question stringlengths 97 97 | solution stringlengths 7 8 | eval_prompt stringlengths 526 526 | eval_internal_cot stringclasses 1
value | eval_solution stringlengths 1.38k 2.66k | raw_eval_prompt stringlengths 526 526 | judge_correct bool 2
classes | judge_reasoning stringlengths 118 450 |
|---|---|---|---|---|---|---|---|
What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step. | 29198946 | What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step.
Break this question 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, ... | To solve \( 8274 \times 3529 \) using the distributive property of multiplication over addition, we break down the multiplication based on each digit of the second number \( 3529\) and account for its place value.
We can rewrite \( 3529\) as \( 3000 + 500 + 20 + 9 \).
Now we will multiply \( 8274\) by each of these c... | What is the solution to the long multiplication equation below?
8274 x 3529
Think step by step.
Break this question 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, ... | true | The provided solution correctly utilizes the distributive property of multiplication and accurately adds the results of each step. The final computed product of \( 8274 \times 3529 \) matches the ground truth solution of \( 29198946 \) precisely. | |
What is the solution to the long multiplication equation below?
9341 x 4130
Think step by step. | 38578330 | What is the solution to the long multiplication equation below?
9341 x 4130
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9341 \times 4130 \) using the distributive property, we'll break it down step by step by multiplying \( 9341 \) by each digit of \( 4130 \), taking the place value into account.
We can express \( 4130 \) as:
\[
4130 = 4000 + 100 + 30 + 0
\]
Now, we will multiply \( 9341 \) by each part... | What is the solution to the long multiplication equation below?
9341 x 4130
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication of 9341 by the parts of 4130. Each partial multiplication is accurately calculated, and the final addition of these partial results is also correct. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
6637 x 5510
Think step by step. | 36569870 | What is the solution to the long multiplication equation below?
6637 x 5510
Think step by step.
Break this question 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, ... | To find the product of 6637 and 5510 using the distributive property of multiplication over addition, we can break down the second number (5510) into its individual digits accounting for their place value:
\[ 5510 = 5000 + 500 + 10 + 0 \]
Now we will multiply the first number (6637) by each part of the second number ... | What is the solution to the long multiplication equation below?
6637 x 5510
Think step by step.
Break this question 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, ... | true | The solution provided uses the distributive property correctly to break down the multiplication into manageable parts and performs each step of the calculation accurately. The addition of the intermediate results is also done correctly, leading to the correct final product of 6637 and 5510, which matches the ground tru... | |
What is the solution to the long multiplication equation below?
5086 x 6642
Think step by step. | 33781212 | What is the solution to the long multiplication equation below?
5086 x 6642
Think step by step.
Break this question 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, ... | To solve the multiplication \( 5086 \times 6642 \) using the distributive property, we can break it down step by step. We'll expand the second number \( 6642 \) into its place values and multiply it by \( 5086 \).
1. **Expand 6642**:
\[
6642 = 6000 + 600 + 40 + 2
\]
2. **Distribute \( 5086 \) across each ter... | What is the solution to the long multiplication equation below?
5086 x 6642
Think step by step.
Break this question 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, ... | true | The solution correctly decomposes the multiplication using the distributive property, calculates the partial results accurately, adds them correctly, and verifies the final answer through direct multiplication, confirming that the result is indeed 33781212. | |
What is the solution to the long multiplication equation below?
8996 x 8373
Think step by step. | 75323508 | What is the solution to the long multiplication equation below?
8996 x 8373
Think step by step.
Break this question 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, ... | To solve the multiplication \( 8996 \times 8373 \) using the distributive property, we will break down the numbers into simpler parts and then carry out the multiplication step by step.
**Step 1: Breakdown the Numbers**
We can express \( 8373 \) as:
\[
8373 = 8000 + 300 + 70 + 3
\]
So, we can rewrite the multiplica... | What is the solution to the long multiplication equation below?
8996 x 8373
Think step by step.
Break this question 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, ... | false | The final result calculated in the solution is incorrect. It states the product of 8996 and 8373 is 75295068, while the ground truth solution is 75323508. | |
What is the solution to the long multiplication equation below?
9275 x 6116
Think step by step. | 56725900 | What is the solution to the long multiplication equation below?
9275 x 6116
Think step by step.
Break this question 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, ... | To solve the multiplication \(9275 \times 6116\) using the distributive property, we will break down each digit of \(6116\) and multiply it with \(9275\), accounting for its place value.
### Step 1: Break down the numbers
The number \(6116\) can be expressed in terms of its digits and their place value:
\[
6116 = 60... | What is the solution to the long multiplication equation below?
9275 x 6116
Think step by step.
Break this question 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, ... | false | The calculated result was 56607200, while the ground truth solution is 56725900. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
1556 x 1996
Think step by step. | 3105776 | What is the solution to the long multiplication equation below?
1556 x 1996
Think step by step.
Break this question 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, ... | To solve \( 1556 \times 1996 \) using the distributive property, we first break down \( 1996 \) into its place values:
\[
1996 = 1000 + 900 + 90 + 6
\]
Now we can distribute \( 1556 \) over each component of \( 1996 \):
\[
1556 \times 1996 = 1556 \times (1000 + 900 + 90 + 6)
\]
Using the distributive property, we c... | What is the solution to the long multiplication equation below?
1556 x 1996
Think step by step.
Break this question 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, ... | false | The solution calculates the product of 1556 and 1996 as 3106176, but the ground truth solution states the correct product is 3105776. The final computed result is incorrect. | |
What is the solution to the long multiplication equation below?
3622 x 5165
Think step by step. | 18707630 | What is the solution to the long multiplication equation below?
3622 x 5165
Think step by step.
Break this question 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, ... | To solve the multiplication \( 3622 \times 5165 \) using the distributive property, we will break it down step by step.
### Step 1: Break down the second number
We can separate \( 5165 \) into its individual digits according to their place values:
\[
5165 = 5000 + 100 + 60 + 5
\]
### Step 2: Apply the distributive... | What is the solution to the long multiplication equation below?
3622 x 5165
Think step by step.
Break this question 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, ... | false | The calculated result of 18615730 is incorrect, as the ground truth solution is 18707630. The discrepancy indicates an error occurred in the addition of partial products. | |
What is the solution to the long multiplication equation below?
6624 x 7409
Think step by step. | 49077216 | What is the solution to the long multiplication equation below?
6624 x 7409
Think step by step.
Break this question 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, ... | To solve the multiplication \( 6624 \times 7409 \) step by step using the distributive property of multiplication over addition, we can break down the second number \( 7409 \) into its individual digits, accounting for their place values.
### Step 1: Break down 7409
The number \( 7409 \) can be expressed in terms of ... | What is the solution to the long multiplication equation below?
6624 x 7409
Think step by step.
Break this question 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, ... | false | The solution provides step-by-step calculations using the distributive property to multiply 6624 by each component of 7409, and then sums the partial products. However, the final result calculated as 48977216 does not match the ground truth solution of 49077216. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
2861 x 2656
Think step by step. | 7598816 | What is the solution to the long multiplication equation below?
2861 x 2656
Think step by step.
Break this question 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, ... | To solve the multiplication problem \(2861 \times 2656\) using the distributive property, we can break down \(2656\) into its individual digits and their respective place values:
\[
2656 = 2000 + 600 + 50 + 6
\]
Now, we can multiply \(2861\) by each part of \(2656\):
1. **Multiply by 2000**:
\[
2861 \times 200... | What is the solution to the long multiplication equation below?
2861 x 2656
Think step by step.
Break this question 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, ... | false | The calculated product of 2861 times 2656, which was provided as 7608816, does not match the ground truth solution of 7598816. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
5432 x 5137
Think step by step. | 27904184 | What is the solution to the long multiplication equation below?
5432 x 5137
Think step by step.
Break this question 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, ... | To solve \(5432 \times 5137\) using the distributive property of multiplication, we'll break it down step by step by multiplying 5432 by each digit of 5137, taking into account the respective place values.
### Step 1: Break Down the Numbers
We can express \(5137\) as:
\[
5137 = 5000 + 100 + 30 + 7
\]
We'll calculate \... | What is the solution to the long multiplication equation below?
5432 x 5137
Think step by step.
Break this question 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, ... | false | The final result of the multiplication is incorrectly calculated as 27869684, while the correct result is 27904184. The breakdown and additions were done correctly, but the final summation yielded the wrong outcome. | |
What is the solution to the long multiplication equation below?
3333 x 6350
Think step by step. | 21164550 | What is the solution to the long multiplication equation below?
3333 x 6350
Think step by step.
Break this question 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, ... | To solve the multiplication \( 3333 \times 6350 \) using the distributive property, we break down \( 6350 \) into its place value components:
\[
6350 = 6000 + 300 + 50
\]
Now, we can use the distributive property to express the multiplication as:
\[
3333 \times 6350 = 3333 \times (6000 + 300 + 50)
\]
This can be e... | What is the solution to the long multiplication equation below?
3333 x 6350
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to decompose the multiplication, computes each component accurately, and properly adds them together. The final answer matches the ground truth, confirming its correctness. | |
What is the solution to the long multiplication equation below?
