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?
6897 x 1817
Think step by step. | 12531849 | What is the solution to the long multiplication equation below?
6897 x 1817
Think step by step. | To solve the long multiplication problem \( 6897 \times 1817 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 6897 \) by each digit of \( 1817 \) (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?
6897 x 1817
Think step by step. | true | The solution correctly employs the distributive property of multiplication and accurately calculates each step, leading to the correct final result of 6897 times 1817, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8732 x 6358
Think step by step. | 55518056 | What is the solution to the long multiplication equation below?
8732 x 6358
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: 8,732 and 6,358. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of *... | What is the solution to the long multiplication equation below?
8732 x 6358
Think step by step. | true | The provided solution accurately calculates the multiplication of 8,732 and 6,358 using the long multiplication method and correctly sums the partial products to arrive at the final result of 55,518,056, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7565 x 1108
Think step by step. | 8382020 | What is the solution to the long multiplication equation below?
7565 x 1108
Think step by step. | To solve the long multiplication equation \( 7565 \times 1108 \), 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 (1108)
The number \( 1108 \) can be expressed as:
\[ 1108... | What is the solution to the long multiplication equation below?
7565 x 1108
Think step by step. | true | The provided solution correctly uses the distributive property to break down the multiplication, calculates the intermediate products accurately, adds them correctly, and checks the final result with an alternative method. Therefore, it is correct. | |
What is the solution to the long multiplication equation below?
7496 x 7688
Think step by step. | 57629248 | What is the solution to the long multiplication equation below?
7496 x 7688
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: 7,496 and 7,688. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of b... | What is the solution to the long multiplication equation below?
7496 x 7688
Think step by step. | true | The solution correctly performs the multiplication of the two large numbers 7,496 and 7,688, incorporating the long multiplication method and confirming the result by additional calculations. The final result of 57,629,248 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4874 x 2061
Think step by step. | 10045314 | What is the solution to the long multiplication equation below?
4874 x 2061
Think step by step. | To solve the long multiplication equation \( 4874 \times 2061 \), 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 (2061)
The multiplier \( 2061 \) can be expressed as:
\[ 2061 = 2000 + 60 + 1 \]
### Step 2: Mul... | What is the solution to the long multiplication equation below?
4874 x 2061
Think step by step. | true | The solution correctly multiplies the numbers using the distributive property and accurately calculates the total, matching the ground truth solution when formatted without commas. | |
What is the solution to the long multiplication equation below?
7468 x 8340
Think step by step. | 62283120 | What is the solution to the long multiplication equation below?
7468 x 8340
Think step by step. | To solve the long multiplication equation \( 7468 \times 8340 \), 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 \( 8340 \) as \( 8000 + 300 + 40 \). This allows us to multiply \( 7468 \) by each component sepa... | What is the solution to the long multiplication equation below?
7468 x 8340
Think step by step. | true | The provided solution correctly breaks down the multiplication process and verifies the result using both breakdown and standard long multiplication methods. The final result of \( 7468 \times 8340 \) is \( 62,283,120 \), which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8655 x 7926
Think step by step. | 68599530 | What is the solution to the long multiplication equation below?
8655 x 7926
Think step by step. | To solve the long multiplication equation \( 8655 \times 7926 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8655 \) by each digit of \( 7926 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
8655 x 7926
Think step by step. | true | The solution provided correctly applies the distributive property of multiplication, systematically breaks down the components, performs accurate calculations for each multiplication step, and correctly sums all partial results. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6933 x 3048
Think step by step. | 21131784 | What is the solution to the long multiplication equation below?
6933 x 3048
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6933** and **3048**. 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?
6933 x 3048
Think step by step. | true | The solution correctly implements the long multiplication method, breaks down the problem into manageable components, and verifies the final sum accurately. The arithmetic throughout is correct, leading to the final answer matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
3458 x 7374
Think step by step. | 25499292 | What is the solution to the long multiplication equation below?
3458 x 7374
Think step by step. | To solve the multiplication problem \( 3458 \times 7374 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3458 \) by each digit of \( 7374 \), starting from the rightmost digit (units place), and shift the partial results acc... | What is the solution to the long multiplication equation below?
3458 x 7374
Think step by step. | true | The solution correctly applies the long multiplication method step by step and arrives at the correct final product for the multiplication problem, matching the ground truth solution when both are expressed in numerical form (25499292). The answer is formatted correctly with commas for readability. | |
What is the solution to the long multiplication equation below?
9211 x 7868
Think step by step. | 72472148 | What is the solution to the long multiplication equation below?
9211 x 7868
Think step by step. | To solve the long multiplication problem \( 9211 \times 7868 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9211 \) by each digit of \( 7868 \) (considering their place values) and then sum all the partial results.
### Step 1: Break down the mu... | What is the solution to the long multiplication equation below?
9211 x 7868
Think step by step. | true | The given solution follows a correct application of the distributive property of multiplication, correctly breaks down the numbers involved, computes the individual products accurately, and sums them up to achieve the correct final value. Additionally, the alternative verification check using standard long multiplicati... | |
What is the solution to the long multiplication equation below?
1242 x 2524
Think step by step. | 3134808 | What is the solution to the long multiplication equation below?
1242 x 2524
Think step by step. | To solve the long multiplication equation \(1242 \times 2524\), 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 (2524) by each digit of the first number (1242) and then summing the results.
### Step 1... | What is the solution to the long multiplication equation below?
1242 x 2524
Think step by step. | true | The solution correctly applies the distributive property of multiplication, breaks down the components accurately, performs each multiplication correctly, and sums the results to arrive at the final product of 1242 and 2524, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3155 x 2224
Think step by step. | 7016720 | What is the solution to the long multiplication equation below?
3155 x 2224
Think step by step. | To solve the multiplication problem \( 3155 \times 2224 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, considering their place values, and then adding the results together.
### Step 1: B... | What is the solution to the long multiplication equation below?
3155 x 2224
Think step by step. | true | The provided solution correctly utilizes the distributive property to break down the multiplication of 3155 by 2224 into manageable parts, accurately calculates each part, sums them correctly, and verifies the answer through standard long multiplication. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8959 x 9026
Think step by step. | 80863934 | What is the solution to the long multiplication equation below?
8959 x 9026
Think step by step. | To solve the long multiplication equation \( 8959 \times 9026 \), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying each digit of the second number (9026) by each digit of the first number (8959) and then summing the results. Here's a step-by-step ... | What is the solution to the long multiplication equation below?
8959 x 9026
Think step by step. | true | The provided solution breaks down the multiplication using the distributive property, correctly calculates each partial product, and accurately sums the final results. The final computed value matches the ground truth solution, 80863934, indicating that the solution is correct. | |
What is the solution to the long multiplication equation below?
3915 x 8031
Think step by step. | 31441365 | What is the solution to the long multiplication equation below?
3915 x 8031
Think step by step. | To solve the long multiplication equation \( 3915 \times 8031 \), 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... | What is the solution to the long multiplication equation below?
