurately calculates each step of the multiplication process. The final answer matches the ground truth of 54114060. | |
What is the solution to the long multiplication equation below?
2335 x 2844
Think step by step. | 6640740 | What is the solution to the long multiplication equation below?
2335 x 2844
Think step by step. | To solve the long multiplication equation \( 2335 \times 2844 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2335 \) by each digit of \( 2844 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
2335 x 2844
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts, performs each calculation accurately, and sums the partial results correctly. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8811 x 6837
Think step by step. | 60240807 | What is the solution to the long multiplication equation below?
8811 x 6837
Think step by step. | To solve the multiplication problem \( 8811 \times 6837 \), 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 \( 6837 \) as \( 6000 + 800 + 30 + 7 \). Multiplying \( 8811 \) by each of these component... | What is the solution to the long multiplication equation below?
8811 x 6837
Think step by step. | true | The solution correctly applies the long multiplication method and combines the individual products accurately. The final computed result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5043 x 6118
Think step by step. | 30853074 | What is the solution to the long multiplication equation below?
5043 x 6118
Think step by step. | To solve the multiplication problem \(5043 \times 6118\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5043\) by each digit of \(6118\), starting from the rightmost digit (units place) and moving left. Remember to account for ... | What is the solution to the long multiplication equation below?
5043 x 6118
Think step by step. | true | The solution correctly follows the long multiplication method step by step, calculates each intermediate result accurately, and verifies the addition of the partial products correctly, leading to the final answer of 30853074, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7219 x 4786
Think step by step. | 34550134 | What is the solution to the long multiplication equation below?
7219 x 4786
Think step by step. | To solve the long multiplication equation \( 7219 \times 4786 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7219 \) by each digit of \( 4786 \), accounting for the place value, and then sum all the partial products.
### Step 1: Br... | What is the solution to the long multiplication equation below?
7219 x 4786
Think step by step. | true | The provided solution accurately breaks down the multiplication step by step using the distributive property. Each partial product is calculated correctly, and the final sum of all the partial products equals the ground truth solution of 34,550,134 when formatted. The final answer is equivalent to the ground truth solu... | |
What is the solution to the long multiplication equation below?
8080 x 2683
Think step by step. | 21678640 | What is the solution to the long multiplication equation below?
8080 x 2683
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8080** and **2683**. At first glance, this seems daunting because both numbers are in the thousands. However, breaking it down into simpler, more manageable parts can make the process easier.
### Breaking Down the Multiplication
One effect... | What is the solution to the long multiplication equation below?
8080 x 2683
Think step by step. | true | The provided solution employs the long multiplication method accurately, breaking down both numbers and calculating partial products correctly. The sums of these partial products were also verified step-by-step and consistently arrived at the same final result of 21,678,640, which matches the ground truth. Therefore, t... | |
What is the solution to the long multiplication equation below?
2508 x 6198
Think step by step. | 15544584 | What is the solution to the long multiplication equation below?
2508 x 6198
Think step by step. | To solve the multiplication problem \( 2508 \times 6198 \), 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 \( 6198 \) as \( 6000 + 200 - 2 \) (since \( 6000 + 200 - 2 = 6198 \)). This allows us to ... | What is the solution to the long multiplication equation below?
2508 x 6198
Think step by step. | true | The provided solution correctly calculates the product of 2508 and 6198 using both the distributive property and long multiplication, ultimately confirming the answer as 15544584, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1623 x 7460
Think step by step. | 12107580 | What is the solution to the long multiplication equation below?
1623 x 7460
Think step by step. | To solve the long multiplication equation \(1623 \times 7460\), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can express \(7460\) as \(7000 + 400 + 60 + 0\). This allows us to multiply \(1623\) by each component separat... | What is the solution to the long multiplication equation below?
1623 x 7460
Think step by step. | true | The step-by-step approach presented in the solution correctly breaks down the multiplication, calculates each component accurately, and sums them up correctly. The final answer matches the ground truth solution, thus confirming its correctness. | |
What is the solution to the long multiplication equation below?
5494 x 1866
Think step by step. | 10251804 | What is the solution to the long multiplication equation below?
5494 x 1866
Think step by step. | To solve the long multiplication equation \( 5494 \times 1866 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (5494) by each digit of the multiplier (1866), starting from the rightmost digit, and then summing the... | What is the solution to the long multiplication equation below?
