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?
3858 x 4539
Think step by step. | 17511462 | What is the solution to the long multiplication equation below?
3858 x 4539
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3858** and **4539**. 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: The Distrib... | What is the solution to the long multiplication equation below?
3858 x 4539
Think step by step. | true | The solution correctly calculates the product of 3858 and 4539 through the use of the distributive property, breaks down the problem into manageable parts, and verifies the accuracy of the final result with long multiplication. The final answer of 1.7511462 × 10^7 is equivalent to the ground truth solution of 17511462. | |
What is the solution to the long multiplication equation below?
8852 x 9918
Think step by step. | 87794136 | What is the solution to the long multiplication equation below?
8852 x 9918
Think step by step. | To solve the multiplication problem \( 8852 \times 9918 \), 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 \( 9918 \) as \( 10000 - 82 \), which allows us to rewrite the multiplication as:
\[
8852 ... | What is the solution to the long multiplication equation below?
8852 x 9918
Think step by step. | false | The final answer given in the solution is 87,794,136, but the ground truth solution states it as 87794136, which is missing the commas for clarity but is actually the same numerical value. However, if the expected output format strictly requires matching (including commas or formatting), then the provided solution coul... | |
What is the solution to the long multiplication equation below?
5444 x 6710
Think step by step. | 36529240 | What is the solution to the long multiplication equation below?
5444 x 6710
Think step by step. | To solve the long multiplication equation \(5444 \times 6710\), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to break the problem into smaller parts. Specifically, we can mu... | What is the solution to the long multiplication equation below?
5444 x 6710
Think step by step. | true | The given solution provides a detailed step-by-step process for computing the product of 5444 and 6710 and arrives at the final answer of 36,529,240, which matches the ground truth solution provided (36529240). The formatting difference with commas does not affect the numerical correctness, confirming that the answer i... | |
What is the solution to the long multiplication equation below?
5614 x 1767
Think step by step. | 9919938 | What is the solution to the long multiplication equation below?
5614 x 1767
Think step by step. | To solve the long multiplication equation \(5614 \times 1767\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5614\) by each digit of \(1767\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | What is the solution to the long multiplication equation below?
5614 x 1767
Think step by step. | true | The solution provided matches the ground truth solution of 9919938 after proper calculations through both the distributive property breakdown and verifying through standard long multiplication. The steps taken are clear, systematic, and arrive at the correct final product. | |
What is the solution to the long multiplication equation below?
3912 x 3777
Think step by step. | 14775624 | What is the solution to the long multiplication equation below?
3912 x 3777
Think step by step. | To solve the multiplication problem \( 3912 \times 3777 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 3777 \) as \( 4000 - 223 \). This allows us to rewrite the multiplication as:
\[
3912 \times 3777 = 3912 \times (4000 -... | What is the solution to the long multiplication equation below?
3912 x 3777
Think step by step. | false | The solution provided calculated the final answer as 14,775,624, while the ground truth solution states the correct answer is 14,775,624. The two numbers, despite appearing similar, actually differ after the conversion to standard numerical format. The mistakes in the multiplications or additions cannot be traced preci... | |
What is the solution to the long multiplication equation below?
7421 x 7349
Think step by step. | 54536929 | What is the solution to the long multiplication equation below?
7421 x 7349
Think step by step. | To solve the long multiplication equation \(7421 \times 7349\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (7349) by the first number (7421) and then summing the results. Here's the step-by-step solution:
###... | What is the solution to the long multiplication equation below?
7421 x 7349
Think step by step. | true | The provided solution correctly follows the steps of long multiplication and verifies the result using both the distributive property and the long multiplication method, arriving at the same final product of 54,536,929. | |
What is the solution to the long multiplication equation below?
7454 x 6402
Think step by step. | 47720508 | What is the solution to the long multiplication equation below?
7454 x 6402
Think step by step. | To solve the long multiplication equation \(7454 \times 6402\), 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 the results.
### Step 1: Bre... | What is the solution to the long multiplication equation below?
7454 x 6402
Think step by step. | true | The provided solution correctly uses the distributive property to perform long multiplication and arrives at the correct final result of 47720508, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6773 x 6103
Think step by step. | 41335619 | What is the solution to the long multiplication equation below?
6773 x 6103
Think step by step. | To solve the long multiplication equation \( 6773 \times 6103 \), we can use the **distributive property of multiplication over addition**, also known as the **FOIL method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Express \( 6103 \) as \( 6000 + 100 + 3 \). Then multiply \( 6773 \) ... | What is the solution to the long multiplication equation below?
6773 x 6103
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication and accurately calculates the products and the final sum, resulting in the correct answer of 41335619, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
9634 x 7708
Think step by step. | 74258872 | What is the solution to the long multiplication equation below?
9634 x 7708
Think step by step. | To solve the long multiplication equation \(9634 \times 7708\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9634\) by each digit of \(7708\) (from right to left), shifting the partial results appropriately, and then add them together.... | What is the solution to the long multiplication equation below?
9634 x 7708
Think step by step. | true | The solution provided follows a step-by-step breakdown of the long multiplication process, accurately applying the distributive property of multiplication and correctly summing the partial products to arrive at the final result of 74,258,872. This matches the ground truth solution, confirming that the solution is corre... | |
What is the solution to the long multiplication equation below?
3779 x 8361
Think step by step. | 31596219 | What is the solution to the long multiplication equation below?
3779 x 8361
Think step by step. | To solve the multiplication problem \( 3779 \times 8361 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \( 3779 \) by each digit of \( 8361 \), starting from the rightmost digit (units place), and shift the partial results according... | What is the solution to the long multiplication equation below?
3779 x 8361
Think step by step. | true | The solution provided uses long multiplication accurately, breaking down the multiplication into manageable parts by correctly calculating each partial product and aligning them according to their place values. The final sum of the partial products correctly results in the answer 31596219, which matches the ground trut... | |
What is the solution to the long multiplication equation below?
4907 x 4934
Think step by step. | 24211138 | What is the solution to the long multiplication equation below?
4907 x 4934
Think step by step. | To solve the long multiplication equation \( 4907 \times 4934 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4907 \) by each digit of \( 4934 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | What is the solution to the long multiplication equation below?
4907 x 4934
Think step by step. | false | The solution provided sums the results incorrectly and has a formatting mistake in the final answer. The final total calculated as '24,211,138' is not equal to the ground truth '24211138' due to the inclusion of an unnecessary comma, which alters the numerical value. Therefore, the final solution is incorrect. | |
What is the solution to the long multiplication equation below?
3522 x 2181
Think step by step. | 7681482 | What is the solution to the long multiplication equation below?
3522 x 2181
Think step by step. | To solve the multiplication problem \( 3522 \times 2181 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3522 \) by each digit of \( 2181 \), starting from the rightmost digit (units place), and shift the partial results acc... | What is the solution to the long multiplication equation below?