3915 x 8031
Think step by step. | true | The solution correctly applied the distributive property to break down the multiplication into manageable parts, performed each multiplication correctly, and summed the results accurately. The final answer presented in the boxed solution format matches the ground truth solution after removing the commas. | |
What is the solution to the long multiplication equation below?
1767 x 2587
Think step by step. | 4571229 | What is the solution to the long multiplication equation below?
1767 x 2587
Think step by step. | To solve the long multiplication equation \(1767 \times 2587\), 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 the results.
### Step ... | What is the solution to the long multiplication equation below?
1767 x 2587
Think step by step. | true | The solution follows the correct procedure by breaking down the multiplication using the distributive property and then verifying the result with standard long multiplication. In both methods, the final result is the same, which confirms its correctness. The boxed answer of 4,571,229 matches the ground truth of 4571229... | |
What is the solution to the long multiplication equation below?
4454 x 6681
Think step by step. | 29757174 | What is the solution to the long multiplication equation below?
4454 x 6681
Think step by step. | To solve the long multiplication equation \(4454 \times 6681\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4454) by each digit of the multiplier (6681), starting from the rightmost digit, and then summing up th... | What is the solution to the long multiplication equation below?
4454 x 6681
Think step by step. | true | The solution correctly applies the distributive property of multiplication, breaks down the multiplication of 4454 and 6681 into manageable parts, and sums the partial results accurately. Additionally, the verification through standard long multiplication confirms the final result of 29757174, which matches the ground ... | |
What is the solution to the long multiplication equation below?
8752 x 8732
Think step by step. | 76422464 | What is the solution to the long multiplication equation below?
8752 x 8732
Think step by step. | To solve the multiplication problem \( 8752 \times 8732 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 8752 \) by each digit of \( 8732 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{ali... | What is the solution to the long multiplication equation below?
8752 x 8732
Think step by step. | true | The solution correctly applies the long multiplication method, breaks down the multiplication into partial products, and accurately sums them up to arrive at the correct final result. The answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4139 x 4806
Think step by step. | 19892034 | What is the solution to the long multiplication equation below?
4139 x 4806
Think step by step. | To solve the multiplication problem \( 4139 \times 4806 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 4806 \) as \( 4000 + 800 + 6 \). This allows us to multiply \( 4139 \) by each component separately and then add the re... | What is the solution to the long multiplication equation below?
4139 x 4806
Think step by step. | true | The submitted solution correctly computes the multiplication of 4139 and 4806 using the long multiplication method, producing the same final result as the ground truth solution of 19892034. | |
What is the solution to the long multiplication equation below?
1233 x 8241
Think step by step. | 10161153 | What is the solution to the long multiplication equation below?
1233 x 8241
Think step by step. | To solve the long multiplication equation \(1233 \times 8241\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1233\) by each digit of \(8241\) (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?
1233 x 8241
Think step by step. | true | The solution correctly calculates the product of 1233 and 8241 using the distributive property and verifies it with the standard long multiplication method. The final result of 10,161,153 matches the ground truth solution (10161153), accounting for formatting (the use of commas). Thus, the solution is correct. | |
What is the solution to the long multiplication equation below?
1866 x 3066
Think step by step. | 5721156 | What is the solution to the long multiplication equation below?
1866 x 3066
Think step by step. | To solve the multiplication problem \(1866 \times 3066\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(3066\) as \(3000 + 60 + 6\). This allows us to multiply \(1866\) by each component separately and then add the results.
\... | What is the solution to the long multiplication equation below?
1866 x 3066
Think step by step. | true | The solution provided uses the long multiplication method accurately and verifies the calculations for each step. The final result matches the ground truth solution of 5721156. | |
What is the solution to the long multiplication equation below?
9118 x 3261
Think step by step. | 29733798 | What is the solution to the long multiplication equation below?
9118 x 3261
Think step by step. | To solve the long multiplication equation \( 9118 \times 3261 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9118 \) by each digit of \( 3261 \) (from right to left), shifting the partial results appropriately, and then add them tog... | What is the solution to the long multiplication equation below?
9118 x 3261
Think step by step. | true | The calculated result of the multiplication 9118 x 3261, as shown in the step-by-step breakdown, equals 29,733,798, which matches the ground truth solution after removing the formatting commas. The solution method is correct, and the answer has been verified successfully through both methods. | |
What is the solution to the long multiplication equation below?
3437 x 6971
Think step by step. | 23959327 | What is the solution to the long multiplication equation below?
3437 x 6971
Think step by step. | To solve the multiplication problem \(3437 \times 6971\), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \(3437\) by each digit of \(6971\) (from right to left), shifting the partial results appropriately.
\[
\begin{array}{r}
\ph... | What is the solution to the long multiplication equation below?
3437 x 6971
Think step by step. | true | The solution provided calculates the multiplication of 3437 by 6971 step-by-step, using long multiplication method correctly. Each multiplication of the digit contributes to the correct intermediate sums, and the final addition is executed accurately, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
6660 x 4880
Think step by step. | 32500800 | What is the solution to the long multiplication equation below?
6660 x 4880
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a simple multiplication of two large numbers: 6,660 and 4,880. The goal is to find the product of these two numbers.
### Breaking Down the Numbers
Multiplying large numbers directly can be complex, so I recall that breaking t... | What is the solution to the long multiplication equation below?
6660 x 4880
Think step by step. | true | The provided solution follows a detailed step-by-step methodology to multiply 6,660 and 4,880, arriving consistently at the final product of 32,500,800. The ground truth solution is also 32,500,800. Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
3247 x 6784
Think step by step. | 22027648 | What is the solution to the long multiplication equation below?
3247 x 6784
Think step by step. | To solve the long multiplication problem \( 3247 \times 6784 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3247 \) by each digit of \( 6784 \), starting from the rightmost digit, and then sum the results, taking into account the place values.
... | What is the solution to the long multiplication equation below?
3247 x 6784
Think step by step. | true | The solution provided correctly applies the distributive property to calculate the product of 3247 and 6784. The partial products are computed accurately, and the final result of 22,027,648 matches the ground truth solution of 22027648 after formatting consistency is considered (leading zeros or formatting differences ... | |
What is the solution to the long multiplication equation below?
9808 x 5772
Think step by step. | 56611776 | What is the solution to the long multiplication equation below?
9808 x 5772
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9808** and **5772**. 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 98... | What is the solution to the long multiplication equation below?
9808 x 5772
Think step by step. | true | The solution correctly multiplies the two numbers (9808 and 5772) using long multiplication and breaks down the steps accurately. Every partial result is calculated correctly and added to arrive at the final answer, which matches the ground truth solution of 56611776. | |
What is the solution to the long multiplication equation below?
5915 x 1864
Think step by step. | 11025560 | What is the solution to the long multiplication equation below?
5915 x 1864
Think step by step. | To solve the long multiplication equation \(5915 \times 1864\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5915\) by each digit of \(1864\) (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?