3873 x 5395
Think step by step. | 20894835 | What is the solution to the long multiplication equation below?
3873 x 5395
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 3873 \times 5395 \) using the **distributive property**, we can break it down as follows:
1. **Break down the second number (5395)**:
\[
5395 = 5000 + 300 + 90 + 5
\]
2. **Multiply 3873 by each part of the second number**:
- Multiply \( 3873 \) by \( 5000 \):
\[... | What is the solution to the long multiplication equation below?
3873 x 5395
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts and accurately adds the results, verifying with standard long multiplication that the final answer is indeed correct. | |
What is the solution to the long multiplication equation below?
8599 x 8263
Think step by step. | 71053537 | What is the solution to the long multiplication equation below?
8599 x 8263
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 8599 \times 8263 \) using the distributive property of multiplication over addition, we first break down the numbers by their place values.
The number \( 8263 \) can be split into:
\[
8263 = 8000 + 200 + 60 + 3
\]
Now we can use this breakdown to distribute \( 8599 \):
\[
859... | What is the solution to the long multiplication equation below?
8599 x 8263
Think step by step.
Break this question 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, ... | true | The solution provided uses the distributive property correctly, calculating each partial product and performing the addition accurately. The final result, 71053537, matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5260 x 3177
Think step by step. | 16711020 | What is the solution to the long multiplication equation below?
5260 x 3177
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 5260 \times 3177 \) using the distributive property, we break this down step by step.
### Step 1: Break down the numbers
**First Number:**
\( 5260 \) can be viewed as \( 5000 + 200 + 60 + 0 \).
**Second Number:**
\( 3177 \) can be viewed as \( 3000 + 100 + 70 + 7 \).
### ... | What is the solution to the long multiplication equation below?
5260 x 3177
Think step by step.
Break this question 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, ... | false | The solution provided gives an answer of 16,211,020, while the ground truth solution states that the correct result of the multiplication is 16,711,020. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
3170 x 6883
Think step by step. | 21819110 | What is the solution to the long multiplication equation below?
3170 x 6883
Think step by step.
Break this question 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, ... | To solve the multiplication of 3170 by 6883 using the distributive property of multiplication, we'll break down the second number (6883) into its individual digits and multiply each digit by the first number (3170), considering the place value of each digit.
We'll start by breaking down 6883 into its components:
- 60... | What is the solution to the long multiplication equation below?
3170 x 6883
Think step by step.
Break this question 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, ... | false | The solution states that the multiplication of 3170 by 6883 yields 21731510, but the ground truth solution provided is 21819110. The final result 21731510 is incorrect as it does not match the ground truth. | |
What is the solution to the long multiplication equation below?
7940 x 3761
Think step by step. | 29862340 | What is the solution to the long multiplication equation below?
7940 x 3761
Think step by step.
Break this question 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, ... | To solve \( 7940 \times 3761 \) using the **distributive property of multiplication over addition**, we can break down \( 3761 \) into its place values: \( 3000 + 700 + 60 + 1 \). Then, we will multiply \( 7940 \) by each of these components individually and finally add the results.
### Step 1: Break down \( 3761 \)
-... | What is the solution to the long multiplication equation below?
7940 x 3761
Think step by step.
Break this question 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, ... | true | The solution provided correctly applies the distributive property to multiply 7940 by the components of 3761. Each multiplication step is accurate, and the subsequent additions of the partial results are also performed correctly. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8439 x 3868
Think step by step. | 32642052 | What is the solution to the long multiplication equation below?
8439 x 3868
Think step by step.
Break this question 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, ... | To solve the multiplication of \(8439 \times 3868\) using the distributive property of multiplication over addition, we can break down \(3868\) into its individual digits. Specifically, we will treat \(3868\) as \(3000 + 800 + 60 + 8\).
### Step 1: Distributing \(8439\)
Using the distributed form:
\[
8439 \times 38... | What is the solution to the long multiplication equation below?
8439 x 3868
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication in the solution is 32644632, while the provided ground truth solution is 32642052. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
3965 x 8023
Think step by step. | 31811195 | What is the solution to the long multiplication equation below?
3965 x 8023
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 3965 \times 8023 \) using the distributive property of multiplication over addition, we will break the second number (8023) into its place value components and multiply each component by the first number (3965).
The number 8023 can be expressed as:
\[
8023 = 8000 + 0200 + 0000 +... | What is the solution to the long multiplication equation below?
3965 x 8023
Think step by step.
Break this question 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, ... | false | The final result of the multiplication was calculated incorrectly, as the original calculations suggested a sum of 32524895. However, the ground truth solution is 31811195, indicating a significant discrepancy. | |
What is the solution to the long multiplication equation below?
8151 x 9564
Think step by step. | 77956164 | What is the solution to the long multiplication equation below?
8151 x 9564
Think step by step.
Break this question 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, ... | To multiply \( 8151 \) by \( 9564 \) using the distributive property of multiplication over addition, we will break down the numbers based on their place values.
1. **Breaking Down the Numbers**:
- \( 9564 \) can be separated into its digits based on their place values:
- \( 9000 \) (9000)
- \( 500 \) (... | What is the solution to the long multiplication equation below?
8151 x 9564
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to multiply each component of 9564 by 8151, adds the partial results accurately, and verifies the final answer. The final result matches the ground truth solution, confirming it is correct. | |
What is the solution to the long multiplication equation below?
9467 x 7280
Think step by step. | 68919760 | What is the solution to the long multiplication equation below?
9467 x 7280
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9467 \times 7280 \) using the distributive property, we first break down \( 7280 \) into its constituent parts based on place value:
\[
7280 = 7000 + 200 + 80
\]
Now, we'll multiply \( 9467 \) by each of these parts separately:
1. **Multiply by 7000**:
\[
9467 \times 7000 = 9467 ... | What is the solution to the long multiplication equation below?
9467 x 7280
Think step by step.
Break this question 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, ... | false | The solution provided calculates the multiplication of 9467 and 7280 as 69019760. However, the ground truth solution indicates that the correct answer is 68919760, which means the solution is incorrect. | |
What is the solution to the long multiplication equation below?
2094 x 5907
Think step by step. | 12369258 | What is the solution to the long multiplication equation below?
2094 x 5907
Think step by step.
Break this question 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, ... | To solve \( 2094 \times 5907 \) using the distributive property of multiplication over addition, we can break down \( 5907 \) into its individual digits, which are \( 5000, 900, 0, \) and \( 7 \). We can then multiply \( 2094 \) by each of these values separately and add the results.
### Step-by-Step Multiplication
1... | What is the solution to the long multiplication equation below?
2094 x 5907
Think step by step.
Break this question 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, ... | true | The provided solution accurately applies the distributive property of multiplication to calculate the product of 2094 and 5907. Each step is correct, including breaking down 5907, performing the multiplications, and correctly adding the results together. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4203 x 4688
Think step by step. | 19703664 | What is the solution to the long multiplication equation below?
4203 x 4688
Think step by step.
Break this question 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, ... | To solve \( 4203 \times 4688 \) using the distributive property of multiplication over addition, we can break down the second number (4688) into its place values. This will help us multiply \( 4203 \) by each part of \( 4688 \) step by step.
The breakdown of \( 4688 \) is:
\[
4688 = 4000 + 600 + 80 + 8
\]
Now we will... | What is the solution to the long multiplication equation below?
4203 x 4688
Think step by step.
Break this question 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, ... | false | The solution correctly applied the distributive property and broke down the numbers correctly, performing the calculations step-by-step. However, the final result calculated by the solution is 19673664, but the ground truth solution states that the correct answer is 19703664. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
3048 x 2402
Think step by step. | 7321296 | What is the solution to the long multiplication equation below?
3048 x 2402
Think step by step.
Break this question 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, ... | To solve the multiplication \( 3048 \times 2402 \) using the distributive property, we will break down the second number \( 2402 \) into its constituent place values: \( 2000 + 400 + 0 + 2 \). Then, we will multiply each of these components by \( 3048 \) and sum the results.
### Step 1: Breakdown of \( 2402 \)
We rewr... | What is the solution to the long multiplication equation below?
3048 x 2402
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication is different from the ground truth solution. The provided solution correctly follows the distributive property and performs the calculations accurately based on the steps, but it ultimately leads to an incorrect final answer. | |
What is the solution to the long multiplication equation below?
9070 x 8127
Think step by step. | 73711890 | What is the solution to the long multiplication equation below?
9070 x 8127
Think step by step.
Break this question 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, ... | Let's break down the multiplication of \( 9070 \times 8127 \) step by step using the **distributive property of multiplication over addition**.
First, we can express \( 8127 \) in terms of its place values:
\[
8127 = 8000 + 100 + 20 + 7
\]
Now, we can use the distributive property to multiply \( 9070 \) by each part... | What is the solution to the long multiplication equation below?
9070 x 8127
Think step by step.
Break this question 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, ... | false | The calculated product of 9070 and 8127 using the distributive property was found to be 73691890, but the ground truth solution states that the correct answer is 73711890. Therefore, the solution provided is incorrect. | |
What is the solution to the long multiplication equation below?
9857 x 4502
Think step by step. | 44376214 | What is the solution to the long multiplication equation below?