3522 x 2181
Think step by step. | true | The solution provided follows the long multiplication method accurately step by step and correctly computes the final product of 3522 and 2181, which matches the ground truth solution of 7681482. | |
What is the solution to the long multiplication equation below?
4317 x 2004
Think step by step. | 8651268 | What is the solution to the long multiplication equation below?
4317 x 2004
Think step by step. | To solve the multiplication problem \(4317 \times 2004\), 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 (2004)
The number \(2004\) can be expressed as:
\[ 2004 = 2000 + 4 \]
### Step 2: Multiply 4317 by e... | What is the solution to the long multiplication equation below?
4317 x 2004
Think step by step. | true | The solution provided correctly applies the distributive property to break down the multiplication of 4317 by 2004, resulting in the same final answer as the ground truth. The calculations for both parts (4317 times 2000 and 4317 times 4) are accurate, leading to the correct final result of 8651268. This matches exactl... | |
What is the solution to the long multiplication equation below?
5685 x 1506
Think step by step. | 8561610 | What is the solution to the long multiplication equation below?
5685 x 1506
Think step by step. | To solve the long multiplication equation \( 5685 \times 1506 \), 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 (1506)
The number \( 1506 \) can be expressed as:
\[ 1506 = 1000 + 500 + 6 \]
### Step 2: Multip... | What is the solution to the long multiplication equation below?
5685 x 1506
Think step by step. | true | The solution follows a correct method for long multiplication using the distributive property, and the calculated answer of 8,561,610 matches the ground truth solution of 8561610. | |
What is the solution to the long multiplication equation below?
7029 x 5683
Think step by step. | 39945807 | What is the solution to the long multiplication equation below?
7029 x 5683
Think step by step. | To solve the long multiplication equation \(7029 \times 5683\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(7029\) by each digit of \(5683\), starting from the rightmost digit, and then sum the results, taking care to align the partia... | What is the solution to the long multiplication equation below?
7029 x 5683
Think step by step. | false | The final result of the solution provided is 39,945,807, which does not match the ground truth solution of 39,945,807 due to a typographical difference in formatting. The numbers are indeed equal, but the presentation leads to the interpretation of a discrepancy. | |
What is the solution to the long multiplication equation below?
5016 x 1507
Think step by step. | 7559112 | What is the solution to the long multiplication equation below?
5016 x 1507
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: **5016** and **1507**. 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... | What is the solution to the long multiplication equation below?
5016 x 1507
Think step by step. | true | The solution correctly breaks down the multiplication steps using long multiplication and verifies its calculations through alternative methods, arriving at the same final product of 7,559,112, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2403 x 7261
Think step by step. | 17448183 | What is the solution to the long multiplication equation below?
2403 x 7261
Think step by step. | To solve the long multiplication equation \( 2403 \times 7261 \), 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 (7261) by each digit of the first number (2403) and then summing the results.
### Step... | What is the solution to the long multiplication equation below?
2403 x 7261
Think step by step. | false | The solution provided calculates the multiplication correctly step by step but concludes with the wrong final result. The correct result of the multiplication is indeed 17,448,183, but the ground truth solution lists it as 17448183, which is incorrectly formatted (missing the thousands separator). However, it is clear ... | |
What is the solution to the long multiplication equation below?
3712 x 6657
Think step by step. | 24710784 | What is the solution to the long multiplication equation below?
3712 x 6657
Think step by step. | To solve the multiplication problem \( 3712 \times 6657 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3712 \) by each digit of \( 6657 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | What is the solution to the long multiplication equation below?
3712 x 6657
Think step by step. | true | The solution has correctly performed the long multiplication of 3712 and 6657, providing accurate partial products and correctly summing them up to arrive at the final answer of 24,710,784. This matches the ground truth solution when formatted without commas. | |
What is the solution to the long multiplication equation below?
4058 x 5159
Think step by step. | 20935222 | What is the solution to the long multiplication equation below?
4058 x 5159
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4058** and **5159**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts.
### Breaking Down the Multip... | What is the solution to the long multiplication equation below?
4058 x 5159
Think step by step. | true | The solution correctly outlined the steps for long multiplication, carefully computed all partial products, and accurately added them to arrive at the correct final result of 20,935,222. The verification using an alternative method confirmed the accuracy of the calculations. | |
What is the solution to the long multiplication equation below?
4171 x 8596
Think step by step. | 35853916 | What is the solution to the long multiplication equation below?
4171 x 8596
Think step by step. | To solve the long multiplication equation \( 4171 \times 8596 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (8596) by each digit of the first number (4171) and then summing the results. Here's a step-by-step ... | What is the solution to the long multiplication equation below?
4171 x 8596
Think step by step. | true | The solution follows a valid step-by-step approach using the distributive property of multiplication. I have verified the final result of the multiplication, which matches the ground truth solution exactly. Therefore, the solution is deemed correct. | |
What is the solution to the long multiplication equation below?
8666 x 5029
Think step by step. | 43581314 | What is the solution to the long multiplication equation below?
8666 x 5029
Think step by step. | To solve the long multiplication equation \( 8666 \times 5029 \), 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?
8666 x 5029
Think step by step. | true | The solution provided correctly uses the distributive property to perform the long multiplication, and the final addition is accurate. The result of the multiplication, 43,581,314, matches the ground truth solution when represented in numerical form without formatting, thus confirming its correctness. | |
What is the solution to the long multiplication equation below?
1081 x 1558
Think step by step. | 1684198 | What is the solution to the long multiplication equation below?
1081 x 1558
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1081** and **1558**. 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?
1081 x 1558
Think step by step. | true | The solution provided is correct as it accurately calculates the product of 1081 and 1558 using long multiplication and verifies it with multiple methods, arriving at the correct final answer of 1,684,198 which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7720 x 4107
Think step by step. | 31706040 | What is the solution to the long multiplication equation below?
7720 x 4107
Think step by step. | To solve the long multiplication equation \( 7720 \times 4107 \), 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 (4107)
We can express \( 4107 \) as:
\[ 4107 = 4000 + 100 + 7 \]
### Step 2: Multiply 7720 ... | What is the solution to the long multiplication equation below?
7720 x 4107
Think step by step. | true | The provided solution correctly follows the steps for long multiplication and accurately computes the product of 7720 and 4107, yielding a final result of 31706040, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
9281 x 5795
Think step by step. | 53783395 | What is the solution to the long multiplication equation below?
9281 x 5795
Think step by step. | To solve the multiplication problem \( 9281 \times 5795 \), 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 \( 5795 \) as \( 5000 + 700 + 90 + 5 \). Multiplying \( 9281 \) by each of these component... | What is the solution to the long multiplication equation below?
9281 x 5795
Think step by step. | true | The provided solution correctly follows the long multiplication method, breaking down the calculations accurately and summing them properly. The final result matches the ground truth solution when formatted without commas. | |
What is the solution to the long multiplication equation below?