5494 x 1866
Think step by step. | true | The solution provided follows the correct process for performing long multiplication, applying the distributive property accurately, and results in the same final answer as the ground truth solution (10,251,804). The calculations for the multiplicative parts are correct, the addition is carried out correctly, and the f... | |
What is the solution to the long multiplication equation below?
1057 x 1747
Think step by step. | 1846579 | What is the solution to the long multiplication equation below?
1057 x 1747
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1057** and **1747**. At first glance, both numbers are in the thousands, and multiplying them directly seems daunting. However, I recall that breaking the problem into smaller, more manageable parts can make it easier. This is where the **lon... | What is the solution to the long multiplication equation below?
1057 x 1747
Think step by step. | true | The provided solution is correct as it accurately calculated the product of the two numbers, 1057 and 1747, resulting in 1846579, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1779 x 7459
Think step by step. | 13269561 | What is the solution to the long multiplication equation below?
1779 x 7459
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1779** and **7459**. 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 (7459) by the first ... | What is the solution to the long multiplication equation below?
1779 x 7459
Think step by step. | true | The provided solution correctly implements the multiplication of the two large numbers 1779 and 7459 using the breakdown and addition of partial products. It confirms each step with the distributive property and validates the final sum using both step-by-step recounting and traditional long multiplication, ultimately a... | |
What is the solution to the long multiplication equation below?
3919 x 3698
Think step by step. | 14492462 | What is the solution to the long multiplication equation below?
3919 x 3698
Think step by step. | To solve the long multiplication equation \( 3919 \times 3698 \), 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... | What is the solution to the long multiplication equation below?
3919 x 3698
Think step by step. | true | The solution outlined the multiplication process through the distributive property correctly, computed all the partial products accurately, and presented the final sum matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
1559 x 6696
Think step by step. | 10439064 | What is the solution to the long multiplication equation below?
1559 x 6696
Think step by step. | To solve the multiplication \( 1559 \times 6696 \), 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 \( 6696 \) as \( 6000 + 600 + 90 + 6 \), and then multiply \( 1559 \) by each of these components ... | What is the solution to the long multiplication equation below?
1559 x 6696
Think step by step. | true | The solution correctly employs the long multiplication method and accurately breaks down the multiplication into manageable components. All partial products were calculated correctly, and the final sum of these products matches the ground truth solution of 10439064. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
8754 x 9055
Think step by step. | 79267470 | What is the solution to the long multiplication equation below?
8754 x 9055
Think step by step. | To solve the multiplication problem \( 8754 \times 9055 \), we'll break it down using the **long multiplication method**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 9055 \) as \( 9000 + 50 + 5 \). This allows us to multiply \( 8754 \) by each component separately and th... | What is the solution to the long multiplication equation below?
8754 x 9055
Think step by step. | true | The solution provided correctly uses the long multiplication method to break down the multiplication of 8754 and 9055, accurately calculates each component separately, and then correctly adds them together to arrive at the final result. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8105 x 7436
Think step by step. | 60268780 | What is the solution to the long multiplication equation below?
8105 x 7436
Think step by step. | To solve the long multiplication equation \( 8105 \times 7436 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8105 \) by each digit of \( 7436 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
8105 x 7436
Think step by step. | true | The solution accurately calculates the product of 8105 and 7436 using step-by-step multiplication and addition of partial products. The final result of 60268780 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1993 x 7799
Think step by step. | 15543407 | What is the solution to the long multiplication equation below?
1993 x 7799
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1993** and **7799**. 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... | What is the solution to the long multiplication equation below?
1993 x 7799
Think step by step. | true | The solution provided correctly calculates the product of 1993 and 7799, arriving at the answer 15,543,407, which matches the ground truth solution. The steps taken, including long multiplication and alternative verifying methods, are thorough and accurate. | |
What is the solution to the long multiplication equation below?
8959 x 5378
Think step by step. | 48181502 | What is the solution to the long multiplication equation below?
8959 x 5378
Think step by step. | To solve the long multiplication equation \( 8959 \times 5378 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8959 \) by each digit of \( 5378 \), starting from the rightmost digit, and then sum the results, taking into account the p... | What is the solution to the long multiplication equation below?
8959 x 5378
Think step by step. | true | The solution correctly calculates the product of 8959 and 5378 using both the distributive property and standard long multiplication methods. Both methods yield the same result of 48181502, albeit formatted differently; the lead zeroes are just for clarity in formatting. Thus, the final result, boxed as 48,181,502, mat... | |
What is the solution to the long multiplication equation below?
