Answer key for division practice with two-digit divisors.
Division with two-digit divisors worksheet with six long division problems and answer key.
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Step-by-step solution for: Long Division Worksheets: Division with Decimal Results
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Show Answer Key & Explanations
Step-by-step solution for: Long Division Worksheets: Division with Decimal Results
The image appears to be a math worksheet focused on division problems involving two-digit divisors. The task is to solve the division problems and fill in the answers. Below, I will solve each problem step by step.
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The worksheet is divided into three columns, with each column containing three rows of division problems. Here are the problems:
#### Column 1:
1. \( 506 \div 3 \)
2. \( 165 \div 7 \)
3. \( 975 \div 2 \)
#### Column 2:
1. \( 443 \div 9 \)
2. \( 684 \div 4 \)
3. \( 481 \div 8 \)
#### Column 3:
1. \( 330 \div 3 \)
2. \( 675 \div 3 \)
3. \( 778 \div 7 \)
---
#### Column 1:
1. Problem: \( 506 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 5 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 5 - 3 = 2 \).
- Bring down \( 0 \): \( 20 \).
- \( 3 \) goes into \( 20 \) six times (write \( 6 \)).
- \( 6 \times 3 = 18 \), subtract: \( 20 - 18 = 2 \).
- Bring down \( 6 \): \( 26 \).
- \( 3 \) goes into \( 26 \) eight times (write \( 8 \)).
- \( 8 \times 3 = 24 \), subtract: \( 26 - 24 = 2 \).
- Quotient: \( 168 \), Remainder: \( 2 \).
- Answer: \( 168 \text{ R } 2 \)
2. Problem: \( 165 \div 7 \)
- Perform long division:
- \( 7 \) goes into \( 16 \) twice (write \( 2 \)).
- \( 2 \times 7 = 14 \), subtract: \( 16 - 14 = 2 \).
- Bring down \( 5 \): \( 25 \).
- \( 7 \) goes into \( 25 \) three times (write \( 3 \)).
- \( 3 \times 7 = 21 \), subtract: \( 25 - 21 = 4 \).
- Quotient: \( 23 \), Remainder: \( 4 \).
- Answer: \( 23 \text{ R } 4 \)
3. Problem: \( 975 \div 2 \)
- Perform long division:
- \( 2 \) goes into \( 9 \) four times (write \( 4 \)).
- \( 4 \times 2 = 8 \), subtract: \( 9 - 8 = 1 \).
- Bring down \( 7 \): \( 17 \).
- \( 2 \) goes into \( 17 \) eight times (write \( 8 \)).
- \( 8 \times 2 = 16 \), subtract: \( 17 - 16 = 1 \).
- Bring down \( 5 \): \( 15 \).
- \( 2 \) goes into \( 15 \) seven times (write \( 7 \)).
- \( 7 \times 2 = 14 \), subtract: \( 15 - 14 = 1 \).
- Quotient: \( 487 \), Remainder: \( 1 \).
- Answer: \( 487 \text{ R } 1 \)
---
#### Column 2:
1. Problem: \( 443 \div 9 \)
- Perform long division:
- \( 9 \) goes into \( 44 \) four times (write \( 4 \)).
- \( 4 \times 9 = 36 \), subtract: \( 44 - 36 = 8 \).
- Bring down \( 3 \): \( 83 \).
- \( 9 \) goes into \( 83 \) nine times (write \( 9 \)).
- \( 9 \times 9 = 81 \), subtract: \( 83 - 81 = 2 \).
- Quotient: \( 49 \), Remainder: \( 2 \).
- Answer: \( 49 \text{ R } 2 \)
2. Problem: \( 684 \div 4 \)
- Perform long division:
- \( 4 \) goes into \( 6 \) once (write \( 1 \)).
- \( 1 \times 4 = 4 \), subtract: \( 6 - 4 = 2 \).
- Bring down \( 8 \): \( 28 \).
- \( 4 \) goes into \( 28 \) seven times (write \( 7 \)).
- \( 7 \times 4 = 28 \), subtract: \( 28 - 28 = 0 \).
- Bring down \( 4 \): \( 4 \).
- \( 4 \) goes into \( 4 \) once (write \( 1 \)).
- \( 1 \times 4 = 4 \), subtract: \( 4 - 4 = 0 \).
- Quotient: \( 171 \), Remainder: \( 0 \).
- Answer: \( 171 \)
3. Problem: \( 481 \div 8 \)
- Perform long division:
- \( 8 \) goes into \( 48 \) six times (write \( 6 \)).
- \( 6 \times 8 = 48 \), subtract: \( 48 - 48 = 0 \).
- Bring down \( 1 \): \( 1 \).
- Quotient: \( 60 \), Remainder: \( 1 \).
- Answer: \( 60 \text{ R } 1 \)
---
#### Column 3:
1. Problem: \( 330 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 3 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 3 - 3 = 0 \).
- Bring down \( 3 \): \( 3 \).
- \( 3 \) goes into \( 3 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 3 - 3 = 0 \).
- Bring down \( 0 \): \( 0 \).
- \( 3 \) goes into \( 0 \) zero times (write \( 0 \)).
- \( 0 \times 3 = 0 \), subtract: \( 0 - 0 = 0 \).
- Quotient: \( 110 \), Remainder: \( 0 \).
- Answer: \( 110 \)
2. Problem: \( 675 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 6 \) twice (write \( 2 \)).
- \( 2 \times 3 = 6 \), subtract: \( 6 - 6 = 0 \).
- Bring down \( 7 \): \( 7 \).