1894 x 8700
Think step by step. | 16477800 | What is the solution to the long multiplication equation below?
1894 x 8700
Think step by step. | To solve the long multiplication equation \( 1894 \times 8700 \), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 8700 \) can be written as \( 87 \times 100 \). So, we can rewrite the multiplication as:
\[
1894 \times 8700 = 1894 \times ... | What is the solution to the long multiplication equation below?
1894 x 8700
Think step by step. | true | The solution correctly follows the steps of breaking down the multiplication into simpler parts, performs each multiplication accurately, and arrives at the final answer. The calculations for both methods provided lead to the same result, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1992 x 3347
Think step by step. | 6667224 | What is the solution to the long multiplication equation below?
1992 x 3347
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1992** and **3347**. 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. I recall that long multiplication involves multipl... | What is the solution to the long multiplication equation below?
1992 x 3347
Think step by step. | true | The solution provided correctly follows the steps of multiplication, breaking down each part according to distribution, and confirms the final result through different methods including long multiplication and cross-verification with a calculator. The final result matches the ground truth, which is 6667224. | |
What is the solution to the long multiplication equation below?
3648 x 6679
Think step by step. | 24364992 | What is the solution to the long multiplication equation below?
3648 x 6679
Think step by step. | To solve the multiplication problem \( 3648 \times 6679 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3648 \) by each digit of \( 6679 \) from right to left, keeping track of the place values by adding zeros as we go.
\[
... | What is the solution to the long multiplication equation below?
3648 x 6679
Think step by step. | true | The solution and ground truth both provide the same numerical result for the multiplication of 3648 by 6679, which is represented differently in terms of formatting (with commas vs without). However, the numerical value is identical as '24364992' = '24,364,992' when commas are ignored. Thus, the solution is correct. | |
What is the solution to the long multiplication equation below?
2979 x 3314
Think step by step. | 9872406 | What is the solution to the long multiplication equation below?
2979 x 3314
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2979** and **3314**. 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?
2979 x 3314
Think step by step. | true | The solution provided correctly performs the multiplication of 2979 and 3314 using the long multiplication method step by step. It breaks down the numbers accurately, computes each partial product correctly, and finally sums them to arrive at the correct total, which matches the ground truth solution of 9872406. | |
What is the solution to the long multiplication equation below?
9461 x 8077
Think step by step. | 76416497 | What is the solution to the long multiplication equation below?
9461 x 8077
Think step by step. | To solve the multiplication \( 9461 \times 8077 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 9461 \) by each digit of \( 8077 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
& ... | What is the solution to the long multiplication equation below?
9461 x 8077
Think step by step. | false | The solution provided calculates the multiplication using long multiplication but contains a mistake during the addition of the partial products. The correct answer as per the ground truth is 76416497, while the solution calculated 76436497. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
7031 x 3766
Think step by step. | 26478746 | What is the solution to the long multiplication equation below?
7031 x 3766
Think step by step. | To solve the long multiplication equation \(7031 \times 3766\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (3766) by the first number (7031) and then summing the results. Here's the step-by-step solution:
###... | What is the solution to the long multiplication equation below?
7031 x 3766
Think step by step. | true | The solution provided for the multiplication of 7031 and 3766 is correct. Both the detailed breakdown and the final result of 26,478,746 match the ground truth solution of 26478746, as they represent the same numerical value without formatting differences. Thus, the given solution is correct. | |
What is the solution to the long multiplication equation below?
7099 x 2975
Think step by step. | 21119525 | What is the solution to the long multiplication equation below?
7099 x 2975
Think step by step. | To solve the long multiplication equation \(7099 \times 2975\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(7099\) by each component of \(2975\) (which is \(2000 + 900 + 70 + 5\)) and then sum the results.
### Step 1: Break down the multiplier (2... | What is the solution to the long multiplication equation below?
7099 x 2975
Think step by step. | true | The solution provided uses the distributive property correctly, breaks down the multiplication into manageable parts, and accurately sums the results. Moreover, the final verification via long multiplication confirms the arithmetic is correct, yielding the same total as the ground truth solution. | |
What is the solution to the long multiplication equation below?
3839 x 6538
Think step by step. | 25099382 | What is the solution to the long multiplication equation below?
3839 x 6538
Think step by step. | To solve the long multiplication equation \( 3839 \times 6538 \), 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 \( 3839 \) by each digit of \( 6538 \), starting from the rightmost digit (units place) and moving l... | What is the solution to the long multiplication equation below?
3839 x 6538
Think step by step. | false | The long multiplication of 3839 and 6538 must be computed to reach the correct result, which is 25099382. The lengthy details of the solution were absent in the provided solution, and without valid calculations, it cannot be considered correct. | |
What is the solution to the long multiplication equation below?
7765 x 7184
Think step by step. | 55783760 | What is the solution to the long multiplication equation below?
7765 x 7184
Think step by step. | To solve the long multiplication equation \( 7765 \times 7184 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7765) by each digit of the multiplier (7184), starting from the rightmost digit, and then summing up ... | What is the solution to the long multiplication equation below?
7765 x 7184
Think step by step. | true | The provided solution correctly calculates the value of the multiplication step by step, arriving at the final answer of 55,783,760, which matches the ground truth solution of 55783760. Both answers represent the same number. | |
What is the solution to the long multiplication equation below?
2757 x 3460
Think step by step. | 9539220 | What is the solution to the long multiplication equation below?
2757 x 3460
Think step by step. | To solve the long multiplication equation \(2757 \times 3460\), 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 break the problem into smaller parts. Multiply \(27... | What is the solution to the long multiplication equation below?
2757 x 3460
Think step by step. | true | The solution correctly calculated the multiplication of 2757 and 3460, breaking it down into parts and confirming the result through standard long multiplication. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5927 x 9098
Think step by step. | 53923846 | What is the solution to the long multiplication equation below?
5927 x 9098
Think step by step. | To solve the long multiplication equation \(5927 \times 9098\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (9098) by the first number (5927) and then summing the results, taking into account the place values.
... | What is the solution to the long multiplication equation below?
5927 x 9098
Think step by step. | false | The solution arrived at 53,923,846 with a comma, while the ground truth solution is presented without the comma (53923846). Both represent the same number, but the formatting does not match. | |
What is the solution to the long multiplication equation below?
8967 x 6826
Think step by step. | 61208742 | What is the solution to the long multiplication equation below?
8967 x 6826
Think step by step. | To solve the long multiplication equation \( 8967 \times 6826 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8967 \) by each digit of \( 6826 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
8967 x 6826
Think step by step. | true | The solution has correctly computed each step of the long multiplication and arrived at the correct final answer of 61208742, matching the ground truth. | |
What is the solution to the long multiplication equation below?
8361 x 8727
Think step by step. | 72966447 | What is the solution to the long multiplication equation below?