9857 x 4502
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 9857 \times 4502 \) step by step using the **distributive property of multiplication over addition**, we will break down the second number \( 4502 \) and multiply each digit of it by \( 9857 \), accounting for their place values.
1. **Break down the second number \( 4502 \)**:
... | What is the solution to the long multiplication equation below?
9857 x 4502
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property of multiplication to break down the multiplication of 9857 and 4502 into smaller parts, computes each part accurately, and sums them correctly to arrive at the final product. The final answer matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3302 x 4938
Think step by step. | 16305276 | What is the solution to the long multiplication equation below?
3302 x 4938
Think step by step.
Break this question 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, ... | To multiply \(3302\) by \(4938\) using the distributive property, we'll break down \(4938\) into its place values:
\[
4938 = 4000 + 900 + 30 + 8
\]
We will multiply \(3302\) by each component of \(4938\):
1. **Multiply by 4000:**
\[
3302 \times 4000 = 3302 \times 4 \times 1000 = 13208 \times 1000 = 13208000
... | What is the solution to the long multiplication equation below?
3302 x 4938
Think step by step.
Break this question 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, ... | false | The calculated final result of the multiplication using the distributive property is incorrect as it does not match the ground truth solution. The solution provided in the SOLUTION box states that the final result is \(16215676\), while the ground truth solution is \(16305276\). Therefore, the solution is not correct. | |
What is the solution to the long multiplication equation below?
2298 x 1579
Think step by step. | 3628542 | What is the solution to the long multiplication equation below?
2298 x 1579
Think step by step.
Break this question 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, ... | To solve the multiplication \( 2298 \times 1579 \) using the distributive property, we will break it down into manageable steps. We'll represent \( 1579 \) as \( 1000 + 500 + 70 + 9 \) and distribute \( 2298 \) across each of these components.
**Step 1: Expand using the distributive property**
\[
2298 \times 1579 = 2... | What is the solution to the long multiplication equation below?
2298 x 1579
Think step by step.
Break this question 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, ... | true | The solution provided uses the distributive property correctly, breaking down the multiplication into simpler parts and accurately computing each part. The final addition of the partial results leads to the correct answer, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2924 x 7977
Think step by step. | 23324748 | What is the solution to the long multiplication equation below?
2924 x 7977
Think step by step.
Break this question 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, ... | To solve the multiplication of 2924 by 7977 using the distributive property of multiplication over addition, we will break down the second number (7977) into its digits, accounting for their place values, and multiply each by the first number (2924).
Here’s how to do it step-by-step:
### Step 1: Break down 7977
We c... | What is the solution to the long multiplication equation below?
2924 x 7977
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property of multiplication, providing step-by-step calculations for each partial product. Each step is accurately calculated and correctly summed, leading to the final result which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3869 x 3758
Think step by step. | 14539702 | What is the solution to the long multiplication equation below?
3869 x 3758
Think step by step.
Break this question 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, ... | To solve the multiplication of \( 3869 \times 3758 \) using the **distributive property of multiplication over addition**, we will break down \( 3758 \) into its individual digits considering their place value, compute the partial products, and then add them together.
### Step 1: Break down the second number
The numb... | What is the solution to the long multiplication equation below?
3869 x 3758
Think step by step.
Break this question 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, ... | false | The solution provided the result of the multiplication as 14539602, while the ground truth solution states the correct multiplication result is 14539702. This indicates that there is an error in the calculations or additions performed in the proposed solution. | |
What is the solution to the long multiplication equation below?
4474 x 9008
Think step by step. | 40301792 | What is the solution to the long multiplication equation below?
4474 x 9008
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 4474 \times 9008 \) using the distributive property of multiplication over addition, we can break this down step by step.
### Step 1: Break down the second number
We can break down \( 9008 \) into its components:
\[
9008 = 9000 + 8
\]
### Step 2: Distribute \( 4474 \) over \( ... | What is the solution to the long multiplication equation below?
4474 x 9008
Think step by step.
Break this question 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, ... | false | The calculated result of 4474 × 9008 was found to be 40299992, while the ground truth solution states it should be 40301792. This discrepancy shows the presented solution is incorrect. | |
What is the solution to the long multiplication equation below?
1506 x 4037
Think step by step. | 6079722 | What is the solution to the long multiplication equation below?
1506 x 4037
Think step by step.
Break this question 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, ... | To solve the multiplication \(1506 \times 4037\) using the distributive property of multiplication over addition, we can break down the problem step by step.
### Step 1: Break Down the Second Number (4037)
First, we can represent \(4037\) using its place values:
\[
4037 = 4000 + 30 + 7
\]
### Step 2: Distribute the... | What is the solution to the long multiplication equation below?
1506 x 4037
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication into manageable parts, accurately computes each multiplication step, and properly adds the partial results. The final answer matches the ground truth solution, confirming its correctness. | |
What is the solution to the long multiplication equation below?
8915 x 3999
Think step by step. | 35651085 | What is the solution to the long multiplication equation below?
8915 x 3999
Think step by step.
Break this question 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, ... | To find the product of \(8915 \times 3999\) using the **distributive property of multiplication over addition**, we can break down 3999 into its place values:
\[
3999 = 3000 + 900 + 90 + 9
\]
Now, we can multiply 8915 by each of these parts separately, and then add the results together.
### Step 1: Multiply 8915 by ... | What is the solution to the long multiplication equation below?
8915 x 3999
Think step by step.
Break this question 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, ... | false | The computed answer of 35568085 is incorrect as compared to the ground truth solution of 35651085. The incorrect multiplication or addition leads to this error. | |
What is the solution to the long multiplication equation below?
4629 x 7389
Think step by step. | 34203681 | What is the solution to the long multiplication equation below?
4629 x 7389
Think step by step.
Break this question 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, ... | To solve the multiplication of 4629 by 7389 using the distributive property, we will break down 7389 into its components based on place value and then multiply 4629 by each of those components. Let’s break this down step by step.
### Step 1: Break Down the Second Number
The number 7389 can be broken down as:
- 7000 (7... | What is the solution to the long multiplication equation below?
4629 x 7389
Think step by step.
Break this question 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, ... | false | The calculated result of 4629 multiplied by 7389 is 34199981, which does not match the ground truth solution of 34203681. | |
What is the solution to the long multiplication equation below?
8365 x 7965
Think step by step. | 66627225 | What is the solution to the long multiplication equation below?
8365 x 7965
Think step by step.
Break this question 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, ... | To solve the multiplication \( 8365 \times 7965 \) using the distributive property of multiplication over addition, we can break down the second number into its place values:
- \( 7965 = 7000 + 900 + 60 + 5 \)
Now, we will multiply \( 8365 \) by each part of \( 7965 \) separately and then add the results together.
... | What is the solution to the long multiplication equation below?
8365 x 7965
Think step by step.
Break this question 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, ... | false | The calculated result of 66587225 does not match the ground truth solution of 66627225, indicating an error in the calculations. | |
What is the solution to the long multiplication equation below?
9659 x 2514
Think step by step. | 24282726 | What is the solution to the long multiplication equation below?
9659 x 2514
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 9659 \times 2514 \) using the distributive property of multiplication over addition, we can break down \( 2514 \) into its individual digits by their place value:
\[
2514 = 2000 + 500 + 10 + 4
\]
Now, we can multiply \( 9659 \) by each of these components individually, and then ... | What is the solution to the long multiplication equation below?
9659 x 2514
Think step by step.
Break this question 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, ... | true | The provided solution correctly applied the distributive property of multiplication and accurately calculated the individual components, leading to the correct final result of the multiplication problem. The addition steps were also verified and found to be correct. Thus, the solution matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
1834 x 5854
Think step by step. | 10736236 | What is the solution to the long multiplication equation below?
1834 x 5854
Think step by step.
Break this question 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, ... | To solve the multiplication \( 1834 \times 5854 \) using the distributive property of multiplication over addition, we'll break down the second number (5854) by its digits and then multiply each part by 1834 while accounting for place value.
### Step 1: Break down 5854
The number 5854 can be expressed as:
\[
5854 = ... | What is the solution to the long multiplication equation below?
1834 x 5854
Think step by step.
Break this question 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, ... | false | The final result of the multiplication computed in the solution is 10732156, whereas the ground truth solution is 10736236. The arithmetic does not yield the correct product, therefore the solution is incorrect. | |
What is the solution to the long multiplication equation below?
6332 x 1853
Think step by step. | 11733196 | What is the solution to the long multiplication equation below?
6332 x 1853
Think step by step.
Break this question 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, ... | To solve the multiplication using the **distributive property of multiplication over addition**, we can break down the numbers and multiply each part step by step.
The multiplication we want to perform is:
\[
6332 \times 1853
\]
Now, we can break down \(1853\) into its place values:
\[
1853 = 1000 + 800 + 50 + 3
\]... | What is the solution to the long multiplication equation below?
6332 x 1853
Think step by step.
Break this question 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, ... | false | The computed final result of 11783196 from the provided solution does not match the ground truth solution of 11733196, indicating an error in the calculations. | |
What is the solution to the long multiplication equation below?
6587 x 2961
Think step by step. | 19504107 | What is the solution to the long multiplication equation below?