5915 x 1864
Think step by step. | true | The provided solution correctly breaks down the multiplication of 5915 and 1864 using the distributive property, performs all calculations accurately, and arrives at the correct final answer of 11,025,560, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2429 x 8475
Think step by step. | 20585775 | What is the solution to the long multiplication equation below?
2429 x 8475
Think step by step. | To solve the long multiplication equation \(2429 \times 8475\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(2429\) by each digit of \(8475\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
Expr... | What is the solution to the long multiplication equation below?
2429 x 8475
Think step by step. | true | The solution presented correctly follows the steps of long multiplication using the distributive property, accurately computing the individual products and their sums. Both the boxed answer and the ground truth result represent the same numerical value (20,585,775), confirming the correctness of the solution. | |
What is the solution to the long multiplication equation below?
4555 x 5936
Think step by step. | 27038480 | What is the solution to the long multiplication equation below?
4555 x 5936
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: 4555 and 5936. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the method of **l... | What is the solution to the long multiplication equation below?
4555 x 5936
Think step by step. | true | The solution correctly breaks down the multiplication into manageable parts using long multiplication, calculates each partial product accurately, and sums them up correctly to arrive at the final result. The final answer provided matches the ground truth solution of 27038480. | |
What is the solution to the long multiplication equation below?
8530 x 5324
Think step by step. | 45413720 | What is the solution to the long multiplication equation below?
8530 x 5324
Think step by step. | To solve the long multiplication equation \(8530 \times 5324\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(8530\) by each digit of \(5324\) (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?
8530 x 5324
Think step by step. | true | The solution correctly performs the long multiplication by breaking down the numbers into their component parts, multiplying accordingly, and summing the results accurately. The final answer matches the ground truth solution exactly. | |
What is the solution to the long multiplication equation below?
9191 x 7527
Think step by step. | 69180657 | What is the solution to the long multiplication equation below?
9191 x 7527
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: 9191 and 7527. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall the concept of **... | What is the solution to the long multiplication equation below?
9191 x 7527
Think step by step. | true | The evaluation of the multiplication process and the final addition matches the ground truth solution of 69,180,657, thus demonstrating that the solution is correct. | |
What is the solution to the long multiplication equation below?
1157 x 3300
Think step by step. | 3818100 | What is the solution to the long multiplication equation below?
1157 x 3300
Think step by step. | ### Understanding the Problem
First, I need to understand what the problem is asking. It's a multiplication of two numbers: 1157 and 3300. At first glance, both numbers seem large, and multiplying them directly might be complex. But I recall that breaking down the problem can make it simpler.
### Breaking Down the Mu... | What is the solution to the long multiplication equation below?
1157 x 3300
Think step by step. | true | The solution correctly calculates the product of 1157 and 3300 using various methods, confirming the accuracy by achieving the same final result through different techniques. | |
What is the solution to the long multiplication equation below?
4110 x 9748
Think step by step. | 40064280 | What is the solution to the long multiplication equation below?
4110 x 9748
Think step by step. | To solve the long multiplication equation \( 4110 \times 9748 \), 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 (9748) by each digit of the first number (4110) and then summing the results.
### Step... | What is the solution to the long multiplication equation below?
4110 x 9748
Think step by step. | true | The solution correctly applies the distributive property of multiplication and accurately computes the intermediate products before summing them. The final answer provided (oxed{40,064,280}) is actually equivalent to the ground truth solution (40064280), confirming that the solution is correct despite the formatting o... | |
What is the solution to the long multiplication equation below?
2181 x 5668
Think step by step. | 12361908 | What is the solution to the long multiplication equation below?
2181 x 5668
Think step by step. | To solve the multiplication problem \( 2181 \times 5668 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2181 \) by each digit of \( 5668 \), starting from the rightmost digit, and then sum the results.
\[
\begin{align*}
&5... | What is the solution to the long multiplication equation below?
2181 x 5668
Think step by step. | true | The solution correctly follows the long multiplication method, accurately calculates each partial product, and correctly sums them to arrive at the final answer of 12361908. This matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5893 x 4775
Think step by step. | 28139075 | What is the solution to the long multiplication equation below?
5893 x 4775
Think step by step. | To solve the long multiplication problem \( 5893 \times 4775 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 5893 \) by each digit of \( 4775 \) (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?
5893 x 4775
Think step by step. | true | The solution correctly breaks down the multiplication of 5893 and 4775 using the distributive property, calculates each partial result accurately, and sums them correctly to arrive at the final answer of 28139075, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7715 x 2555
Think step by step. | 19711825 | What is the solution to the long multiplication equation below?
7715 x 2555
Think step by step. | To solve the long multiplication equation \(7715 \times 2555\), 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)
The number \(2555\) can be expressed as:
\[
2555 = 2000 + 500 + 50 + 5
\]
### Step 2: M... | What is the solution to the long multiplication equation below?
7715 x 2555
Think step by step. | false | The solution provided states that the final result of multiplying 7715 by 2555 is \(19,711,825\), while the ground truth solution indicates that the correct answer is \(19,711,825\) as well. However, it seems that there is a formatting discrepancy: the ground truth does not have the commas included. Therefore, the nume... | |
What is the solution to the long multiplication equation below?
1789 x 4376
Think step by step. | 7828664 | What is the solution to the long multiplication equation below?
1789 x 4376
Think step by step. | To solve the long multiplication equation \(1789 \times 4376\), 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?
1789 x 4376
Think step by step. | true | The solution correctly uses the distributive property to break down the multiplication, calculates each part accurately, and sums the partial results correctly, leading to the accurate final answer of 7,828,664. | |
What is the solution to the long multiplication equation below?
2911 x 7100
Think step by step. | 20668100 | What is the solution to the long multiplication equation below?
2911 x 7100
Think step by step. | To solve the long multiplication equation \( 2911 \times 7100 \), we can break it down into simpler steps. Here's a step-by-step solution:
### Step 1: Break down the multiplication
Notice that \( 7100 \) can be written as \( 7 \times 100 \times 10 \), but for simplicity, we'll treat it as \( 7100 = 7000 + 100 \). This... | What is the solution to the long multiplication equation below?
2911 x 7100
Think step by step. | true | The solution provided matches perfectly with the ground truth solution. The step-by-step breakdown is accurate, leading to the correct final answer of 20,668,100. | |
What is the solution to the long multiplication equation below?
9832 x 5512
Think step by step. | 54193984 | What is the solution to the long multiplication equation below?
9832 x 5512
Think step by step. | To solve the long multiplication equation \(9832 \times 5512\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9832) by each digit of the multiplier (5512), starting from the rightmost digit, and then summing up th... | What is the solution to the long multiplication equation below?
9832 x 5512
Think step by step. | true | The solution correctly follows the steps of long multiplication, breaking down the problem using the distributive property and confirming the answer using standard long multiplication. The final computed result matches the ground truth solution, confirming its accuracy. | |
What is the solution to the long multiplication equation below?
4508 x 4156
Think step by step. | 18735248 | What is the solution to the long multiplication equation below?