8361 x 8727
Think step by step. | To solve the multiplication problem \( 8361 \times 8727 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8361 \) by each digit of \( 8727 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | What is the solution to the long multiplication equation below?
8361 x 8727
Think step by step. | false | The solution formats the final result with commas as 72,966,447, which differs from the ground truth solution of 72966447 that does not include commas. Therefore, while the numerical value is correct, the formatting discrepancy leads to the solution being incorrect. | |
What is the solution to the long multiplication equation below?
4861 x 8210
Think step by step. | 39908810 | What is the solution to the long multiplication equation below?
4861 x 8210
Think step by step. | To solve the long multiplication equation \( 4861 \times 8210 \), we can break it down into simpler, more manageable steps. Here's how you can approach it:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication over addition** to simplify the calculation. This means we can m... | What is the solution to the long multiplication equation below?
4861 x 8210
Think step by step. | true | The solution correctly follows the steps of long multiplication, applying the distributive property correctly, and accurately sums the partial results to arrive at the final product, which matches the ground truth solution of 39908810. | |
What is the solution to the long multiplication equation below?
1302 x 4154
Think step by step. | 5408508 | What is the solution to the long multiplication equation below?
1302 x 4154
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1302** and **4154**. 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?
1302 x 4154
Think step by step. | true | The solution provided is a detailed and step-by-step analysis of multiplying 1302 and 4154 using long multiplication and also verifies the result using the distributive property. Both the final answer from the solution and the ground truth solution match (5,408,508). Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
8492 x 1956
Think step by step. | 16610352 | What is the solution to the long multiplication equation below?
8492 x 1956
Think step by step. | To solve the long multiplication problem \( 8492 \times 1956 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 8492 by each digit of 1956, accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
The number 195... | What is the solution to the long multiplication equation below?
8492 x 1956
Think step by step. | true | The provided solution and the ground truth solution both yield the same result of 16610352 for the multiplication of 8492 and 1956. The step-by-step breakdown is mathematically sound and verified through both distribution and standard long multiplication methods. | |
What is the solution to the long multiplication equation below?
1705 x 2207
Think step by step. | 3762935 | What is the solution to the long multiplication equation below?
1705 x 2207
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a straightforward multiplication of two four-digit numbers: 1705 and 2207. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers can be complex, but breaking it dow... | What is the solution to the long multiplication equation below?
1705 x 2207
Think step by step. | true | The provided solution accurately calculates the product of 1705 and 2207, showing all necessary steps and verification methods to confirm that the final product is indeed 3,762,935, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6610 x 3754
Think step by step. | 24813940 | What is the solution to the long multiplication equation below?
6610 x 3754
Think step by step. | To solve the long multiplication equation \( 6610 \times 3754 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6610) by each digit of the multiplier (3754), starting from the rightmost digit, and then summing up ... | What is the solution to the long multiplication equation below?
6610 x 3754
Think step by step. | true | The solution provided correctly breaks down the multiplication, calculates each partial product accurately, sums them properly, and verifies the final result through long multiplication. The final answer matches the ground truth solution when formatted properly. | |
What is the solution to the long multiplication equation below?
1815 x 2555
Think step by step. | 4637325 | What is the solution to the long multiplication equation below?
1815 x 2555
Think step by step. | To solve the multiplication problem \(1815 \times 2555\), 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 (2555)
We can express \(2555\) as \(2000 + 500 + 50 + 5\). This allows us to multiply \(1815\) by eac... | What is the solution to the long multiplication equation below?
1815 x 2555
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication, accurately calculates the products of each individual component, and properly adds the results to arrive at the final total. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4984 x 4771
Think step by step. | 23778664 | What is the solution to the long multiplication equation below?
4984 x 4771
Think step by step. | To solve the multiplication problem \( 4984 \times 4771 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4984 \) by each digit of \( 4771 \) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}... | What is the solution to the long multiplication equation below?
4984 x 4771
Think step by step. | false | To verify the correctness of the solution provided for the multiplication of 4984 and 4771 using long multiplication, I computed the product using both standard multiplication and the long multiplication method described in the solution. Upon calculations, 4984 multiplied by 4771 yields 23778664. However, the answer gi... | |
What is the solution to the long multiplication equation below?
8485 x 6266
Think step by step. | 53167010 | What is the solution to the long multiplication equation below?
8485 x 6266
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8,485** and **6,266**. Breaking this down, I recall that long multiplication involves multiplying each digit of the second number (the multiplier) by the entire first number (the multiplicand) and then adding all the partial products together... | What is the solution to the long multiplication equation below?
8485 x 6266
Think step by step. | true | The detailed solution correctly computes the product of 8,485 and 6,266 using both the distributive method and standard long multiplication, arriving at the correct result of 53,167,010, as confirmed by the ground truth solution. | |
What is the solution to the long multiplication equation below?
3423 x 6533
Think step by step. | 22362459 | What is the solution to the long multiplication equation below?
3423 x 6533
Think step by step. | To solve the long multiplication equation \(3423 \times 6533\), we'll break it down step by step using the **long multiplication method**. Here's how it works:
### Step 1: Write the numbers vertically
```
3423
× 6533
________
```
### Step 2: Multiply 3423 by each digit of 6533, starting from the right
###... | What is the solution to the long multiplication equation below?
3423 x 6533
Think step by step. | true | The provided solution correctly follows the long multiplication steps and verifies the addition accurately. The final result of the multiplication is consistent with the ground truth solution. | |
What is the solution to the long multiplication equation below?
8782 x 5024
Think step by step. | 44120768 | What is the solution to the long multiplication equation below?
8782 x 5024
Think step by step. | To solve the long multiplication equation \( 8782 \times 5024 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8782) by each digit of the multiplier (5024), considering their place values, and then adding all the... | What is the solution to the long multiplication equation below?
8782 x 5024
Think step by step. | true | The calculated product of 8782 and 5024 is correctly computed as 44,120,768. The intermediate steps and multiplication breakdown leading to the final addition are correctly outlined. The solution method was verified with long multiplication, confirming its accuracy. Thus, the solution matches the ground truth. | |
What is the solution to the long multiplication equation below?
1375 x 5729
Think step by step. | 7877375 | What is the solution to the long multiplication equation below?
1375 x 5729
Think step by step. | To solve the long multiplication equation \(1375 \times 5729\), 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, one at a time, and then adding all the partial results together.
### Step 1: Bre... | What is the solution to the long multiplication equation below?
1375 x 5729
Think step by step. | true | The calculated result of the multiplication, 7,877,375, matches the ground truth solution of 7877375 when commas are removed. Thus, the solution is correct. | |
What is the solution to the long multiplication equation below?
1197 x 9488
Think step by step. | 11357136 | What is the solution to the long multiplication equation below?
1197 x 9488
Think step by step. | To solve the long multiplication equation \( 1197 \times 9488 \), 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 summing the results.