6587 x 2961
Think step by step.
Break this question 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, ... | To solve \( 6587 \times 2961 \) using the distributive property of multiplication over addition, we can break each number into its parts based on place value.
1. **Break down the numbers:**
- \( 2961 = 2000 + 900 + 60 + 1 \)
- \( 6587 \) remains as \( 6587 \).
2. **Use the distributive property:**
We will mu... | What is the solution to the long multiplication equation below?
6587 x 2961
Think step by step.
Break this question 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, ... | false | The calculated result of 6587 multiplied by 2961 is 19514107, while the ground truth solution provided is 19504107. Thus, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
6009 x 5460
Think step by step. | 32809140 | What is the solution to the long multiplication equation below?
6009 x 5460
Think step by step.
Break this question 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, ... | To compute \( 6009 \times 5460 \) using the distributive property of multiplication over addition, we can break down the numbers based on their place values.
### Step 1: Breakdown the numbers
We can decompose \( 5460 \) as follows:
\[
5460 = 5000 + 400 + 60
\]
### Step 2: Multiply \( 6009 \) by each component of \( 5... | What is the solution to the long multiplication equation below?
6009 x 5460
Think step by step.
Break this question 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, ... | false | The solution computes the product of 6009 and 5460 by using the distributive property correctly and follows the steps for multiplication and addition. However, the final sum of the individual products is incorrectly calculated. The ground truth solution of 32809140 is the correct answer for 6009 x 5460, indicating an e... | |
What is the solution to the long multiplication equation below?
1720 x 4837
Think step by step. | 8319640 | What is the solution to the long multiplication equation below?
1720 x 4837
Think step by step.
Break this question 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, ... | To solve the multiplication of 1720 by 4837 using the distributive property of multiplication over addition, we can break the problem down into parts based on the digits of the second number (4837).
### Step 1: Break down 4837
4837 can be broken down into thousands, hundreds, tens, and units:
- \( 4837 = 4000 + 800 +... | What is the solution to the long multiplication equation below?
1720 x 4837
Think step by step.
Break this question 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, ... | false | The solution presented provides a detailed method using the distributive property. However, the final result, \( \boxed{8293840} \), does not match the ground truth solution, which is \( 8319640 \). Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
7771 x 6243
Think step by step. | 48514353 | What is the solution to the long multiplication equation below?
7771 x 6243
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 7771 \times 6243 \) using the **distributive property of multiplication over addition**, we can break down \( 6243 \) into its place values:
\[
6243 = 6000 + 200 + 40 + 3
\]
Now we can multiply \( 7771 \) by each of the components of \( 6243 \):
1. **Multiply by 6000**:
\[
... | What is the solution to the long multiplication equation below?
7771 x 6243
Think step by step.
Break this question 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, ... | false | The calculated result of 7771 x 6243 is shown to be 48414353, but the ground truth solution states it is 48514353. Therefore, the answer provided in the solution is incorrect as it differs from the ground truth. | |
What is the solution to the long multiplication equation below?
6582 x 6291
Think step by step. | 41407362 | What is the solution to the long multiplication equation below?
6582 x 6291
Think step by step.
Break this question 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, ... | To solve the multiplication \( 6582 \times 6291 \) using the distributive property, we will break it down step-by-step by multiplying \( 6582 \) by each digit of \( 6291 \), taking into account the place value of each digit.
### Step 1: Break down \( 6291 \)
The number \( 6291 \) can be broken down as:
\[ 6291 = 600... | What is the solution to the long multiplication equation below?
6582 x 6291
Think step by step.
Break this question 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, ... | true | The provided solution accurately follows the distributive property for multiplication and correctly calculates each partial product. The final summation of the partial products leads to the correct result of 41407362, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8898 x 1750
Think step by step. | 15571500 | What is the solution to the long multiplication equation below?
8898 x 1750
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 8898 \times 1750 \) using the distributive property of multiplication over addition, we can break down the number \( 1750 \) into its components:
\[
1750 = 1000 + 700 + 50 + 0
\]
Now we can multiply \( 8898 \) by each part of \( 1750 \):
1. **Multiply by 1000:**
\[
8898 \... | What is the solution to the long multiplication equation below?
8898 x 1750
Think step by step.
Break this question 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, ... | false | The solution provided calculates the multiplication of 8898 and 1750 using the distributive property but arrives at a sum of 15621500, which is incorrect when compared to the ground truth solution of 15571500. The discrepancy indicates at least one arithmetic error occurred while summing the partial results. | |
What is the solution to the long multiplication equation below?
8307 x 8131
Think step by step. | 67544217 | What is the solution to the long multiplication equation below?
8307 x 8131
Think step by step.
Break this question 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, ... | To solve \( 8307 \times 8131 \) using the distributive property of multiplication over addition, we will break down the second number (8131) into its individual digits, considering their place values.
The number 8131 can be expressed as:
\[
8131 = 8000 + 100 + 30 + 1
\]
We will multiply \( 8307 \) by each component o... | What is the solution to the long multiplication equation below?
8307 x 8131
Think step by step.
Break this question 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, ... | true | The given solution correctly applies the distributive property by breaking down 8131 into its components, performing the multiplications accurately, and summing the results correctly. The final product calculated matches the ground truth, confirming the correctness of the solution. | |
What is the solution to the long multiplication equation below?
9874 x 4589
Think step by step. | 45311786 | What is the solution to the long multiplication equation below?
9874 x 4589
Think step by step.
Break this question 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, ... | To multiply 9874 by 4589 using the distributive property, we can break down the second number (4589) into its individual digits, taking into account their place values.
### Step 1: Expand the Second Number
We can express 4589 as:
\[
4589 = 4000 + 500 + 80 + 9
\]
### Step 2: Multiply Each Part by 9874
Now we will dis... | What is the solution to the long multiplication equation below?
9874 x 4589
Think step by step.
Break this question 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, ... | true | The provided solution correctly follows the distributive property for multiplication, with accurate step-by-step calculations and a final result that matches the ground truth result of 45311786. | |
What is the solution to the long multiplication equation below?
5000 x 3258
Think step by step. | 16290000 | What is the solution to the long multiplication equation below?
5000 x 3258
Think step by step.
Break this question 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, ... | To solve \(5000 \times 3258\) using the distributive property of multiplication over addition, let's break it down step by step.
We can rewrite \(3258\) as a sum of its place values:
\[
3258 = 3000 + 200 + 50 + 8
\]
Now, we can distribute \(5000\) across each of these terms:
1. **Multiply by 3000**:
\[
5000 \ti... | What is the solution to the long multiplication equation below?
5000 x 3258
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication of 5000 and 3258 into smaller parts, calculates each part accurately, and then adds them correctly. The final answer is consistent with the ground truth. | |
What is the solution to the long multiplication equation below?
8519 x 6185
Think step by step. | 52690015 | What is the solution to the long multiplication equation below?
8519 x 6185
Think step by step.
Break this question 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, ... | Sure! Let's break down the multiplication of \( 8519 \times 6185 \) step by step using the distributive property, focusing on each digit of the second number and how it influences the multiplication.
### Step 1: Breakdown the Second Number
We can break down the number \( 6185 \) into its individual components based on... | What is the solution to the long multiplication equation below?
8519 x 6185
Think step by step.
Break this question 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, ... | false | The computed result of the multiplication, 52689915, is incorrect as it does not match the ground truth solution of 52690015. The slight discrepancy suggests there may have been an error in addition or in one of the multiplication steps. | |
What is the solution to the long multiplication equation below?
6686 x 8827
Think step by step. | 59017322 | What is the solution to the long multiplication equation below?
6686 x 8827
Think step by step.
Break this question 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, ... | To solve the multiplication \( 6686 \times 8827 \) using the distributive property, we can break down \( 8827 \) into its place values:
\[
8827 = 8000 + 800 + 20 + 7
\]
Now, we will multiply \( 6686 \) by each of these terms separately.
### Step 1: Multiply \( 6686 \) by \( 8000 \)
\[
6686 \times 8000 = 6686 \times... | What is the solution to the long multiplication equation below?
6686 x 8827
Think step by step.
Break this question 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, ... | false | The solution presented miscalculates the final addition of the partial results. The correct value calculated is 59017322, which indicates that the final answer should be this number instead of the incorrectly calculated 58906882. | |
What is the solution to the long multiplication equation below?
4416 x 5084
Think step by step. | 22450944 | What is the solution to the long multiplication equation below?
4416 x 5084
Think step by step.
Break this question 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, ... | Let's break down the multiplication \( 4416 \times 5084 \) using the distributive property step by step.
### Step 1: Break down the second number (5084)
We can express \( 5084 \) in terms of its place value:
\[
5084 = 5000 + 80 + 4
\]
### Step 2: Distribute \( 4416 \) across the components of \( 5084 \)
We will multi... | What is the solution to the long multiplication equation below?
4416 x 5084
Think step by step.
Break this question 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, ... | true | The solution correctly applied the distributive property of multiplication and verified the result through direct multiplication. Both methods yield the same product of 22450944, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2165 x 2976
Think step by step. | 6443040 | What is the solution to the long multiplication equation below?
2165 x 2976
Think step by step.