4354 x 7343
Think step by step. | 31971422 | What is the solution to the long multiplication equation below?
4354 x 7343
Think step by step. | To solve the long multiplication equation \(4354 \times 7343\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4354) by each digit of the multiplier (7343), starting from the rightmost digit, and then summing all t... | What is the solution to the long multiplication equation below?
4354 x 7343
Think step by step. | true | The calculated result of 31,971,422 matches the ground truth solution of 31971422 when formatted without commas. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
9748 x 5875
Think step by step. | 57269500 | What is the solution to the long multiplication equation below?
9748 x 5875
Think step by step. | To solve the long multiplication equation \( 9748 \times 5875 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9748 \) by each digit of \( 5875 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
9748 x 5875
Think step by step. | true | The solution provided accurately breaks down and computes the multiplication of 9748 by 5875 step by step, using the distributive property correctly. The final answer is formatted correctly with commas, matching the ground truth solution of 57269500 exactly. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
6755 x 8339
Think step by step. | 56329945 | What is the solution to the long multiplication equation below?
6755 x 8339
Think step by step. | To solve the long multiplication equation \( 6755 \times 8339 \), 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 (8339) by the first number (6755) and then summing the results.
### Step 1: Break down... | What is the solution to the long multiplication equation below?
6755 x 8339
Think step by step. | true | The provided solution correctly follows the distributive property of multiplication over addition to calculate the product of 6755 and 8339. Each partial multiplication is carried out correctly, and the sums of the intermediate results lead accurately to the final answer. Both the solution and the ground truth match, c... | |
What is the solution to the long multiplication equation below?
1927 x 8910
Think step by step. | 17169570 | What is the solution to the long multiplication equation below?
1927 x 8910
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1927** and **8910**. 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 ... | What is the solution to the long multiplication equation below?
1927 x 8910
Think step by step. | true | The solution provided arrives at the correct final product of multiplying 1927 and 8910, which is indeed 17169570. The calculation process is detailed and correct, using appropriate multiplication methods and verifying the answer through an alternate method. The final boxed answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4506 x 1304
Think step by step. | 5875824 | What is the solution to the long multiplication equation below?
4506 x 1304
Think step by step. | To solve the long multiplication equation \(4506 \times 1304\), 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... | What is the solution to the long multiplication equation below?
4506 x 1304
Think step by step. | true | The final answer from the solution is written as 5,875,824 with commas, while the ground truth solution is presented as 5875824 without commas. However, they represent the same numerical value because the commas are just formatting and do not affect the value. Thus, the solution is correct. | |
What is the solution to the long multiplication equation below?
2525 x 4943
Think step by step. | 12481075 | What is the solution to the long multiplication equation below?
2525 x 4943
Think step by step. | To solve the multiplication problem \(2525 \times 4943\), 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 \(4943\) as \(5000 - 57\), which allows us to rewrite the multiplication as:
\[
2525 \times ... | What is the solution to the long multiplication equation below?
2525 x 4943
Think step by step. | true | The solution correctly uses the long multiplication method and applies the distributive property to break down the multiplication of 2525 and 4943. Each step is performed accurately, resulting in the correct final answer of 12481075. | |
What is the solution to the long multiplication equation below?
2732 x 4179
Think step by step. | 11417028 | What is the solution to the long multiplication equation below?
2732 x 4179
Think step by step. | To solve the long multiplication equation \( 2732 \times 4179 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2732 \) by each digit of \( 4179 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
2732 x 4179
Think step by step. | true | The solution provided correctly follows the steps of long multiplication, breaks down the components accurately, and sums the partial results to arrive at the final answer of 11,417,028, which matches the ground truth solution of 11417028. | |
What is the solution to the long multiplication equation below?
5677 x 6727
Think step by step. | 38189179 | What is the solution to the long multiplication equation below?
5677 x 6727
Think step by step. | To solve the multiplication problem \(5677 \times 6727\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(5677\) by each digit of \(6727\) (from right to left), keeping track of the place values by adding zeros as we move left.
... | What is the solution to the long multiplication equation below?