### St... | What is the solution to the long multiplication equation below?
1197 x 9488
Think step by step. | true | The provided solution for the multiplication of 1197 and 9488 correctly follows the distributive property, breaks down the terms appropriately, calculates each multiplication accurately, and sums the partial products correctly. The final answer is presented in the correct format and matches the ground truth solution of... | |
What is the solution to the long multiplication equation below?
8118 x 5745
Think step by step. | 46637910 | What is the solution to the long multiplication equation below?
8118 x 5745
Think step by step. | To solve the long multiplication equation \( 8118 \times 5745 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (8118) by each digit of the multiplier (5745) and then summing the partial results.
### Step 1: Break down the mul... | What is the solution to the long multiplication equation below?
8118 x 5745
Think step by step. | true | The solution correctly follows the steps of the distributive property to perform long multiplication, breaking down each part of the multiplier and adding the partial results. The arithmetic is accurate and matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3354 x 6186
Think step by step. | 20747844 | What is the solution to the long multiplication equation below?
3354 x 6186
Think step by step. | To solve the long multiplication equation \( 3354 \times 6186 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3354 \) by each digit of \( 6186 \), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
E... | What is the solution to the long multiplication equation below?
3354 x 6186
Think step by step. | true | The solution correctly employs the distributive property of multiplication and accurately performs the calculations, as evidenced by both the partial products and the verification through standard long multiplication, yielding the correct final answer. | |
What is the solution to the long multiplication equation below?
3637 x 3968
Think step by step. | 14431616 | What is the solution to the long multiplication equation below?
3637 x 3968
Think step by step. | To solve the multiplication problem \( 3637 \times 3968 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 3968 \) as \( 4000 - 32 \). This allows us to use the **distributive property** of multiplication to simplify the calcu... | What is the solution to the long multiplication equation below?
3637 x 3968
Think step by step. | true | The provided solution correctly utilizes the distributive property of multiplication to break down the problem and accurately computes both parts before subtracting, leading to the correct final result of 14,431,616. This result is consistent with the ground truth solution. | |
What is the solution to the long multiplication equation below?
8165 x 1741
Think step by step. | 14215265 | What is the solution to the long multiplication equation below?
8165 x 1741
Think step by step. | To solve the multiplication problem \( 8165 \times 1741 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8165 \) by each digit of \( 1741 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | What is the solution to the long multiplication equation below?
8165 x 1741
Think step by step. | true | The solution provided follows the correct steps for multiplication using the long multiplication method, and the final result of the multiplication is accurate. The answer of 14,215,265 matches the ground truth solution of 14215265 when formatted without a comma, confirming the correctness of the solution. | |
What is the solution to the long multiplication equation below?
2464 x 8334
Think step by step. | 20534976 | What is the solution to the long multiplication equation below?
2464 x 8334
Think step by step. | To solve the long multiplication equation \(2464 \times 8334\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2464) by each digit of the multiplier (8334) and then summing the partial products.
### Step 1: Break ... | What is the solution to the long multiplication equation below?
2464 x 8334
Think step by step. | true | The solution provided correctly uses the distributive property to break down the multiplication problem into smaller parts, computes each part accurately, summarizes the partial products correctly, and verifies the final answer by confirming it via another method (long multiplication). The final result of 20,534,976 ma... | |
What is the solution to the long multiplication equation below?
9410 x 8451
Think step by step. | 79523910 | What is the solution to the long multiplication equation below?
9410 x 8451
Think step by step. | To solve the long multiplication equation \(9410 \times 8451\), 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 (8451) by each digit of the first number (9410) and then summing the partial results.
##... | What is the solution to the long multiplication equation below?
9410 x 8451
Think step by step. | true | The provided solution correctly applies the distributive property of multiplication and accurately sums the partial products, resulting in the correct final answer, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3685 x 9397
Think step by step. | 34627945 | What is the solution to the long multiplication equation below?
3685 x 9397
Think step by step. | To solve the long multiplication equation \( 3685 \times 9397 \), 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 summing all the partial prod... | What is the solution to the long multiplication equation below?
3685 x 9397
Think step by step. | true | The given solution correctly performs the multiplication of 3685 by 9397 using the distributive property, calculates each partial product accurately, and correctly sums them to yield the final result. The format of the answer in the SOLUTION is consistent with the GROUND TRUTH SOLUTION, aside from the inclusion of comm... | |
What is the solution to the long multiplication equation below?
6509 x 4637
Think step by step. | 30182233 | What is the solution to the long multiplication equation below?
6509 x 4637
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6509** and **4637**. 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?
6509 x 4637
Think step by step. | true | The solution correctly outlines the steps for multiplying 6509 and 4637. Each partial product is computed accurately, and summing these partial products leads to the correct final answer, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4829 x 1517
Think step by step. | 7325593 | What is the solution to the long multiplication equation below?
4829 x 1517
Think step by step. | To solve the multiplication problem \( 4829 \times 1517 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 1517 \) as \( 1000 + 500 + 10 + 7 \). This allows us to multiply \( 4829 \) by each component separately and then add t... | What is the solution to the long multiplication equation below?
4829 x 1517
Think step by step. | true | The solution correctly performs the long multiplication, breaking down the components and summing them accurately to arrive at the final answer, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
4340 x 7552
Think step by step. | 32775680 | What is the solution to the long multiplication equation below?
4340 x 7552
Think step by step. | To solve the multiplication problem \(4340 \times 7552\), 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 (7552)
Express \(7552\) as \(8000 - 448\) to simplify the multiplication:
\[
4340 \times 7552 = 4340 ... | What is the solution to the long multiplication equation below?
4340 x 7552
Think step by step. | true | The solution provided correctly follows the steps of breaking down the multiplication using the distributive property and calculates the intermediate products accurately. The final answer matches the ground truth solution after adjusting for formatting, making it correct. | |
What is the solution to the long multiplication equation below?
1109 x 2148
Think step by step. | 2382132 | What is the solution to the long multiplication equation below?
1109 x 2148
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **1109** and **2148**. 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: The Distrib... | What is the solution to the long multiplication equation below?
1109 x 2148
Think step by step. | true | The solution correctly breaks down the multiplication of 1109 and 2148 using the distributive property, provides accurate intermediate calculations for each part, and validates the final result through traditional long multiplication. The final answer given matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2731 x 2546
Think step by step. | 6953126 | What is the solution to the long multiplication equation below?
2731 x 2546
Think step by step. | To solve the long multiplication equation \(2731 \times 2546\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2731\) by each digit of \(2546\) (from right to left), shifting the partial results appropriately, and then add them together.... | What is the solution to the long multiplication equation below?
2731 x 2546
Think step by step. | true | The provided solution describes the long multiplication process accurately and arrives at the correct final answer of 6,953,126, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
6258 x 9796
Think step by step. | 61303368 | What is the solution to the long multiplication equation below?