Break this question 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, ... | To solve the multiplication \( 2165 \times 2976 \) using the distributive property of multiplication over addition, we will break down the second number, \( 2976 \), into its components:
\[
2976 = 2000 + 900 + 70 + 6
\]
Now, we will multiply \( 2165 \) by each of these components and then sum the results.
### Step ... | What is the solution to the long multiplication equation below?
2165 x 2976
Think step by step.
Break this question 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, ... | false | The calculated product of 2165 times 2976 was found to be 6431040, while the ground truth solution indicates it is 6443040. The two results do not match, signaling a computational error in the solution. | |
What is the solution to the long multiplication equation below?
6601 x 1713
Think step by step. | 11307513 | What is the solution to the long multiplication equation below?
6601 x 1713
Think step by step.
Break this question 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, ... | To solve the multiplication of \( 6601 \times 1713 \) using the **distributive property of multiplication over addition**, we can break down the multiplication step by step.
### Step 1: Break down the second number (1713)
We can express \( 1713 \) as:
\[
1713 = 1000 + 700 + 10 + 3
\]
### Step 2: Apply the distributiv... | What is the solution to the long multiplication equation below?
6601 x 1713
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication is 11316513, while the ground truth solution states it should be 11307513. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
4503 x 3441
Think step by step. | 15494823 | What is the solution to the long multiplication equation below?
4503 x 3441
Think step by step.
Break this question 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, ... | To solve the multiplication of 4503 by 3441 using the distributive property of multiplication over addition, we will break down the second number (3441) into its place value components. This method will allow us to multiply 4503 by each component separately and then sum the results.
### Step 1: Breakdown the second nu... | What is the solution to the long multiplication equation below?
4503 x 3441
Think step by step.
Break this question 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, ... | false | The computed result of the multiplication of 4503 by 3441 using the distributive property is incorrectly stated as 15422883. The correct value, as indicated by the ground truth solution, is 15494823. This indicates that the calculations performed in the evaluation of the sum are incorrect, leading to the wrong final re... | |
What is the solution to the long multiplication equation below?
5257 x 8393
Think step by step. | 44122001 | What is the solution to the long multiplication equation below?
5257 x 8393
Think step by step.
Break this question 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, ... | To solve the multiplication \(5257 \times 8393\) using the distributive property, we can break it down as follows:
1. **Break down the second number (8393)**:
\[
8393 = 8000 + 300 + 90 + 3
\]
2. **Multiply each component of 8393 by 5257**:
- **First, multiply by 8000**:
\[
5257 \times 8000 = 420... | What is the solution to the long multiplication equation below?
5257 x 8393
Think step by step.
Break this question 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, ... | true | The provided solution correctly applies the distributive property, performs the multiplications accurately, and sums the results correctly to reach the final answer of 44122001, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
3592 x 1116
Think step by step. | 4008672 | What is the solution to the long multiplication equation below?
3592 x 1116
Think step by step.
Break this question 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, ... | To solve the multiplication \(3592 \times 1116\) using the distributive property of multiplication over addition, we can break down the process step by step.
### Step 1: Break down the second number
First, express \(1116\) as a sum of its digits, taking into account their places:
\[
1116 = 1000 + 100 + 10 + 6
\]
##... | What is the solution to the long multiplication equation below?
3592 x 1116
Think step by step.
Break this question 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, ... | true | The provided solution correctly applies the distributive property to multiply 3592 by 1116 and accurately calculates each partial product. Additionally, the final result of the calculation is verified through both the distribution method and direct multiplication, confirming that the answer is indeed correct. | |
What is the solution to the long multiplication equation below?
9540 x 1875
Think step by step. | 17887500 | What is the solution to the long multiplication equation below?
9540 x 1875
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9540 \times 1875 \) using the distributive property, we will break the second number \( 1875 \) down into its components based on its place value.
### Step 1: Break down \( 1875 \)
We can express \( 1875 \) in terms of its constituent digits:
\[
1875 = 1000 + 800 + 70 + 5
\]
### Step 2... | What is the solution to the long multiplication equation below?
9540 x 1875
Think step by step.
Break this question 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, ... | false | The final result of the multiplication calculated by the solution (17827500) does not match the ground truth solution (17887500), indicating an error in the calculations. | |
What is the solution to the long multiplication equation below?
5256 x 5185
Think step by step. | 27252360 | What is the solution to the long multiplication equation below?
5256 x 5185
Think step by step.
Break this question 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, ... | To solve \( 5256 \times 5185 \) step by step using the **distributive property of multiplication over addition**, we will break down \( 5185 \) into its place value components:
\[
5185 = 5000 + 100 + 80 + 5
\]
We will multiply \( 5256 \) by each of these components and then add the results together.
#### Step 1: Mul... | What is the solution to the long multiplication equation below?
5256 x 5185
Think step by step.
Break this question 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, ... | false | The provided solution gives a product of 27252460, while the ground truth solution states the product is 27252360. Since these two results do not match, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
4396 x 7461
Think step by step. | 32798556 | What is the solution to the long multiplication equation below?
4396 x 7461
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 4396 \times 7461 \) using the distributive property of multiplication over addition, we can break it down step-by-step.
1. **Break down the second number (7461)** into its place values:
\[
7461 = 7000 + 400 + 60 + 1
\]
2. **Multiply each part by 4396**:
- **Step 1**... | What is the solution to the long multiplication equation below?
4396 x 7461
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication problem and accurately computes all partial products and their sum, matching the ground truth solution. | |
What is the solution to the long multiplication equation below?
4665 x 2421
Think step by step. | 11293965 | What is the solution to the long multiplication equation below?
4665 x 2421
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 4665 \times 2421 \) using the distributive property, we break it down step by step:
1. **Break Down the Second Number**:
We'll break down \( 2421 \) into its place value components:
\[
2421 = 2000 + 400 + 20 + 1
\]
2. **Multiply Each Component by \( 4665 \)**:
Now... | What is the solution to the long multiplication equation below?
4665 x 2421
Think step by step.
Break this question 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, ... | false | The provided solution shows the process of calculating the multiplication of 4665 and 2421 correctly, yet the final answer of 11218665 does not match the ground truth solution of 11293965. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
8509 x 6410
Think step by step. | 54542690 | What is the solution to the long multiplication equation below?
8509 x 6410
Think step by step.
Break this question 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, ... | To solve \(8509 \times 6410\) using the distributive property of multiplication over addition, we'll break down the second number, \(6410\), into its individual digits based on their place values, which are 6000, 400, 10, and 0.
The expression can be expanded as follows:
\[
8509 \times 6410 = 8509 \times (6000 + 400... | What is the solution to the long multiplication equation below?
8509 x 6410
Think step by step.
Break this question 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, ... | false | The solution provided incorrectly calculates the final sum of the products, leading to an incorrect final result. The ground truth solution is correct, which is 54542690. | |
What is the solution to the long multiplication equation below?
7117 x 8636
Think step by step. | 61462412 | What is the solution to the long multiplication equation below?
7117 x 8636
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 7117 \times 8636 \) using the distributive property of multiplication over addition, we'll break it down step by step.
### Step 1: Break Down the Numbers
We'll break the second number \( 8636 \) into its place values:
- \( 8636 = 8000 + 600 + 30 + 6 \)
### Step 2: Multiply by Ea... | What is the solution to the long multiplication equation below?
7117 x 8636
Think step by step.
Break this question 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, ... | false | The final calculated product of the multiplication problem was stated as 61,485,892, while the correct ground truth solution is 61,462,412. There is a discrepancy of 23,480, indicating the multiplication and subsequent steps were flawed. | |
What is the solution to the long multiplication equation below?
1111 x 5441
Think step by step. | 6044951 | What is the solution to the long multiplication equation below?
1111 x 5441
Think step by step.
Break this question 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, ... | To perform the multiplication \(1111 \times 5441\) using the distributive property, we break down the second number, \(5441\), into its place values. The number \(5441\) can be represented as:
\[
5441 = 5000 + 400 + 40 + 1
\]
Next, we'll multiply \(1111\) by each of these components separately, taking into account th... | What is the solution to the long multiplication equation below?
1111 x 5441
Think step by step.
Break this question 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, ... | true | The provided solution accurately applies the distributive property to decompose the multiplication into manageable components, performs the calculations correctly, and correctly sums up the partial results. Additionally, the verification by long multiplication corroborates the final result. Therefore, the solution is c... | |
What is the solution to the long multiplication equation below?
7026 x 6617
Think step by step. | 46491042 | What is the solution to the long multiplication equation below?
7026 x 6617
Think step by step.
Break this question 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, ... | To solve the multiplication \( 7026 \times 6617 \) using the distributive property of multiplication over addition, we can break the numbers down into their component parts based on place value. Here's a step-by-step breakdown:
### Step 1: Break Down the Numbers
Break \( 6617 \) into its components:
- \( 6617 = 6000 ... | What is the solution to the long multiplication equation below?
7026 x 6617
Think step by step.
Break this question 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, ... | false | The provided solution calculates the product of 7026 and 6617 correctly to be 46406742 based on the step-by-step breakdown using the distributive property. However, the ground truth solution states that the correct answer is 46491042, which indicates that the provided solution is incorrect. | |
What is the solution to the long multiplication equation below?