4508 x 4156
Think step by step. | To solve the long multiplication equation \(4508 \times 4156\), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (4508) by each digit of the multiplier (4156), starting from the rightmost digit, and then summing up th... | What is the solution to the long multiplication equation below?
4508 x 4156
Think step by step. | true | The provided solution accurately calculates the product of 4508 and 4156 using the distributive property, correctly arrives at the final result of 18,735,248, and matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1070 x 1471
Think step by step. | 1573970 | What is the solution to the long multiplication equation below?
1070 x 1471
Think step by step. | To solve the multiplication problem \(1070 \times 1471\), 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 multiplication
We can express \(1070 \times 1471\) as:
\[
1070 \times 1471 = 1070 \times (1000 + 400 + 70 + 1)
\... | What is the solution to the long multiplication equation below?
1070 x 1471
Think step by step. | true | The solution correctly applies the distributive property of multiplication, carefully calculates each component, and accurately sums all the partial results to arrive at the final answer of 1,573,970, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3689 x 1482
Think step by step. | 5467098 | What is the solution to the long multiplication equation below?
3689 x 1482
Think step by step. | To solve the multiplication problem \( 3689 \times 1482 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 3689 \) by each digit of \( 1482 \), starting from the rightmost digit (units place), and shift the partial results acco... | What is the solution to the long multiplication equation below?
3689 x 1482
Think step by step. | true | The solution follows a correct, systematic method of long multiplication, breaks down each component accurately, performs all necessary shifts for place values, and adds all partial results correctly. The final product calculated matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
9984 x 5013
Think step by step. | 50049792 | What is the solution to the long multiplication equation below?
9984 x 5013
Think step by step. | To solve the multiplication problem \( 9984 \times 5013 \), we can use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \( 5013 \) as \( 5000 + 13 \). This allows us to multiply \( 9984 \) by each part separately and then add the results.
\[... | What is the solution to the long multiplication equation below?
9984 x 5013
Think step by step. | false | The solution provided arrived at an answer of 50,049,792, which is incorrectly formatted with commas. The correct ground truth solution is 50,049,792 (without additional formatting). Despite this minor formatting issue, the arithmetic calculation is indeed correct. | |
What is the solution to the long multiplication equation below?
3320 x 8509
Think step by step. | 28249880 | What is the solution to the long multiplication equation below?
3320 x 8509
Think step by step. | To solve the long multiplication equation \( 3320 \times 8509 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 8509 \) as \( 8000 + 500 + 0 + 9 \)... | What is the solution to the long multiplication equation below?
3320 x 8509
Think step by step. | true | The solution correctly applies the distributive property of multiplication to break down the multiplication problem into smaller components, performs the individual multiplications accurately, and sums the results correctly, yielding the exact ground truth answer of 28249880. | |
What is the solution to the long multiplication equation below?
6874 x 5162
Think step by step. | 35483588 | What is the solution to the long multiplication equation below?
6874 x 5162
Think step by step. | To solve the long multiplication problem \(6874 \times 5162\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(6874\) by each digit of \(5162\), starting from the rightmost digit, and then sum the partial results. Here's the step-by-step solution:
##... | What is the solution to the long multiplication equation below?
6874 x 5162
Think step by step. | true | The provided solution and the ground truth solution represent the same numerical value, albeit with a minor formatting difference in the representation of the number (use of commas). The arithmetic steps are correct and lead to the final result of 35,483,588, which matches the ground truth solution when re-formatted. | |
What is the solution to the long multiplication equation below?
7432 x 1435
Think step by step. | 10664920 | What is the solution to the long multiplication equation below?
7432 x 1435
Think step by step. | To solve the multiplication problem \(7432 \times 1435\), we'll break it down using the **long multiplication** method. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We'll multiply \(7432\) by each digit of \(1435\), starting from the rightmost digit (units place), and shift the partial res... | What is the solution to the long multiplication equation below?
7432 x 1435
Think step by step. | true | The solution correctly follows the long multiplication method, breaking down the calculation into manageable steps. Each multiplication and addition of partial results is performed accurately, leading to the correct final answer of 10664920. | |
What is the solution to the long multiplication equation below?
5137 x 9917
Think step by step. | 50943629 | What is the solution to the long multiplication equation below?
5137 x 9917
Think step by step. | To solve the multiplication problem \(5137 \times 9917\), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We can express \(9917\) as \(10000 - 83\), which allows us to rewrite the multiplication as:
\[
5137 \times 9917 = 5137 \times (10000 - 83)... | What is the solution to the long multiplication equation below?
5137 x 9917
Think step by step. | false | The calculated result is 50,943,629, but the ground truth provided is 50,943,629 without the comma. The two values are actually equivalent despite the format difference, but it's important to recognize that the solution should match the ground truth exactly, including formatting. Therefore, the solution is incorrect as... | |
What is the solution to the long multiplication equation below?
2493 x 2185
Think step by step. | 5447205 | What is the solution to the long multiplication equation below?
2493 x 2185
Think step by step. | To solve the long multiplication equation \( 2493 \times 2185 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 2493 \) by each digit of \( 2185 \), accounting for the place value, and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
2493 x 2185
Think step by step. | true | The solution provided evaluates the multiplication of 2493 and 2185 meticulously, breaking it down using the distributive property and verifying with long multiplication. The calculations yield the correct total of 5,447,205, which matches the ground truth solution of 5447205. | |
What is the solution to the long multiplication equation below?
6493 x 7979
Think step by step. | 51807647 | What is the solution to the long multiplication equation below?
6493 x 7979
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6493** and **7979**. 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?
6493 x 7979
Think step by step. | true | The solution provided accurately computes the product of 6493 and 7979, breaking it down into manageable steps using both the distributive property and long multiplication. The final result of 51,807,647 matches the ground truth solution of 51807647, confirming that the calculations and methodology are correct. | |
What is the solution to the long multiplication equation below?
2395 x 1280
Think step by step. | 3065600 | What is the solution to the long multiplication equation below?
2395 x 1280
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: 2395 and 1280. 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 that breaking it ... | What is the solution to the long multiplication equation below?
2395 x 1280
Think step by step. | true | The solution correctly performs the multiplication of 2395 and 1280 using detailed steps and confirms the final product is 3,065,600, matching the ground truth. | |
What is the solution to the long multiplication equation below?
9580 x 9694
Think step by step. | 92868520 | What is the solution to the long multiplication equation below?
9580 x 9694
Think step by step. | To solve the multiplication problem \(9580 \times 9694\), 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 (9694)
Express \(9694\) as \((10,000 - 306)\) to simplify the multiplication:
\[
9580 \times 9694 = 9... | What is the solution to the long multiplication equation below?
9580 x 9694
Think step by step. | true | The solution provided correctly applies the distributive property of multiplication and breaks down the numbers step-by-step. Both the interim calculations and the final answer of 92,868,520 match the ground truth solution of 92868520 when formatted without commas. Hence, the answer given in both the solution and groun... | |
What is the solution to the long multiplication equation below?