6258 x 9796
Think step by step. | To solve the long multiplication equation \( 6258 \times 9796 \), we'll use the **standard multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication using the distributive property
We can express \( 9796 \) as \( 10,000 - 204 \), since:
\[
9796 = 10,000 - 204
\]
Thus, the mult... | What is the solution to the long multiplication equation below?
6258 x 9796
Think step by step. | true | The solution process correctly applies the distributive property and utilizes both the distributive method and standard long multiplication for verification, resulting in the right final answer. The computed result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4907 x 1048
Think step by step. | 5142536 | What is the solution to the long multiplication equation below?
4907 x 1048
Think step by step. | To solve the long multiplication equation \( 4907 \times 1048 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 4907 \) by each digit of \( 1048 \) (starting from the right) and then sum the results.
### Step 1: Break down the multipl... | What is the solution to the long multiplication equation below?
4907 x 1048
Think step by step. | true | The solution correctly calculates the product of 4907 and 1048 using the distributive property, breaks down the multiplication into manageable steps, and arrives at the correct sum of 5,142,536. This matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4306 x 8140
Think step by step. | 35050840 | What is the solution to the long multiplication equation below?
4306 x 8140
Think step by step. | To solve the long multiplication equation \(4306 \times 8140\), we'll break it down step by step. Here's how you can approach it:
### Step 1: Break down the multiplication
We can use the **distributive property of multiplication** to simplify the calculation. This means we'll multiply \(4306\) by each digit of \(8140\... | What is the solution to the long multiplication equation below?
4306 x 8140
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication of 4306 and 8140, arriving at the correct final answer, 35050840, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4105 x 7078
Think step by step. | 29055190 | What is the solution to the long multiplication equation below?
4105 x 7078
Think step by step. | To solve the long multiplication equation \(4105 \times 7078\), 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 the results.
### Step 1... | What is the solution to the long multiplication equation below?
4105 x 7078
Think step by step. | true | The solution follows the correct steps of the multiplication process using the distributive property, and the final calculated result correctly matches the given ground truth solution when formatted without commas. | |
What is the solution to the long multiplication equation below?
8545 x 4554
Think step by step. | 38913930 | What is the solution to the long multiplication equation below?
8545 x 4554
Think step by step. | To solve the multiplication problem \( 8545 \times 4554 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8545 \) by each digit of \( 4554 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | What is the solution to the long multiplication equation below?
8545 x 4554
Think step by step. | true | The solution correctly performed long multiplication to compute the product of 8545 and 4554, providing detailed steps and verifying the calculation through the distributive property. The final answer of 38913930 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2588 x 2604
Think step by step. | 6739152 | What is the solution to the long multiplication equation below?
2588 x 2604
Think step by step. | To solve the multiplication problem \(2588 \times 2604\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(2604\) as \(2000 + 600 + 4\). This allows us to multiply \(2588\) by each component separately and then add the results.
... | What is the solution to the long multiplication equation below?
2588 x 2604
Think step by step. | true | The solution correctly breaks down the multiplication into manageable components, performs each multiplication correctly, and sums the results accurately. The final answer of 6739152 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1428 x 9421
Think step by step. | 13453188 | What is the solution to the long multiplication equation below?
1428 x 9421
Think step by step. | To solve the multiplication problem \(1428 \times 9421\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(1428\) by each digit of \(9421\) (from right to left), shifting the partial results appropriately.
\[
\begin{align*}
& \qu... | What is the solution to the long multiplication equation below?
1428 x 9421
Think step by step. | false | The calculated result from the process provided (13513188) does not match the ground truth solution (13453188). Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
8043 x 5742
Think step by step. | 46182906 | What is the solution to the long multiplication equation below?
8043 x 5742
Think step by step. | To solve the long multiplication equation \( 8043 \times 5742 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8043 \) by each digit of \( 5742 \), starting from the rightmost digit, and then sum the partial results.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
8043 x 5742
Think step by step. | true | The solution accurately breaks down the multiplication of 8043 by each digit of 5742 and sums the results step by step, leading to the final correct product of 46182906, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
7104 x 7786
Think step by step. | 55311744 | What is the solution to the long multiplication equation below?
7104 x 7786
Think step by step. | To solve the long multiplication equation \(7104 \times 7786\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7104) by each digit of the multiplier (7786) and then summing the partial results.
### Step 1: Break d... | What is the solution to the long multiplication equation below?
7104 x 7786
Think step by step. | true | The solution provided accurately breaks down the multiplication problem using the distributive property, computes each partial product correctly, and sums them accurately, leading to the final result of 55311744, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4079 x 4951
Think step by step. | 20195129 | What is the solution to the long multiplication equation below?
4079 x 4951
Think step by step. | To solve the multiplication problem \( 4079 \times 4951 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 4079 \) by each digit of \( 4951 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{al... | What is the solution to the long multiplication equation below?
4079 x 4951
Think step by step. | true | The solution provided follows the long multiplication process correctly, detailing each step and accurately summing the results of the partial products. The final answer matches the ground truth solution, indicating that the multiplication of 4079 and 4951 is indeed equal to 20195129. | |
What is the solution to the long multiplication equation below?
8598 x 2282
Think step by step. | 19620636 | What is the solution to the long multiplication equation below?
8598 x 2282
Think step by step. | To solve the long multiplication problem \( 8598 \times 2282 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply 8598 by each digit of 2282, accounting for place values, and then sum the results.
### Step 1: Break down the multiplier (2282)
The multipl... | What is the solution to the long multiplication equation below?
8598 x 2282
Think step by step. | false | The provided solution has a formatting issue with commas in the final answer, whereas the ground truth solution is given without commas. The answer "19,620,636" should be represented as "19620636" for it to match the ground truth. | |
What is the solution to the long multiplication equation below?
3663 x 8242
Think step by step. | 30190446 | What is the solution to the long multiplication equation below?
3663 x 8242
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: 3663 and 8242. My goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall th... | What is the solution to the long multiplication equation below?
3663 x 8242
Think step by step. | true | The solution correctly calculated the product of 3663 and 8242, arriving at 30,190,446, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6876 x 3603
Think step by step. | 24774228 | What is the solution to the long multiplication equation below?
6876 x 3603
Think step by step. | To solve the long multiplication equation \( 6876 \times 3603 \), 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 multiplier (3603)
The number \( 3603 \) can be expressed as:
\[ 3603... | What is the solution to the long multiplication equation below?
6876 x 3603
Think step by step. | true | The solution correctly performed the multiplication of 6876 and 3603 using the distributive property and verified the result through standard long multiplication. Both methods yielded the same result of 24,774,228, which matches the ground truth (24774228) when accounting for formatting (commas). Thus, the solution is ... | |
What is the solution to the long multiplication equation below?
4935 x 2030
Think step by step. | 10018050 | What is the solution to the long multiplication equation below?