1713 x 3976
Think step by step. | 6810888 | What is the solution to the long multiplication equation below?
1713 x 3976
Think step by step.
Break this question 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, ... | To calculate \( 1713 \times 3976 \) using the distributive property, we can break down the multiplication into smaller parts, considering each digit of the second number (3976) and its place value. Here’s how to do it step by step:
### Step 1: Break down the second number
The number \( 3976 \) can be split into its hu... | What is the solution to the long multiplication equation below?
1713 x 3976
Think step by step.
Break this question 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, ... | false | The solution correctly describes the use of the distributive property to perform multiplication, breaks down the numbers correctly, and computes partial products accurately. However, there is an error in the final sum of the partial products. The verified long multiplication shows that the correct result of the multipl... | |
What is the solution to the long multiplication equation below?
7718 x 7089
Think step by step. | 54712902 | What is the solution to the long multiplication equation below?
7718 x 7089
Think step by step.
Break this question 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, ... | To solve the multiplication \( 7718 \times 7089 \) using the distributive property, we can break down the second number \( 7089 \) into its place values. The number can be expressed as:
\[
7089 = 7000 + 80 + 9
\]
Now, we will multiply \( 7718 \) by each of these components separately and then add all the results tog... | What is the solution to the long multiplication equation below?
7718 x 7089
Think step by step.
Break this question 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, ... | false | The solution provided arrived at the final result of 54742902, but the ground truth solution states the correct answer is 54712902. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
2126 x 6425
Think step by step. | 13659550 | What is the solution to the long multiplication equation below?
2126 x 6425
Think step by step.
Break this question 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, ... | To solve the multiplication \( 2126 \times 6425 \) using the distributive property of multiplication over addition, we'll break it down step by step.
First, we can express \( 6425 \) in terms of its place value:
\[
6425 = 6000 + 400 + 20 + 5
\]
Now we will multiply \( 2126 \) by each of these components separately:
... | What is the solution to the long multiplication equation below?
2126 x 6425
Think step by step.
Break this question 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, ... | false | The final answer provided in the solution is 13559550, but the ground truth solution states the correct result is 13659550. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
5330 x 9102
Think step by step. | 48513660 | What is the solution to the long multiplication equation below?
5330 x 9102
Think step by step.
Break this question 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, ... | Sure! Let's break down the multiplication of \( 5330 \) and \( 9102 \) using the **distributive property of multiplication over addition**. Here’s how we can do that step-by-step:
### Step 1: Break down the numbers
First, we can express \( 9102 \) in terms of its place values:
\[
9102 = 9000 + 100 + 2
\]
### Step 2... | What is the solution to the long multiplication equation below?
5330 x 9102
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property, performs the calculations accurately, checks the result through direct multiplication, and arrives at the correct final answer of 48513660, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
9523 x 8589
Think step by step. | 81793047 | What is the solution to the long multiplication equation below?
9523 x 8589
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9523 \times 8589 \) step-by-step using the **distributive property**, we can first break down \( 8589 \) into its place values:
\[
8589 = 8000 + 500 + 80 + 9
\]
Now we will multiply \( 9523 \) by each of these components separately and account for the place value by adjusting the result... | What is the solution to the long multiplication equation below?
9523 x 8589
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to multiply by breaking down the second number into its components and accurately summing the partial products. The final calculated value matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
8013 x 4459
Think step by step. | 35729967 | What is the solution to the long multiplication equation below?
8013 x 4459
Think step by step.
Break this question 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, ... | To solve the multiplication \(8013 \times 4459\) using the distributive property of multiplication over addition, we can break it down into parts.
### Step 1: Break down the second number
First, we can break down \(4459\) into its place value components:
\[
4459 = 4000 + 400 + 50 + 9
\]
### Step 2: Distribute the fir... | What is the solution to the long multiplication equation below?
8013 x 4459
Think step by step.
Break this question 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, ... | false | The calculated result by the provided solution is oxed{35629967}, while the ground truth solution states that the correct result should be oxed{35729967}. There is a discrepancy of 100000, indicating that the multiplication was not performed correctly. | |
What is the solution to the long multiplication equation below?
8339 x 3250
Think step by step. | 27101750 | What is the solution to the long multiplication equation below?
8339 x 3250
Think step by step.
Break this question 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, ... | To solve \( 8339 \times 3250 \) using the distributive property of multiplication over addition, we can break it down as follows:
1. **Break down the second number into its place values**:
\[
3250 = 3000 + 200 + 50 + 0
\]
2. **Use the distributive property**:
Using the property, we can express \( 8339 \t... | What is the solution to the long multiplication equation below?
8339 x 3250
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property to break down the multiplication of 8339 and 3250 into manageable parts. All partial products were calculated accurately, and the final answer, after summing, matches the ground truth solution of 27101750. | |
What is the solution to the long multiplication equation below?
7102 x 4592
Think step by step. | 32612384 | What is the solution to the long multiplication equation below?
7102 x 4592
Think step by step.
Break this question 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, ... | To solve the problem \( 7102 \times 4592 \) step by step using the **distributive property of multiplication over addition**, we can break it down as follows:
1. **Break Down the Numbers**:
We can express \( 4592 \) in terms of its digits:
\[
4592 = 4000 + 500 + 90 + 2
\]
2. **Use the Distributive Propert... | What is the solution to the long multiplication equation below?
7102 x 4592
Think step by step.
Break this question 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, ... | true | The solution correctly applies the distributive property of multiplication, breaks down the numbers accurately, performs each multiplication step properly, adds the results correctly, and finally verifies each calculation. The final result matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5186 x 5585
Think step by step. | 28963810 | What is the solution to the long multiplication equation below?
5186 x 5585
Think step by step.
Break this question 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, ... | To solve the multiplication \( 5186 \times 5585 \) using the **distributive property of multiplication over addition**, we can break it down as follows:
1. **Write the Second Number in Expanded Form**:
Let's break down \( 5585 \) into its components based on place value:
\[
5585 = 5000 + 500 + 80 + 5
\]
2... | What is the solution to the long multiplication equation below?
5186 x 5585
Think step by step.
Break this question 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, ... | true | The solution correctly uses the distributive property to break down the multiplication, calculates each term accurately, and adds the partial results correctly to arrive at the correct final answer of 28963810. | |
What is the solution to the long multiplication equation below?
4008 x 8708
Think step by step. | 34901664 | What is the solution to the long multiplication equation below?
4008 x 8708
Think step by step.
Break this question 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, ... | To solve the multiplication of 4008 and 8708 using the distributive property, we can break down the numbers based on their place values.
### Step 1: Break down the numbers
We can express 8708 as:
\[
8708 = 8000 + 700 + 0 + 8
\]
Thus, we can rewrite the multiplication:
\[
4008 \times 8708 = 4008 \times (8000 + 700 + ... | What is the solution to the long multiplication equation below?
4008 x 8708
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication of 4008 and 8708 is incorrect. The solution provided arrived at 34897664 instead of the ground truth 34901664, thus it contains an error. | |
What is the solution to the long multiplication equation below?
8674 x 1565
Think step by step. | 13574810 | What is the solution to the long multiplication equation below?
8674 x 1565
Think step by step.
Break this question 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, ... | To solve the long multiplication of \(8674 \times 1565\) using the distributive property, we start by breaking down the second number, \(1565\), into its individual digits, each multiplied by the entire first number, \(8674\), while accounting for their respective place values.
The number \(1565\) can be expressed as:... | What is the solution to the long multiplication equation below?
8674 x 1565
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication of 8674 by 1565 is 13583810, while the correct ground truth solution is 13574810. Therefore, the solution provided is incorrect. | |
What is the solution to the long multiplication equation below?
9635 x 9111
Think step by step. | 87784485 | What is the solution to the long multiplication equation below?
9635 x 9111
Think step by step.
Break this question 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, ... | To solve \( 9635 \times 9111 \) using the distributive property of multiplication, we will break down the multiplication by each digit of the second number (9111) and account for place values.
### Step 1: Break 9111 into its place values
We can break \( 9111 \) down as:
\[
9111 = 9000 + 100 + 10 + 1
\]
### Step 2: Mu... | What is the solution to the long multiplication equation below?
9635 x 9111
Think step by step.
Break this question 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, ... | true | The solution accurately applies the distributive property of multiplication, breaks down 9111 correctly, performs all multiplications and additions correctly, and verifies the result through standard long multiplication. Therefore, the result of 9635 times 9111 is indeed 87784485. | |
What is the solution to the long multiplication equation below?
4731 x 9027
Think step by step. | 42706737 | What is the solution to the long multiplication equation below?
4731 x 9027
Think step by step.
Break this question 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, ... | To solve \( 4731 \times 9027 \) using the distributive property of multiplication over addition, we can break down \( 9027 \) into its individual digits. The number \( 9027 \) can be expressed as \( 9000 + 0 + 20 + 7 \). Thus, we have:
\[
4731 \times 9027 = 4731 \times (9000 + 0 + 20 + 7)
\]
Using the distributive pr... | What is the solution to the long multiplication equation below?
4731 x 9027
Think step by step.