5677 x 6727
Think step by step. | true | The solution correctly computes the multiplication of 5677 and 6727 using the long multiplication method, breaking down the steps accurately and summing the results to arrive at the final answer. The final boxed answer matches the ground truth solution when formatted without commas. | |
What is the solution to the long multiplication equation below?
6402 x 5880
Think step by step. | 37643760 | What is the solution to the long multiplication equation below?
6402 x 5880
Think step by step. | To solve the long multiplication equation \( 6402 \times 5880 \), we can break it down into simpler, more manageable steps. Here's a detailed, step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. Notice that \( 5880 \) ... | What is the solution to the long multiplication equation below?
6402 x 5880
Think step by step. | true | The solution provided correctly evaluates the multiplication step-by-step and confirms the final result through two methods. Both the calculated result and the ground truth solution match, therefore the answer is deemed correct. | |
What is the solution to the long multiplication equation below?
5362 x 9925
Think step by step. | 53217850 | What is the solution to the long multiplication equation below?
5362 x 9925
Think step by step. | To solve the multiplication problem \( 5362 \times 9925 \), 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 (9925)
Notice that \( 9925 \) can be expressed as \( 10000 - 75 \). This simplifies the multiplicat... | What is the solution to the long multiplication equation below?
5362 x 9925
Think step by step. | false | The calculated answer in the solution is 53,217,850, while the ground truth solution is 53,217,850. However, upon verifying the subtraction step, the second product is calculated as 402,150. The subtraction of 53,620,000 - 402,150 yields 53,217,850, which confirms that the solution is incorrect due to the earlier misre... | |
What is the solution to the long multiplication equation below?
4805 x 1895
Think step by step. | 9105475 | What is the solution to the long multiplication equation below?
4805 x 1895
Think step by step. | To solve the multiplication problem \(4805 \times 1895\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the second number (1895) into its constituent parts
We can express \(1895\) as:
\[ 1895 = 2000 - 100 - 5 \]
### Step 2: Multiply 4805 by each part of 1895
No... | What is the solution to the long multiplication equation below?
4805 x 1895
Think step by step. | true | The solution provided follows the long multiplication method correctly, breaking down the numbers and performing each multiplication and subtraction as needed. The final result matches the ground truth solution exactly. | |
What is the solution to the long multiplication equation below?
6200 x 2769
Think step by step. | 17167800 | What is the solution to the long multiplication equation below?
6200 x 2769
Think step by step. | To solve the long multiplication equation \(6200 \times 2769\), 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 \(6200 \times 2769\) as:
\[ 6200 \times 2769 = 6200 \times (2000 + 700 + 60... | What is the solution to the long multiplication equation below?
6200 x 2769
Think step by step. | true | The solution correctly calculates the product of 6200 and 2769 step by step using the distributive property and accurately sums the partial products to arrive at the correct final answer of 17167800. | |
What is the solution to the long multiplication equation below?
1548 x 4738
Think step by step. | 7334424 | What is the solution to the long multiplication equation below?
1548 x 4738
Think step by step. | To solve the long multiplication problem \(1548 \times 4738\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(1548\) by each digit of \(4738\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
We ca... | What is the solution to the long multiplication equation below?
1548 x 4738
Think step by step. | true | The solution accurately follows the distributive property of multiplication and correctly executes every multiplication step. The partial products have been correctly calculated and summed up to yield the final result, which matches the ground truth. Thus, the final answer is correct. | |
What is the solution to the long multiplication equation below?
7612 x 4310
Think step by step. | 32807720 | What is the solution to the long multiplication equation below?
7612 x 4310
Think step by step. | To solve the long multiplication equation \( 7612 \times 4310 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 4310 \) as \( 4000 + 300 + 10 \). This allows us to multiply \( 7612 \) by each component sepa... | What is the solution to the long multiplication equation below?
7612 x 4310
Think step by step. | true | The step-by-step solution provided for the multiplication of 7612 and 4310 is accurate. The breakdown into parts, the intermediate calculations for each multiplication, and the final addition of these partial results all lead to the correct final answer of 32,807,720, which matches the ground truth solution of 32807720... | |
What is the solution to the long multiplication equation below?
9280 x 3654
Think step by step. | 33909120 | What is the solution to the long multiplication equation below?
9280 x 3654
Think step by step. | To solve the long multiplication equation \( 9280 \times 3654 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9280) by each digit of the multiplier (3654), starting from the rightmost digit, and then summing up ... | What is the solution to the long multiplication equation below?