4935 x 2030
Think step by step. | To solve the long multiplication equation \( 4935 \times 2030 \), we can break it down into simpler, more manageable steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 2030 \) can be written as \( 2000 + 30 \). This allows us to multiply \( 4935 \) by each part separately a... | What is the solution to the long multiplication equation below?
4935 x 2030
Think step by step. | true | The provided solution correctly computes the product of 4935 and 2030, yielding the final result of 10,018,050. This matches the ground truth solution of 10018050 when formatted as a number without commas. Thus, the final answer is correct. | |
What is the solution to the long multiplication equation below?
4680 x 3130
Think step by step. | 14648400 | What is the solution to the long multiplication equation below?
4680 x 3130
Think step by step. | To solve the long multiplication equation \( 4680 \times 3130 \), 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 \( 3130 \) as \( 3000 + 100 + 30 \). This allows us to multiply \( 4680 \... | What is the solution to the long multiplication equation below?
4680 x 3130
Think step by step. | true | The solution accurately uses the distributive property to break down the multiplication into manageable parts, computes each part correctly, and sums the parts to arrive at the final answer. The computed result of 14,648,400 matches the ground truth solution of 14648400 (ignoring the formatting of commas). Thus, the so... | |
What is the solution to the long multiplication equation below?
8875 x 3393
Think step by step. | 30112875 | What is the solution to the long multiplication equation below?
8875 x 3393
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: 8,875 and 3,393. 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 ... | What is the solution to the long multiplication equation below?
8875 x 3393
Think step by step. | true | The solution provided correctly performs the multiplication step-by-step and arrives at the final product of 8,875 and 3,393, which is indeed 30,112,875. The reasoning is thorough, and the verification step confirms the accuracy of the calculation. | |
What is the solution to the long multiplication equation below?
2451 x 4126
Think step by step. | 10112826 | What is the solution to the long multiplication equation below?
2451 x 4126
Think step by step. | To solve the multiplication problem \( 2451 \times 4126 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2451 \) by each digit of \( 4126 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | What is the solution to the long multiplication equation below?
2451 x 4126
Think step by step. | true | The solution accurately follows the long multiplication method to calculate the product of 2451 and 4126, reaching the final result of 10,112,826. The intermediate steps of multiplication and addition are correctly executed, and the final answer corresponds to the provided ground truth solution. | |
What is the solution to the long multiplication equation below?
9419 x 3031
Think step by step. | 28548989 | What is the solution to the long multiplication equation below?
9419 x 3031
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9419** and **3031**. 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?
9419 x 3031
Think step by step. | true | The solution correctly calculates the product of 9419 and 3031 using long multiplication and verifies the answer by summing the intermediate results. The final result of 28548989 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8848 x 9901
Think step by step. | 87604048 | What is the solution to the long multiplication equation below?
8848 x 9901
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8848** and **9901**. 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?
8848 x 9901
Think step by step. | true | The solution arrives at the product of 8848 and 9901 as 87604048 through both breakdown approaches and traditional long multiplication, correctly confirming the ground truth solution. | |
What is the solution to the long multiplication equation below?
2877 x 5624
Think step by step. | 16180248 | What is the solution to the long multiplication equation below?
2877 x 5624
Think step by step. | To solve the long multiplication problem \(2877 \times 5624\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(2877\) by each digit of \(5624\), accounting for place values, and then sum the results.
### Step 1: Break down the multiplication
We can e... | What is the solution to the long multiplication equation below?
2877 x 5624
Think step by step. | true | The solution provided uses the distributive property correctly, breaks down the multiplication into manageable parts, accurately calculates each part, adds them together correctly, and matches the ground truth answer when evaluated. | |
What is the solution to the long multiplication equation below?
8751 x 6859
Think step by step. | 60023109 | What is the solution to the long multiplication equation below?
8751 x 6859
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8751** and **6859**. 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?
8751 x 6859
Think step by step. | true | The provided solution calculated the product of 8751 and 6859 correctly as 60,023,109, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
8133 x 9673
Think step by step. | 78670509 | What is the solution to the long multiplication equation below?
8133 x 9673
Think step by step. | To solve the long multiplication equation \( 8133 \times 9673 \), 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 (9673) by each digit of the first number (8133) and then summing the results.
### Step... | What is the solution to the long multiplication equation below?
8133 x 9673
Think step by step. | true | The solution provided matches the ground truth solution when considering numerical formatting and removing commas, confirming that the multiplication and all calculations were performed correctly. | |
What is the solution to the long multiplication equation below?
4261 x 8144
Think step by step. | 34701584 | What is the solution to the long multiplication equation below?
4261 x 8144
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **4261** and **8144**. 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 (8144) by the first ... | What is the solution to the long multiplication equation below?
4261 x 8144
Think step by step. | true | The provided solution thoroughly explains the multiplication of 4261 and 8144, breaking it down into manageable parts and verifying each step along the way. The final computed result of 34,701,584 matches the ground truth solution, confirming that the solution is correct. | |
What is the solution to the long multiplication equation below?
5558 x 4352
Think step by step. | 24188416 | What is the solution to the long multiplication equation below?
5558 x 4352
Think step by step. | To solve the long multiplication equation \(5558 \times 4352\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5558\) by each digit of \(4352\) (from right to left), shift the partial results appropriately, and then add them together.
### Step 1: Br... | What is the solution to the long multiplication equation below?
5558 x 4352
Think step by step. | true | The solution correctly applies the distributive property and accurately performs the individual multiplications, adds them correctly, and arrives at the final product of 24188416, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
9005 x 1494
Think step by step. | 13453470 | What is the solution to the long multiplication equation below?
9005 x 1494
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9005** and **1494**. 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?
9005 x 1494
Think step by step. | true | The calculation has been thoroughly checked and verified using the long multiplication method and by adding partial products accurately. The result matches the provided ground truth solution of 13453470. | |
What is the solution to the long multiplication equation below?
8617 x 3912
Think step by step. | 33709704 | What is the solution to the long multiplication equation below?
8617 x 3912
Think step by step. | To solve the long multiplication problem \( 8617 \times 3912 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8617 \) by each digit of \( 3912 \) (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?
8617 x 3912
Think step by step. | true | The provided solution correctly breaks down the multiplication using the distributive property, performing the calculations accurately and arrives at the correct final result. The final answer of \( 8617 \times 3912 = \boxed{33,709,704} \) matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6583 x 9357
Think step by step. | 61597131 | What is the solution to the long multiplication equation below?
6583 x 9357
Think step by step. | To solve the long multiplication equation \(6583 \times 9357\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (6583) by each digit of the multiplier (9357), starting from the rightmost digit, and then summing the partial result... | What is the solution to the long multiplication equation below?
6583 x 9357
Think step by step. | true | The solution correctly applies the distributive property to break down and compute the multiplication step by step, providing the correct final result of \(61,597,131\). The verification using standard long multiplication confirms the accuracy of the result. | |
What is the solution to the long multiplication equation below?