Break this question 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, ... | false | The calculated result of 4731 multiplied by 9027 is incorrect. The breakdown and steps are flawed, leading to an incorrect conclusion of 42734037 instead of the ground truth of 42706737. | |
What is the solution to the long multiplication equation below?
9328 x 2277
Think step by step. | 21239856 | What is the solution to the long multiplication equation below?
9328 x 2277
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9328 \times 2277 \) using the **distributive property of multiplication over addition**, we'll break it down step by step. We can express \( 2277 \) as \( 2000 + 200 + 70 + 7 \).
### Step 1: Break Down the Second Number
We can write:
\[
2277 = 2000 + 200 + 70 + 7
\]
### Step 2: Multiply... | What is the solution to the long multiplication equation below?
9328 x 2277
Think step by step.
Break this question 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, ... | false | The calculated result of 9328 multiplied by 2277 is incorrect. The ground truth solution states the result should be 21239856, while the provided solution claims it is 21238756, which is a discrepancy of 10000. The multiplication steps and verification all lead to the conclusion that the solution is flawed. | |
What is the solution to the long multiplication equation below?
5492 x 1469
Think step by step. | 8067748 | What is the solution to the long multiplication equation below?
5492 x 1469
Think step by step.
Break this question 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, ... | To solve the multiplication \( 5492 \times 1469 \) using the distributive property of multiplication over addition, we will break it down step by step.
### Step 1: Break down 1469
We can express \( 1469 \) in terms of its place values:
\[
1469 = 1000 + 400 + 60 + 9
\]
### Step 2: Multiply each component by 5492
No... | What is the solution to the long multiplication equation below?
5492 x 1469
Think step by step.
Break this question 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, ... | false | The calculated product of 5492 and 1469 using the distributive property was found to be 8089538, whereas the ground truth solution states it is 8067748. Therefore, the solution provided does not match the ground truth, indicating it is incorrect. | |
What is the solution to the long multiplication equation below?
4459 x 3344
Think step by step. | 14910896 | What is the solution to the long multiplication equation below?
4459 x 3344
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 4459 \times 3344 \) using the distributive property of multiplication over addition, we'll break it down step by step.
### Step 1: Break Down the Numbers
We can break down the second number \( 3344 \) into its place values:
\[
3344 = 3000 + 300 + 40 + 4
\]
### Step 2: Distribute... | What is the solution to the long multiplication equation below?
4459 x 3344
Think step by step.
Break this question 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, ... | true | The provided solution correctly applies the distributive property to break down the multiplication of 4459 and 3344, calculates each part correctly, and verifies the final result through long multiplication. Both the verified final result and the ground truth match, indicating the solution is correct. | |
What is the solution to the long multiplication equation below?
4792 x 6273
Think step by step. | 30060216 | What is the solution to the long multiplication equation below?
4792 x 6273
Think step by step.
Break this question 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, ... | To solve the long multiplication of 4792 by 6273 using the distributive property, we will break down 6273 into its place values. The digits in 6273 are 6, 2, 7, and 3, in the thousands, hundreds, tens, and units places, respectively. This means we can express 6273 as follows:
\[
6273 = 6000 + 200 + 70 + 3
\]
Now we c... | What is the solution to the long multiplication equation below?
4792 x 6273
Think step by step.
Break this question 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, ... | true | The solution provided follows the distributive property correctly, breaking down 6273 into its place values and multiplying each part by 4792 accurately. The individual multiplications are correct, and the subsequent addition of the partial results was done step-by-step and verified, yielding the final result of 300602... | |
What is the solution to the long multiplication equation below?
5141 x 4616
Think step by step. | 23730856 | What is the solution to the long multiplication equation below?
5141 x 4616
Think step by step.
Break this question 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, ... | To solve the multiplication of \( 5141 \times 4616 \) using the **distributive property of multiplication over addition**, we will break it down into steps.
### Step 1: Break Down the Numbers
First, we can break down \( 4616 \) into its components based on place value.
\[
4616 = 4000 + 600 + 10 + 6
\]
### Step 2: M... | What is the solution to the long multiplication equation below?
5141 x 4616
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication is incorrect; the ground truth solution states that the correct product of 5141 and 4616 is 23730856. In the solution, the final product calculated is 23930756, which does not match the ground truth. | |
What is the solution to the long multiplication equation below?
1604 x 5544
Think step by step. | 8892576 | What is the solution to the long multiplication equation below?
1604 x 5544
Think step by step.
Break this question 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, ... | To find the product of 1604 and 5544 using the **distributive property of multiplication over addition**, we'll decompose the second number (5544) into its place values and then multiply.
1. **Break down the second number (5544)**:
- 5544 = 5000 + 500 + 40 + 4
2. **Multiply the first number (1604) by each componen... | What is the solution to the long multiplication equation below?
1604 x 5544
Think step by step.
Break this question 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, ... | false | The calculated product of 1604 x 5544 was determined to be 8878176. However, the ground truth solution states the correct product is 8892576. This indicates a discrepancy, meaning the solution provided is incorrect. | |
What is the solution to the long multiplication equation below?
3119 x 1991
Think step by step. | 6209929 | What is the solution to the long multiplication equation below?
3119 x 1991
Think step by step.
Break this question 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, ... | To solve the multiplication \( 3119 \times 1991 \) using the **distributive property of multiplication over addition**, we'll break the second number, \( 1991 \), into its place values:
\[
1991 = 1000 + 900 + 90 + 1
\]
Now, we can use each part to multiply with \( 3119 \):
1. **Calculate \( 3119 \times 1000 \)**:
... | What is the solution to the long multiplication equation below?
3119 x 1991
Think step by step.
Break this question 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, ... | false | The solution arrived at 6208089, while the ground truth solution is 6209929, indicating a computation error in the addition or multiplication process. | |
What is the solution to the long multiplication equation below?
3900 x 2576
Think step by step. | 10046400 | What is the solution to the long multiplication equation below?
3900 x 2576
Think step by step.
Break this question 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, ... | To solve the multiplication problem \(3900 \times 2576\) step by step using the distributive property of multiplication over addition, we'll break it down as follows:
### Step 1: Break down the numbers.
We can break \(2576\) into place values:
\[
2576 = 2000 + 500 + 70 + 6
\]
### Step 2: Apply the distributive proper... | What is the solution to the long multiplication equation below?
3900 x 2576
Think step by step.
Break this question 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, ... | true | The provided solution correctly applies the distributive property of multiplication, performs accurate calculations for each partial multiplication, and correctly sums these partial results to arrive at the final answer, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4385 x 5148
Think step by step. | 22573980 | What is the solution to the long multiplication equation below?
4385 x 5148
Think step by step.
Break this question 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, ... | To solve the problem \( 4385 \times 5148 \) using the distributive property, we will break down the second number, \( 5148 \), into its constituent place values. The number \( 5148 \) can be decomposed as \( 5000 + 100 + 40 + 8 \).
We'll multiply \( 4385 \) by each of these components and then sum the results.
### St... | What is the solution to the long multiplication equation below?
4385 x 5148
Think step by step.
Break this question 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, ... | false | The solution provided calculated the product of 4385 and 5148 accurately by using the distributive property. However, upon verification, the ground truth solution states that the result is 22573980, which indicates that the calculations were incorrect. Therefore, the final answer presented in the solution (22532980) do... | |
What is the solution to the long multiplication equation below?
5341 x 4100
Think step by step. | 21898100 | What is the solution to the long multiplication equation below?
5341 x 4100
Think step by step.
Break this question 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, ... | To solve the multiplication problem \(5341 \times 4100\) using the distributive property, we can break it down into more manageable parts by expressing 4100 in terms of its place values:
\[
4100 = 4000 + 100
\]
Now, we can distribute \(5341\) across the two parts:
\[
5341 \times 4100 = 5341 \times (4000 + 100)
\]
A... | What is the solution to the long multiplication equation below?
5341 x 4100
Think step by step.
Break this question 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, ... | false | The calculated result of the multiplication of 5341 and 4100 is incorrect. The solution states that the final answer is 21997100, but the correct answer, verified through direct multiplication, is 21898100. | |
What is the solution to the long multiplication equation below?
3565 x 4332
Think step by step. | 15443580 | What is the solution to the long multiplication equation below?
3565 x 4332
Think step by step.
Break this question 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, ... | To multiply \( 3565 \) by \( 4332 \) using the distributive property, we break down the numbers based on place value:
1. Break down \( 4332 \) into individual components:
- \( 4332 = 4000 + 300 + 30 + 2 \)
2. Now, we will multiply \( 3565 \) by each of these components of \( 4332 \) one at a time.
### Step 1: Mul... | What is the solution to the long multiplication equation below?
3565 x 4332
Think step by step.
Break this question 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, ... | false | The calculated answer of 15347280 does not match the ground truth solution of 15443580. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
9458 x 9345
Think step by step. | 88385010 | What is the solution to the long multiplication equation below?
9458 x 9345
Think step by step.
Break this question 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, ... | Let's break down the multiplication of \( 9458 \times 9345 \) using the distributive property step-by-step.
### Step 1: Break down the second number
We can express \( 9345 \) as:
\[
9345 = 9000 + 300 + 40 + 5
\]
### Step 2: Distribute the first number over each part of the second number
Now, we will multiply \( 9458 ... | What is the solution to the long multiplication equation below?