3979 x 4655
Think step by step. | 18522245 | What is the solution to the long multiplication equation below?
3979 x 4655
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3979** and **4655**. At first glance, this seems complex because both numbers are in the thousands. To tackle this, I recall that long multiplication breaks down the problem into simpler, more manageable parts. Essentially, I'll multiply 3979... | What is the solution to the long multiplication equation below?
3979 x 4655
Think step by step. | true | The solution correctly follows the long multiplication method, breaks down the numbers into manageable parts, and accurately performs the calculations leading to the final result of 18,522,245. It also verifies the result with an alternative method which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8469 x 2114
Think step by step. | 17903466 | What is the solution to the long multiplication equation below?
8469 x 2114
Think step by step. | To solve the long multiplication equation \( 8469 \times 2114 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8469 \) by each digit of \( 2114 \) (considering their place values) and then add the results together.
### Step 1: Break ... | What is the solution to the long multiplication equation below?
8469 x 2114
Think step by step. | true | The solution correctly performed the multiplication of 8469 and 2114 using both the distributive property and standard long multiplication, arriving at the correct final result of 17,903,466. | |
What is the solution to the long multiplication equation below?
5221 x 4434
Think step by step. | 23149914 | What is the solution to the long multiplication equation below?
5221 x 4434
Think step by step. | To solve the long multiplication equation \(5221 \times 4434\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5221\) by each digit of \(4434\) (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?
5221 x 4434
Think step by step. | true | The solution correctly follows the distributive property for long multiplication and arrives at the correct final result of 23149914, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2117 x 8113
Think step by step. | 17175221 | What is the solution to the long multiplication equation below?
2117 x 8113
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2117** and **8113**. 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 (8113) by the first ... | What is the solution to the long multiplication equation below?
2117 x 8113
Think step by step. | true | The solution methodically breaks down the multiplication into manageable parts, correctly applying the distributive property and ensuring the calculations are accurate. Two verification methods confirm that the result is indeed 17,175,221, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
9635 x 3488
Think step by step. | 33606880 | What is the solution to the long multiplication equation below?
9635 x 3488
Think step by step. | To solve the long multiplication equation \(9635 \times 3488\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(9635\) by each digit of \(3488\) (from right to left), shift the partial results appropriately, and then add them together.
#... | What is the solution to the long multiplication equation below?
9635 x 3488
Think step by step. | true | The solution provided correctly uses the distributive property of multiplication to break down the problem, calculates each part accurately, and compiles the final result correctly. The calculations match the ground truth solution of 33606880. | |
What is the solution to the long multiplication equation below?
3508 x 1375
Think step by step. | 4823500 | What is the solution to the long multiplication equation below?
3508 x 1375
Think step by step. | To solve the multiplication problem \( 3508 \times 1375 \), we can break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each of the digits in the second number, appropriately shifted by their place value, and then adding the results toge... | What is the solution to the long multiplication equation below?
3508 x 1375
Think step by step. | false | The solution provided gives a final answer of 4,823,500, but the ground truth solution states that the correct answer is 4,823,500 (without the comma), which is effectively the same numerical value. However, the solution format suggests that the extra comma could be seen as a formatting issue, causing confusion. The ev... | |
What is the solution to the long multiplication equation below?
2091 x 8951
Think step by step. | 18716541 | What is the solution to the long multiplication equation below?
2091 x 8951
Think step by step. | To solve the multiplication \( 2091 \times 8951 \), we can use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 2091 \) by each digit of \( 8951 \), starting from the rightmost digit, and then sum the partial results.
\[
\begin{align*}
89... | What is the solution to the long multiplication equation below?
2091 x 8951
Think step by step. | true | The given solution to the multiplication problem is correct. It accurately follows the long multiplication method by breaking down the multiplication into manageable parts and correctly summing the partial products to yield the final result of 18716541. | |
What is the solution to the long multiplication equation below?
3042 x 3604
Think step by step. | 10963368 | What is the solution to the long multiplication equation below?
3042 x 3604
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **3042** and **3604**. 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?
3042 x 3604
Think step by step. | true | The solution accurately calculates the product of 3042 and 3604 through detailed breakdown and checks each step, ultimately arriving at the correct final answer of 10,963,368, which matches the ground truth. | |
What is the solution to the long multiplication equation below?
7730 x 7441
Think step by step. | 57518930 | What is the solution to the long multiplication equation below?
7730 x 7441
Think step by step. | To solve the long multiplication equation \( 7730 \times 7441 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (7730) by each digit of the multiplier (7441) and then summing the partial products.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
7730 x 7441
Think step by step. | true | The solution correctly followed the steps of multiplication using the distributive property and accurately computed the total sum of the partial products, which matches the provided ground truth solution. | |
What is the solution to the long multiplication equation below?
9186 x 3061
Think step by step. | 28118346 | What is the solution to the long multiplication equation below?
9186 x 3061
Think step by step. | To solve the long multiplication equation \( 9186 \times 3061 \), 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 (3061)
The multiplier \( 3061 \) can be expressed as:
\[ 3061 = 3000 + 60 + 1 \]
### Step 2: Mu... | What is the solution to the long multiplication equation below?
9186 x 3061
Think step by step. | false | The calculated result of 28,118,346 does not match the ground truth solution of 28,118,346. Therefore, the solution provided is incorrect. It appears there was a misalignment or transcription error in presenting the final answer in the verification step. | |
What is the solution to the long multiplication equation below?
1004 x 4043
Think step by step. | 4059172 | What is the solution to the long multiplication equation below?
1004 x 4043
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: 1004 and 4043. 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 that breaking the... | What is the solution to the long multiplication equation below?
1004 x 4043
Think step by step. | true | The provided solution accurately follows the multiplication steps using different verification methods to arrive at the correct product of 1004 and 4043, which is indeed 4,059,172. The breakdown, calculations, and checks all confirm the final answer. | |
What is the solution to the long multiplication equation below?
9096 x 1701
Think step by step. | 15472296 | What is the solution to the long multiplication equation below?
9096 x 1701
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9096** and **1701**. 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?
9096 x 1701
Think step by step. | true | The solution correctly calculates the product of 9096 and 1701 as 15472296, and verifies the result using an alternative method which yields the same answer. Thus, the solution is accurate. | |
What is the solution to the long multiplication equation below?
4027 x 1639
Think step by step. | 6600253 | What is the solution to the long multiplication equation below?
4027 x 1639
Think step by step. | To solve the long multiplication equation \( 4027 \times 1639 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply 4027 by each digit of 1639 (considering their place values) and then sum the results.
### Step 1: Break down the multiplicati... | What is the solution to the long multiplication equation below?
4027 x 1639
Think step by step. | true | The solution calculated the multiplication of 4027 and 1639 step-by-step correctly using both distributive property and long multiplication, ultimately yielding the correct final result of 6600253, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8813 x 4512
Think step by step. | 39764256 | What is the solution to the long multiplication equation below?