2256 x 6171
Think step by step. | 13921776 | What is the solution to the long multiplication equation below?
2256 x 6171
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2256** and **6171**. 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: The Distrib... | What is the solution to the long multiplication equation below?
2256 x 6171
Think step by step. | true | The solution has correctly calculated the product of 2256 and 6171 through detailed breakdown and verification, confirming that the result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8046 x 7295
Think step by step. | 58695570 | What is the solution to the long multiplication equation below?
8046 x 7295
Think step by step. | To solve the multiplication problem \( 8046 \times 7295 \), 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 \( 7295 \) as \( 7000 + 200 + 90 + 5 \), and then multiply \( 8046 \) by each of these com... | What is the solution to the long multiplication equation below?
8046 x 7295
Think step by step. | true | The solution presented correctly applies the long multiplication method to calculate the product of 8046 and 7295. Each step is detailed and the intermediate results are calculated accurately, leading to the final result of 58,695,570, which matches the ground truth solution of 58695570. | |
What is the solution to the long multiplication equation below?
3310 x 7065
Think step by step. | 23385150 | What is the solution to the long multiplication equation below?
3310 x 7065
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3310** and **7065**. 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 (7065) by the first ... | What is the solution to the long multiplication equation below?
3310 x 7065
Think step by step. | true | The submitted solution accurately goes through the long multiplication process step by step and confirms the final product through an alternative method, aligning perfectly with the ground truth solution of 23385150. | |
What is the solution to the long multiplication equation below?
5270 x 3531
Think step by step. | 18608370 | What is the solution to the long multiplication equation below?
5270 x 3531
Think step by step. | To solve the long multiplication equation \(5270 \times 3531\), 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 (3531)
We can express \(3531\) as:
\[
3531 = 3000 + 500 + 30 + 1
\]
### Step 2: Multiply 5270... | What is the solution to the long multiplication equation below?
5270 x 3531
Think step by step. | true | The solution correctly applies the distributive property of multiplication over addition, breaks down the multiplication into manageable parts, and accurately calculates each component. The addition of these components is also done correctly, leading to the final result being accurate and matching the ground truth solu... | |
What is the solution to the long multiplication equation below?
4461 x 7281
Think step by step. | 32480541 | What is the solution to the long multiplication equation below?
4461 x 7281
Think step by step. | To solve the long multiplication equation \(4461 \times 7281\), 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?
4461 x 7281
Think step by step. | true | The solution correctly follows the steps of the distributive property for multiplication, breaking down the numbers and performing each multiplication individually. The intermediate calculations and the final sum are accurate, leading to the correct total of 32,480,541. The ground truth solution has the same value when... | |
What is the solution to the long multiplication equation below?
8365 x 4733
Think step by step. | 39591545 | What is the solution to the long multiplication equation below?
8365 x 4733
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **8365** and **4733**. At first glance, this seems complex because both numbers are four-digit numbers. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 83... | What is the solution to the long multiplication equation below?
8365 x 4733
Think step by step. | true | The solution provided is accurate; the breakdown of the multiplication steps is correctly calculated, and the final result matches the ground truth solution of 39591545. | |
What is the solution to the long multiplication equation below?
5626 x 1356
Think step by step. | 7628856 | What is the solution to the long multiplication equation below?
5626 x 1356
Think step by step. | To solve the long multiplication equation \(5626 \times 1356\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5626\) by each digit of \(1356\) (considering their place values) and then sum the results.
### Step 1: Break down the multip... | What is the solution to the long multiplication equation below?
5626 x 1356
Think step by step. | false | The solution incorrectly calculated the result of the multiplication as 7,628,856 instead of the correct value, 7,628,856, but also reversed the digits in format. Therefore, the answer should have been presented as `oxed{7628856}` rather than in the presented format. | |
What is the solution to the long multiplication equation below?
8422 x 5692
Think step by step. | 47938024 | What is the solution to the long multiplication equation below?
8422 x 5692
Think step by step. | To solve the long multiplication equation \( 8422 \times 5692 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8422 \) by each digit of \( 5692 \), starting from the rightmost digit, and then sum the results.
### Step 1: Break down t... | What is the solution to the long multiplication equation below?
8422 x 5692
Think step by step. | true | The solution correctly follows the steps of long multiplication and arrives at the right answer of \( 47,938,024 \). The breakdown of the operations and the final verification using long multiplication confirm its accuracy. | |
What is the solution to the long multiplication equation below?
2556 x 9735
Think step by step. | 24882660 | What is the solution to the long multiplication equation below?
2556 x 9735
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2556** and **9735**. At first glance, this seems complex because both numbers are four-digit. However, breaking it down using the long multiplication method should make it manageable.
### Breaking Down the Multiplication
Long multiplication... | What is the solution to the long multiplication equation below?
2556 x 9735
Think step by step. | true | The solution correctly breaks down the multiplication process into detailed steps, performing long multiplication accurately. It verifies the result using the distributive property, leading to the final product of 24882660, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2454 x 6526
Think step by step. | 16014804 | What is the solution to the long multiplication equation below?
2454 x 6526
Think step by step. | To solve the long multiplication equation \( 2454 \times 6526 \), we'll break it down step by step using the standard multiplication method. Here's how it works:
### Step 1: Break down the multiplication
We'll multiply \( 2454 \) by each digit of \( 6526 \), starting from the rightmost digit (the ones place) and movin... | What is the solution to the long multiplication equation below?
2454 x 6526
Think step by step. | true | The solution correctly breaks down the long multiplication of 2454 and 6526, performs the individual multiplications accurately, adds the results properly, and confirms the final sum. The final answer provided, 16,014,804, matches the ground truth solution of 16014804 (ignoring formatting differences in commas). Thus, ... | |
What is the solution to the long multiplication equation below?
8949 x 2264
Think step by step. | 20260536 | What is the solution to the long multiplication equation below?
8949 x 2264
Think step by step. | To solve the long multiplication problem \( 8949 \times 2264 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 8949 \) by each digit of \( 2264 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier \( ... | What is the solution to the long multiplication equation below?
8949 x 2264
Think step by step. | true | The solution correctly applies the distributive property of multiplication, breaks down the multiplier, computes each partial product, and sums them accurately. Additionally, the verification using long multiplication shows consistent results. Therefore, the final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2122 x 9519
Think step by step. | 20199318 | What is the solution to the long multiplication equation below?
2122 x 9519
Think step by step. | To solve the multiplication problem \( 2122 \times 9519 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2122 \) by each digit of \( 9519 \), starting from the rightmost digit (units place), and shift the partial results acco... | What is the solution to the long multiplication equation below?
2122 x 9519
Think step by step. | true | The solution follows the long multiplication method correctly and results in the correct final answer of 20199318 for the multiplication of 2122 and 9519. |
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