9458 x 9345
Think step by step.
Break this question 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, ... | false | The solution provided calculates the product of 9458 and 9345 as 88285010, while the given ground truth solution states that the correct answer is 88385010. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
1029 x 3791
Think step by step. | 3900939 | What is the solution to the long multiplication equation below?
1029 x 3791
Think step by step.
Break this question 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, ... | To multiply 1029 by 3791 using the distributive property of multiplication over addition, we can break it down step by step.
First, we need to decompose the second number, \( 3791 \), into its place values:
\[
3791 = 3000 + 700 + 90 + 1
\]
Now we can multiply \( 1029 \) by each of these parts separately.
1. **Calc... | What is the solution to the long multiplication equation below?
1029 x 3791
Think step by step.
Break this question 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, ... | false | The calculated product of 1029 and 3791 is 3897699 according to the solution provided, whereas the ground truth solution states that the product is 3900939. Therefore, the provided solution is incorrect. | |
What is the solution to the long multiplication equation below?
3918 x 7134
Think step by step. | 27951012 | What is the solution to the long multiplication equation below?
3918 x 7134
Think step by step.
Break this question 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, ... | To multiply 3918 by 7134 using the distributive property of multiplication over addition, we break down the second number (7134) into its place values.
**Step 1: Break Down 7134**
The number 7134 can be separated into:
- 7000
- 100
- 30
- 4
**Step 2: Multiply Each Component by 3918**
Now, we will multiply 3918 by e... | What is the solution to the long multiplication equation below?
3918 x 7134
Think step by step.
Break this question 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, ... | true | The solution provided correctly follows the distributive property of multiplication, breaking down the number 7134 into its components, multiplying each by 3918, and accurately summing the partial products to arrive at the correct final answer of 27951012, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
2076 x 8080
Think step by step. | 16774080 | What is the solution to the long multiplication equation below?
2076 x 8080
Think step by step.
Break this question 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, ... | Let's solve the multiplication \( 2076 \times 8080 \) using the distributive property step by step.
1. **Break down 8080**:
\[
8080 = 8000 + 80
\]
2. **Apply distributive property**:
\[
2076 \times 8080 = 2076 \times (8000 + 80)
\]
By distributing:
\[
2076 \times 8080 = (2076 \times 8000) ... | What is the solution to the long multiplication equation below?
2076 x 8080
Think step by step.
Break this question 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, ... | false | The provided solution calculated the final product of 2076 multiplied by 8080 as 16776180, while the ground truth solution indicates the correct answer is 16774080. This discrepancy shows the calculation in the provided solution is incorrect. | |
What is the solution to the long multiplication equation below?
1046 x 6743
Think step by step. | 7053178 | What is the solution to the long multiplication equation below?
1046 x 6743
Think step by step.
Break this question 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, ... | To solve the multiplication problem \( 1046 \times 6743 \) using the distributive property of multiplication over addition, we can break it down step by step. We will consider \( 6743 \) as \( 6000 + 700 + 40 + 3 \) and then multiply each part by \( 1046 \).
### Step 1: Break down the second number
We can express \( 6... | What is the solution to the long multiplication equation below?
1046 x 6743
Think step by step.
Break this question 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, ... | false | The solution provided has calculated the multiplication of 1046 and 6743 incorrectly. The final result is 7043178, but the ground truth solution states that the correct answer is 7053178. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
4904 x 5189
Think step by step. | 25446856 | What is the solution to the long multiplication equation below?
4904 x 5189
Think step by step.
Break this question 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, ... | To solve the multiplication \( 4904 \times 5189 \) step by step using the **distributive property** of multiplication over addition, we will break down the number \( 5189 \) into its individual digits, taking into account their place values.
### Step 1: Breakdown the Second Number
The number \( 5189 \) can be decompo... | What is the solution to the long multiplication equation below?
4904 x 5189
Think step by step.
Break this question 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, ... | false | The solution provided calculates the product of 4904 and 5189 as 25346856, while the ground truth solution states the product is 25446856. Therefore, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
3150 x 9281
Think step by step. | 29235150 | What is the solution to the long multiplication equation below?
3150 x 9281
Think step by step.
Break this question 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, ... | To solve the multiplication \( 3150 \times 9281 \) using the distributive property of multiplication over addition, we will break down the second number (9281) by its digits, multiplying each digit by the first number (3150), accounting for place value.
### Step 1: Break down 9281
The number \( 9281 \) can be express... | What is the solution to the long multiplication equation below?
3150 x 9281
Think step by step.
Break this question 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, ... | true | The provided solution breaks down the multiplication correctly using the distributive property, computes each part accurately, and sums the results correctly to arrive at the final answer, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
5926 x 5429
Think step by step. | 32172254 | What is the solution to the long multiplication equation below?
5926 x 5429
Think step by step.
Break this question 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, ... | To solve the equation \( 5926 \times 5429 \) using the distributive property of multiplication over addition, we can break it down step by step.
1. **Break down the second number (5429)** by its digits:
\[
5429 = 5000 + 400 + 20 + 9
\]
2. **Multiply 5926 by each digit of 5429** (while considering place value... | What is the solution to the long multiplication equation below?
5926 x 5429
Think step by step.
Break this question 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, ... | true | The calculations using both the distributive property and traditional long multiplication confirm that the result of the multiplication of 5926 and 5429 is indeed 32172254, which matches the ground truth solution. | |
What is the solution to the long multiplication equation below?
4782 x 3136
Think step by step. | 14996352 | What is the solution to the long multiplication equation below?
4782 x 3136
Think step by step.
Break this question 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, ... | To solve the multiplication \(4782 \times 3136\) step by step using the distributive property of multiplication over addition, we'll break down the second number (3136) into its individual digits, emphasizing their place value.
### Step 1: Break Down the Number
We can express 3136 as:
\[
3136 = 3000 + 100 + 30 + 6
\]
... | What is the solution to the long multiplication equation below?
4782 x 3136
Think step by step.
Break this question 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, ... | false | The computed solution of 14909632 does not match the ground truth solution of 14996352, indicating an error in the multiplication or addition process. | |
What is the solution to the long multiplication equation below?
3814 x 6819
Think step by step. | 26007666 | What is the solution to the long multiplication equation below?
3814 x 6819
Think step by step.
Break this question 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, ... | To solve the multiplication problem \(3814 \times 6819\) using the distributive property, we'll break it down step by step. We will first express \(6819\) in terms of its digits and then use place values for multiplication.
1. **Break down \(6819\)**:
\(6819 = 6000 + 800 + 10 + 9\)
2. **Multiply \(3814\) by each p... | What is the solution to the long multiplication equation below?
3814 x 6819
Think step by step.
Break this question 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, ... | false | The computed final answer is \(26010666\), which does not match the ground truth solution of \(26007666\). Thus, the solution is incorrect. | |
What is the solution to the long multiplication equation below?
9929 x 1429
Think step by step. | 14188541 | What is the solution to the long multiplication equation below?
9929 x 1429
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9929 \times 1429 \) using the **distributive property of multiplication over addition**, we will break down the multiplication step by step.
### Step 1: Break Down the Numbers
We'll express \( 1429 \) in terms of its place values:
\[
1429 = 1000 + 400 + 20 + 9
\]
This allows us to distri... | What is the solution to the long multiplication equation below?
9929 x 1429
Think step by step.
Break this question 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, ... | false | The final result for the multiplication \( 9929 \times 1429 \) provided in the solution is \( 14143141 \), while the ground truth solution is \( 14188541 \). This indicates a mistake in the solution as the two results do not match. | |
What is the solution to the long multiplication equation below?
9988 x 1859
Think step by step. | 18567692 | What is the solution to the long multiplication equation below?
9988 x 1859
Think step by step.
Break this question 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, ... | To solve the multiplication \( 9988 \times 1859 \) using the distributive property of multiplication over addition, we can express the number \( 1859 \) in terms of its digits:
\[
1859 = 1000 + 800 + 50 + 9
\]
Now, we will multiply \( 9988 \) by each of these components and then sum the results.
### Step 1: Multiply... | What is the solution to the long multiplication equation below?
9988 x 1859
Think step by step.
Break this question 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, ... | false | The calculated result of 9988 x 1859 using the distributive property is 18571292, while the ground truth solution is 18567692. The discrepancy indicates an error in the solution provided. | |
What is the solution to the long multiplication equation below?
5593 x 1948
Think step by step. | 10895164 | What is the solution to the long multiplication equation below?
5593 x 1948
Think step by step.
Break this question 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, ... | To multiply 5593 by 1948 using the **distributive property of multiplication over addition**, we will break down the numbers involved:
1. **Break down 1948 into its place values**:
- \(1948 = 1000 + 900 + 40 + 8\)
Now we will multiply 5593 by each of these components separately.
2. **Calculate each part**:
- \... | What is the solution to the long multiplication equation below?
5593 x 1948
Think step by step.
Break this question 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, ... | false | The computed product of 5593 and 1948 was determined to be 10986884 in the solution provided, while the ground truth solution states that the correct product is 10895164. Therefore, the solution is incorrect. |
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