8813 x 4512
Think step by step. | To solve the long multiplication equation \( 8813 \times 4512 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 8813 \) by each digit of \( 4512 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
8813 x 4512
Think step by step. | true | Both the solution and the ground truth solution represent the same number (39,764,256) but formatted differently. The ground truth does not show leading zeros, making it equivalent to the boxed answer in the solution. | |
What is the solution to the long multiplication equation below?
9359 x 7055
Think step by step. | 66027745 | What is the solution to the long multiplication equation below?
9359 x 7055
Think step by step. | To solve the long multiplication equation \( 9359 \times 7055 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (9359) by each digit of the multiplier (7055) and then summing the partial products.
### Step 1: Brea... | What is the solution to the long multiplication equation below?
9359 x 7055
Think step by step. | true | The solution provided correctly follows the steps for breaking down the multiplication using the distributive property and arrives at the correct final product. The verification using standard long multiplication also agrees with the result. | |
What is the solution to the long multiplication equation below?
9716 x 7056
Think step by step. | 68556096 | What is the solution to the long multiplication equation below?
9716 x 7056
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9716** and **7056**. 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
O... | What is the solution to the long multiplication equation below?
9716 x 7056
Think step by step. | true | The provided solution correctly performs the multiplication step by step using long multiplication. It verifies the result with an alternative method, confirming that the final answer of 68,556,096 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6311 x 8630
Think step by step. | 54463930 | What is the solution to the long multiplication equation below?
6311 x 8630
Think step by step. | To solve the multiplication problem \(6311 \times 8630\), we can break it down into simpler steps using the **distributive property of multiplication over addition**. Here's how to do it step by step:
### Step 1: Break down the multiplication
First, express \(8630\) as \(8000 + 600 + 30 + 0\). Then, multiply \(6311\) ... | What is the solution to the long multiplication equation below?
6311 x 8630
Think step by step. | true | The solution provides a breakdown of the multiplication using the distributive property and calculates each component correctly. The final result of the addition of the partial products matches the ground truth solution exactly (54463930). Therefore, the solution is correct. | |
What is the solution to the long multiplication equation below?
9637 x 3359
Think step by step. | 32370683 | What is the solution to the long multiplication equation below?
9637 x 3359
Think step by step. | To solve the long multiplication equation \( 9637 \times 3359 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 9637 \) by each digit of \( 3359 \) (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?
9637 x 3359
Think step by step. | true | The calculated result of \( 9637 \times 3359 \) is \( 32,370,683 \), which matches the ground truth solution of \( 32370683 \). The difference in formatting (with or without a comma) does not affect the numerical correctness. Hence, the solution is correct. | |
What is the solution to the long multiplication equation below?
3940 x 7135
Think step by step. | 28111900 | What is the solution to the long multiplication equation below?
3940 x 7135
Think step by step. | To solve the long multiplication equation \( 3940 \times 7135 \), we can break it down into simpler, more manageable steps using the **distributive property of multiplication over addition**. Here's a step-by-step solution:
### Step 1: Break down the multiplication
We can express \( 7135 \) as \( 7000 + 100 + 30 + 5 \... | What is the solution to the long multiplication equation below?
3940 x 7135
Think step by step. | true | The provided solution accurately follows the steps of long multiplication using the distributive property, multiplying each component of the second number by the first number and summing them correctly. The calculations are verified and match the ground truth solution. | |
What is the solution to the long multiplication equation below?
1645 x 3809
Think step by step. | 6265805 | What is the solution to the long multiplication equation below?
1645 x 3809
Think step by step. | To solve the long multiplication equation \(1645 \times 3809\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(1645\) by each digit of \(3809\) (from right to left), shifting the partial results appropriately, and then add them together.... | What is the solution to the long multiplication equation below?
1645 x 3809
Think step by step. | false | The solution provided arrives at an answer of 6,265,805, but the ground truth solution states the product should be 6,265,805, with differing digits for '6265805'. There seems to be a minor error in transcription or initial input, but the evaluation shows the detailed steps are correct and aligned with the multiplicati... | |
What is the solution to the long multiplication equation below?
9319 x 1754
Think step by step. | 16345526 | What is the solution to the long multiplication equation below?
9319 x 1754
Think step by step. | To solve the multiplication problem \(9319 \times 1754\), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
Multiply \(9319\) by each digit of \(1754\), starting from the rightmost digit, and shift the partial results accordingly.
\[
\begin{align*... | What is the solution to the long multiplication equation below?
9319 x 1754
Think step by step. | true | The step-by-step breakdown of the multiplication was executed correctly. Each multiplication and addition contributed accurately to the final result, which matches the ground truth solution of 16345526. | |
What is the solution to the long multiplication equation below?
7721 x 9743
Think step by step. | 75225703 | What is the solution to the long multiplication equation below?
7721 x 9743
Think step by step. | To solve the long multiplication problem \( 7721 \times 9743 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 7721 \) by each digit of \( 9743 \), starting from the rightmost digit, and then sum the results, taking into account the pl... | What is the solution to the long multiplication equation below?
7721 x 9743
Think step by step. | true | The solution accurately applies the distributive property to break down the multiplication of 7721 and 9743, computes each partial product correctly, and sums them correctly to yield the final product. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
9530 x 1615
Think step by step. | 15390950 | What is the solution to the long multiplication equation below?
9530 x 1615
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **9530** and **1615**. 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 (the multiplier) ... | What is the solution to the long multiplication equation below?
9530 x 1615
Think step by step. | true | The solution provided correctly calculates the product of 9530 and 1615 through detailed multiplication steps, and the final result of 15,390,950 matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2824 x 3955
Think step by step. | 11168920 | What is the solution to the long multiplication equation below?
2824 x 3955
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 2824 and 3955. 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 the firs... | What is the solution to the long multiplication equation below?
2824 x 3955
Think step by step. | true | The provided solution accurately decomposes the multiplication of the two numbers, performs the calculations step-by-step, and successfully verifies the result using an alternative method. Both the calculated answer and the ground truth solution match: 11,168,920. | |
What is the solution to the long multiplication equation below?
5817 x 3830
Think step by step. | 22279110 | What is the solution to the long multiplication equation below?
5817 x 3830
Think step by step. | To solve the long multiplication equation \( 5817 \times 3830 \), 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. Specificall... | What is the solution to the long multiplication equation below?
5817 x 3830
Think step by step. | true | The provided solution accurately utilizes the distributive property to break down the multiplication into manageable parts, calculates each part correctly, and sums the results appropriately. The final answer is consistent with the ground truth solution of 22279110, confirming its correctness. | |
What is the solution to the long multiplication equation below?
5025 x 7399
Think step by step. | 37179975 | What is the solution to the long multiplication equation below?
5025 x 7399
Think step by step. | To solve the multiplication problem \(5025 \times 7399\), 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 \(7399\) as \((8000 - 601)\) to simplify the calculation:
\[
5025 \times 7399 = 5025 \times ... | What is the solution to the long multiplication equation below?
5025 x 7399
Think step by step. | true | The computed result of the multiplication, 37179975, matches the ground truth solution exactly. | |
What is the solution to the long multiplication equation below?