9280 x 3654
Think step by step. | true | The solution accurately employs the distributive property to break down the multiplication and arrives at the correct total of 33,909,120, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5759 x 9830
Think step by step. | 56610970 | What is the solution to the long multiplication equation below?
5759 x 9830
Think step by step. | To solve the long multiplication equation \( 5759 \times 9830 \), we can break it down into simpler, more manageable steps. Here's a detailed step-by-step solution:
### Step 1: Break down the multiplication
We can use the distributive property of multiplication over addition to break the problem into smaller parts. Sp... | What is the solution to the long multiplication equation below?
5759 x 9830
Think step by step. | true | The solution correctly follows a systematic long multiplication approach, breaking down the multiplication into parts, calculating each separately, and then summing them up correctly. The final answer matches the ground truth solution, which confirms the correctness. | |
What is the solution to the long multiplication equation below?
1980 x 7203
Think step by step. | 14261940 | What is the solution to the long multiplication equation below?
1980 x 7203
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1980** and **7203**. At first glance, both numbers seem a bit complex, but I recall that breaking them down using the distributive property of multiplication over addition can simplify the process. This is often referred to as the **long mult... | What is the solution to the long multiplication equation below?
1980 x 7203
Think step by step. | true | The provided solution accurately employs the distributive property and verifies calculations through two different methods (long multiplication and FOIL) leading to the final result of 14,261,940. This is exactly equal to the ground truth solution. | |
What is the solution to the long multiplication equation below?
7242 x 4902
Think step by step. | 35500284 | What is the solution to the long multiplication equation below?
7242 x 4902
Think step by step. | To solve the multiplication problem \( 7242 \times 4902 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 4902 \) as \( 5000 - 98 \). This allows us to use the **distributive property** of multiplication over addition/subtrac... | What is the solution to the long multiplication equation below?
7242 x 4902
Think step by step. | true | The solution provided matches the ground truth solution of 35500284. The step-by-step breakdown and verification via long multiplication confirms the accuracy of the calculations. | |
What is the solution to the long multiplication equation below?
3980 x 1169
Think step by step. | 4652620 | What is the solution to the long multiplication equation below?
3980 x 1169
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3980** and **1169**. 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.
### Breaking Down the Multiplication
One effecti... | What is the solution to the long multiplication equation below?
3980 x 1169
Think step by step. | true | The provided solution accurately breaks down the multiplication of 3980 and 1169 using long multiplication, and includes detailed calculations to verify the final result. The final answer matches the ground truth solution of 4652620. | |
What is the solution to the long multiplication equation below?
6827 x 8228
Think step by step. | 56172556 | What is the solution to the long multiplication equation below?
6827 x 8228
Think step by step. | To solve the long multiplication equation \(6827 \times 8228\), 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 (8228) by each digit of the first number (6827) and then adding all the partial products ... | What is the solution to the long multiplication equation below?
6827 x 8228
Think step by step. | true | The provided solution accurately calculates the product of 6827 and 8228 using the distributive property, and the final answer matches the given ground truth solution of 56172556. | |
What is the solution to the long multiplication equation below?
9952 x 3833
Think step by step. | 38146016 | What is the solution to the long multiplication equation below?
9952 x 3833
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9952** and **3833**. 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... | What is the solution to the long multiplication equation below?
9952 x 3833
Think step by step. | true | The calculated result of 38,146,016 from the provided solution matches the ground truth solution of 38146016 exactly. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
7321 x 5326
Think step by step. | 38991646 | What is the solution to the long multiplication equation below?
7321 x 5326
Think step by step. | To solve the long multiplication problem \(7321 \times 5326\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7321\) by each digit of \(5326\), starting from the rightmost digit, and then sum the results, taking care to shift each partia... | What is the solution to the long multiplication equation below?
7321 x 5326
Think step by step. | true | The solution correctly follows the steps of long multiplication, verifies the intermediate calculations, and arrives at the correct final answer of 38,991,646, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2010 x 3587
Think step by step. | 7209870 | What is the solution to the long multiplication equation below?
2010 x 3587
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2010** and **3587**. 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 (3587) by the first ... | What is the solution to the long multiplication equation below?
2010 x 3587
Think step by step. | true | The solution provided arrives at the correct answer of 7,209,870 through various methods, including long multiplication and the distributive property, matching the ground truth solution of 7209870. Therefore, the solution is correct. |
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