2496 x 8556
Think step by step. | 21355776 | What is the solution to the long multiplication equation below?
2496 x 8556
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **2496** and **8556**. 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?
2496 x 8556
Think step by step. | true | The provided solution accurately breaks down the multiplication of the two numbers, calculates each partial product step-by-step, and correctly sums them to arrive at the final result of 21,355,776, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8566 x 4949
Think step by step. | 42393134 | What is the solution to the long multiplication equation below?
8566 x 4949
Think step by step. | To solve the multiplication \( 8566 \times 4949 \), 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 multiplier (4949)
Notice that \( 4949 \) can be written as \( 5000 - 51 \). This allows us to rew... | What is the solution to the long multiplication equation below?
8566 x 4949
Think step by step. | true | The solution correctly applies the distributive property to break down the multiplication of 8566 and 4949, leading to correct calculations for both components of the operation. The final answer is verified with long multiplication, resulting in the same value as the ground truth solution. | |
What is the solution to the long multiplication equation below?
6786 x 3478
Think step by step. | 23601708 | What is the solution to the long multiplication equation below?
6786 x 3478
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **6786** and **3478**. 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?
6786 x 3478
Think step by step. | true | The provided solution meticulously follows the process of long multiplication, breaking down the numbers into their respective place values and correctly calculates each partial product. All steps are verified through both sequential addition of partial results and an alternative grid method, leading to the correct fin... | |
What is the solution to the long multiplication equation below?
1631 x 2138
Think step by step. | 3487078 | What is the solution to the long multiplication equation below?
1631 x 2138
Think step by step. | To solve the long multiplication equation \(1631 \times 2138\), 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 \(1631\) by each digit of \(2138\) (from right to left), shifting the partial results appropriately ba... | What is the solution to the long multiplication equation below?
1631 x 2138
Think step by step. | true | The solution correctly employs the long multiplication method and accurately calculates the product of 1631 and 2138 step by step. The addition of the partial results is verified, and the final result matches the ground truth solution of 3487078. | |
What is the solution to the long multiplication equation below?
6468 x 9884
Think step by step. | 63929712 | What is the solution to the long multiplication equation below?
6468 x 9884
Think step by step. | To solve the long multiplication equation \(6468 \times 9884\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the first number by each digit of the second number, adjusting for place value, and then summing all the partial products.
### Step 1... | What is the solution to the long multiplication equation below?
6468 x 9884
Think step by step. | true | The provided solution correctly uses the distributive property to separately calculate the products of the numbers and then subtracts the correct partial product from the total, arriving at the correct final answer of 63929712. | |
What is the solution to the long multiplication equation below?
3300 x 6919
Think step by step. | 22832700 | What is the solution to the long multiplication equation below?
3300 x 6919
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 3,300 and 6,919. At first glance, this seems daunting because both numbers are in the thousands. However, I recall that breaking down the problem into simpler, more manageable parts can make it easier.
### Breaking Down the Multiplication
On... | What is the solution to the long multiplication equation below?
3300 x 6919
Think step by step. | true | The solution uses the distributive property correctly and verifies the result through an alternate method. Both methods yield the same final result of 22,832,700, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5385 x 4931
Think step by step. | 26553435 | What is the solution to the long multiplication equation below?
5385 x 4931
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: **5385** and **4931**. 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?
5385 x 4931
Think step by step. | true | The solution correctly breaks down the multiplication of 5385 and 4931 using the long multiplication method and verifies the result using the distributive property. Both the step-by-step calculations and the final answer of 26553435 match the ground truth solution. | |
What is the solution to the long multiplication equation below?
2447 x 9264
Think step by step. | 22669008 | What is the solution to the long multiplication equation below?
2447 x 9264
Think step by step. | To solve the long multiplication equation \(2447 \times 9264\), we'll break it down using the **distributive property of multiplication over addition**. This method involves multiplying the multiplicand (2447) by each digit of the multiplier (9264), starting from the rightmost digit, and then summing the partial result... | What is the solution to the long multiplication equation below?
2447 x 9264
Think step by step. | true | The solution provides a correct step-by-step breakdown of the multiplication using the distributive property and verifies the result through standard long multiplication. The final answer was calculated as 22,668,008, which indeed matches the ground truth solution (22669008) when ignoring commas. | |
What is the solution to the long multiplication equation below?
7724 x 9996
Think step by step. | 77209104 | What is the solution to the long multiplication equation below?
7724 x 9996
Think step by step. | ### Understanding the Problem
First, I need to multiply two large numbers: 7,724 and 9,996. Directly multiplying these numbers seems complex, especially because both numbers are close to round numbers that might simplify the calculation.
### Observing Patterns and Simplifying
Looking at the numbers:
- **9,996** is ... | What is the solution to the long multiplication equation below?
7724 x 9996
Think step by step. | true | The solution provided follows a clear logical process for multiplying the two large numbers and employs both the difference of squares and the distributive property methods. The calculations are verified multiple times, arriving consistently at the correct final result of 77,209,104, which matches the ground truth solu... | |
What is the solution to the long multiplication equation below?
6082 x 6407
Think step by step. | 38967374 | What is the solution to the long multiplication equation below?
6082 x 6407
Think step by step. | To solve the multiplication problem \(6082 \times 6407\), 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 \(6407\) as \(6000 + 400 + 7\). This allows us to multiply \(6082\) by each component separately and then add ... | What is the solution to the long multiplication equation below?
6082 x 6407
Think step by step. | true | The solution correctly performs long multiplication by breaking the problem down into manageable parts, calculates each part accurately, and sums the results accurately. The final answer provided matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5381 x 2095
Think step by step. | 11273195 | What is the solution to the long multiplication equation below?
5381 x 2095
Think step by step. | To solve the long multiplication equation \(5381 \times 2095\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(5381\) by each digit of \(2095\), starting from the rightmost digit, and then sum the results.
### Step 1: Break down the mul... | What is the solution to the long multiplication equation below?
5381 x 2095
Think step by step. | true | The solution correctly calculates the product of 5381 and 2095, breaking the multiplication down step by step using the distributive property, and the final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2486 x 3539
Think step by step. | 8797954 | What is the solution to the long multiplication equation below?
2486 x 3539
Think step by step. | To solve the long multiplication equation \(2486 \times 3539\), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \(2486\) by each digit of \(3539\) (from right to left), shift the partial results appropriately, and then add them together.
#... | What is the solution to the long multiplication equation below?
2486 x 3539
Think step by step. | true | The solution provided correctly breaks down the multiplication of 2486 and 3539 into partial products using the distributive property, multiplies correctly, and sums the results accurately. The final answer in the boxed format matches the ground truth solution when disregarding formatting differences (like commas). Thu... | |
What is the solution to the long multiplication equation below?
9246 x 3389
Think step by step. | 31334694 | What is the solution to the long multiplication equation below?
9246 x 3389
Think step by step. | To solve the long multiplication equation \( 9246 \times 3389 \), we'll break it down step by step using the **distributive property of multiplication over addition**. This means we'll multiply \( 9246 \) by each digit of \( 3389 \) (considering their place values) and then sum the results.
### Step 1: Break down the ... | What is the solution to the long multiplication equation below?
9246 x 3389
Think step by step. | true | The solution provided accurately follows the steps for long multiplication and yields the correct result, which matches the ground truth solution when formatted appropriately. | |
What is the solution to the long multiplication equation below?
5326 x 5735
Think step by step. | 30544610 | What is the solution to the long multiplication equation below?
5326 x 5735
Think step by step. | To solve the multiplication problem \( 5326 \times 5735 \), we'll use the **long multiplication** method. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 5326 \) by each digit of \( 5735 \), starting from the rightmost digit, and shift the partial results accordingly.
\[
\... | What is the solution to the long multiplication equation below?
5326 x 5735
Think step by step. | true | The long multiplication method was applied correctly, and the calculations for each step were carried out accurately. The final result of multiplying 5326 by 5735 was computed as 30,544,610, which matches the ground truth solution of 30544610, when both are disregarded for formatting differences (i.e., commas). Therefo... | |
What is the solution to the long multiplication equation below?
9876 x 9160
Think step by step. | 90464160 | What is the solution to the long multiplication equation below?
9876 x 9160
Think step by step. | To solve the multiplication problem \( 9876 \times 9160 \), we can break it down into simpler steps using the distributive property of multiplication over addition. Here's a step-by-step solution:
### Step 1: Break down the multiplier
The multiplier \( 9160 \) can be expressed as:
\[ 9160 = 9000 + 100 + 60 \]
### Ste... | What is the solution to the long multiplication equation below?
9876 x 9160
Think step by step. | true | The solution correctly breaks down the multiplication problem using the distributive property and adds the partial results accurately, matching the ground truth solution of 90464160. | |
What is the solution to the long multiplication equation below?
7354 x 1699
Think step by step. | 12494446 | What is the solution to the long multiplication equation below?
7354 x 1699
Think step by step. | To solve the multiplication problem \(7354 \times 1699\), 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)
Notice that \(1699\) is very close to \(1700\). We can rewrite \(1699\) as:
\[
1699 = 1700 - 1... | What is the solution to the long multiplication equation below?
7354 x 1699
Think step by step. | true | The provided solution correctly follows the distributive property to break down the multiplication of 7354 and 1699. The calculations for both steps are accurate and lead to the final result of 12494446, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
7830 x 2816
Think step by step. | 22049280 | What is the solution to the long multiplication equation below?
7830 x 2816
Think step by step. | To solve the long multiplication equation \( 7830 \times 2816 \), 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 (2816) by each digit of the first number (7830) and then summing the results.
### Step... | What is the solution to the long multiplication equation below?
7830 x 2816
Think step by step. | true | The solution correctly calculates the product of 7830 and 2816 using the distributive property and verifies it with standard long multiplication. The final result is accurately presented in both cases, arriving at 22,049,280, which matches the ground truth solution of 22049280. | |
What is the solution to the long multiplication equation below?
5052 x 5297
Think step by step. | 26760444 | What is the solution to the long multiplication equation below?
5052 x 5297
Think step by step. | To solve the long multiplication problem \(5052 \times 5297\), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \(5052\) by each digit of \(5297\) (considering their place values) and then sum the results.
### Step 1: Break down the multiplication
Expre... | What is the solution to the long multiplication equation below?
5052 x 5297
Think step by step. | true | The solution provided follows the distributive property correctly, breaks down the multiplication into manageable parts, calculates each part accurately, and correctly sums the results. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8644 x 2404
Think step by step. | 20780176 | What is the solution to the long multiplication equation below?
8644 x 2404
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: **8644** and **2404**. 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?
8644 x 2404
Think step by step. | true | The solution clearly details each step of the multiplication process, breaking it down using long multiplication and confirming the final result. The calculations and partial results are accurate, leading to the final product of 8644 and 2404 being correctly stated as 20,780,176. | |
What is the solution to the long multiplication equation below?
3694 x 2334
Think step by step. | 8621796 | What is the solution to the long multiplication equation below?
3694 x 2334
Think step by step. | To solve the long multiplication problem \( 3694 \times 2334 \), we'll break it down using the **distributive property of multiplication over addition**. This means we'll multiply \( 3694 \) by each digit of \( 2334 \) (considering their place values) and then sum the results.
### Step 1: Break down the multiplier (23... | What is the solution to the long multiplication equation below?
3694 x 2334
Think step by step. | true | The solution provided correctly follows the distributive property of multiplication, breaks down the multiplication into manageable parts, and accurately calculates each component. The sum of the partial results totals correctly to the ground truth result of 8621796, confirming the accuracy of the solution. | |
What is the solution to the long multiplication equation below?
9944 x 7111
Think step by step. | 70711784 | What is the solution to the long multiplication equation below?
9944 x 7111
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: 9944 and 7111. 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?
9944 x 7111
Think step by step. | true | The solution provided correctly steps through the problem and calculates the product of 9944 and 7111 accurately, arriving at the correct final answer of 70,711,784, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1982 x 8278
Think step by step. | 16406996 | What is the solution to the long multiplication equation below?
1982 x 8278
Think step by step. | To solve the multiplication \( 1982 \times 8278 \), we'll use the **long multiplication method**. Here's a step-by-step breakdown:
### Step 1: Break down the multiplication
We'll multiply \( 1982 \) by each digit of \( 8278 \), starting from the rightmost digit (units place), and then sum the partial results.
\[
\beg... | What is the solution to the long multiplication equation below?
1982 x 8278
Think step by step. | true | The solution provided uses the long multiplication method correctly and accurately calculates the product of 1982 and 8278, arriving at the correct answer of 16406996. Each step of the multiplication and addition of partial products has been followed properly. | |
What is the solution to the long multiplication equation below?
3834 x 6156
Think step by step. | 23602104 | What is the solution to the long multiplication equation below?
3834 x 6156
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: 3834 and 6156. The goal is to find the product of these two numbers.
### Breaking Down the Multiplication
Multiplying large numbers directly can be complex, so I recall t... | What is the solution to the long multiplication equation below?
3834 x 6156
Think step by step. | true | The provided solution correctly calculates the product of 3834 and 6156 as 23,602,104. It utilizes long multiplication and validates the answer through alternative methods, arriving at the given ground truth solution. | |
What is the solution to the long multiplication equation below?
4035 x 8320
Think step by step. | 33571200 | What is the solution to the long multiplication equation below?
4035 x 8320
Think step by step. | To solve the multiplication problem \( 4035 \times 8320 \), 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 \( 8320 \) as \( 8000 + 300 + 20 \). This allows us to multiply \( 4035 \) by e... | What is the solution to the long multiplication equation below?
4035 x 8320
Think step by step. | true | The solution correctly employs the distributive property of multiplication to break down the problem, calculating each part accurately, and arrives at the final answer of 33,571,200, which matches the ground truth solution. |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.