- \( 3 \) goes into \( 7 \) twice (write \( 2 \)).
- \( 2 \times 3 = 6 \), subtract: \( 7 - 6 = 1 \).
- Bring down \( 5 \): \( 15 \).
- \( 3 \) goes into \( 15 \) five times (write \( 5 \)).
- \( 5 \times 3 = 15 \), subtract: \( 15 - 15 = 0 \).
- Quotient: \( 225 \), Remainder: \( 0 \).
- Answer: \( 225 \)
3. Problem: \( 778 \div 7 \)
- Perform long division:
- \( 7 \) goes into \( 7 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 7 - 7 = 0 \).
- Bring down \( 7 \): \( 7 \).
- \( 7 \) goes into \( 7 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 7 - 7 = 0 \).
- Bring down \( 8 \): \( 8 \).
- \( 7 \) goes into \( 8 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 8 - 7 = 1 \).
- Quotient: \( 111 \), Remainder: \( 1 \).
- Answer: \( 111 \text{ R } 1 \)
---
Here are the answers for all the problems:
| Column 1 | Column 2 | Column 3 |
|-----------------|-----------------|-----------------|
| \( 168 \text{ R } 2 \) | \( 49 \text{ R } 2 \) | \( 110 \) |
| \( 23 \text{ R } 4 \) | \( 171 \) | \( 225 \) |
| \( 487 \text{ R } 1 \) | \( 60 \text{ R } 1 \) | \( 111 \text{ R } 1 \) |
Boxed Final Answer:
\[
\boxed{
\begin{array}{ccc}
168 \text{ R } 2 & 49 \text{ R } 2 & 110 \\
23 \text{ R } 4 & 171 & 225 \\
487 \text{ R } 1 & 60 \text{ R } 1 & 111 \text{ R } 1
\end{array}
}
\]
---
Worksheet Layout
The worksheet is divided into three columns, with each column containing three rows of division problems. Here are the problems:
#### Column 1:
1. \( 506 \div 3 \)
2. \( 165 \div 7 \)
3. \( 975 \div 2 \)
#### Column 2:
1. \( 443 \div 9 \)
2. \( 684 \div 4 \)
3. \( 481 \div 8 \)
#### Column 3:
1. \( 330 \div 3 \)
2. \( 675 \div 3 \)
3. \( 778 \div 7 \)
---
Solutions
#### Column 1:
1. Problem: \( 506 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 5 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 5 - 3 = 2 \).
- Bring down \( 0 \): \( 20 \).
- \( 3 \) goes into \( 20 \) six times (write \( 6 \)).
- \( 6 \times 3 = 18 \), subtract: \( 20 - 18 = 2 \).
- Bring down \( 6 \): \( 26 \).
- \( 3 \) goes into \( 26 \) eight times (write \( 8 \)).
- \( 8 \times 3 = 24 \), subtract: \( 26 - 24 = 2 \).
- Quotient: \( 168 \), Remainder: \( 2 \).
- Answer: \( 168 \text{ R } 2 \)
2. Problem: \( 165 \div 7 \)
- Perform long division:
- \( 7 \) goes into \( 16 \) twice (write \( 2 \)).
- \( 2 \times 7 = 14 \), subtract: \( 16 - 14 = 2 \).
- Bring down \( 5 \): \( 25 \).
- \( 7 \) goes into \( 25 \) three times (write \( 3 \)).
- \( 3 \times 7 = 21 \), subtract: \( 25 - 21 = 4 \).
- Quotient: \( 23 \), Remainder: \( 4 \).
- Answer: \( 23 \text{ R } 4 \)
3. Problem: \( 975 \div 2 \)
- Perform long division:
- \( 2 \) goes into \( 9 \) four times (write \( 4 \)).
- \( 4 \times 2 = 8 \), subtract: \( 9 - 8 = 1 \).
- Bring down \( 7 \): \( 17 \).
- \( 2 \) goes into \( 17 \) eight times (write \( 8 \)).
- \( 8 \times 2 = 16 \), subtract: \( 17 - 16 = 1 \).
- Bring down \( 5 \): \( 15 \).
- \( 2 \) goes into \( 15 \) seven times (write \( 7 \)).
- \( 7 \times 2 = 14 \), subtract: \( 15 - 14 = 1 \).
- Quotient: \( 487 \), Remainder: \( 1 \).
- Answer: \( 487 \text{ R } 1 \)
---
#### Column 2:
1. Problem: \( 443 \div 9 \)
- Perform long division:
- \( 9 \) goes into \( 44 \) four times (write \( 4 \)).
- \( 4 \times 9 = 36 \), subtract: \( 44 - 36 = 8 \).
- Bring down \( 3 \): \( 83 \).
- \( 9 \) goes into \( 83 \) nine times (write \( 9 \)).
- \( 9 \times 9 = 81 \), subtract: \( 83 - 81 = 2 \).
- Quotient: \( 49 \), Remainder: \( 2 \).
- Answer: \( 49 \text{ R } 2 \)
2. Problem: \( 684 \div 4 \)
- Perform long division:
- \( 4 \) goes into \( 6 \) once (write \( 1 \)).
- \( 1 \times 4 = 4 \), subtract: \( 6 - 4 = 2 \).
- Bring down \( 8 \): \( 28 \).
- \( 4 \) goes into \( 28 \) seven times (write \( 7 \)).
- \( 7 \times 4 = 28 \), subtract: \( 28 - 28 = 0 \).
- Bring down \( 4 \): \( 4 \).
- \( 4 \) goes into \( 4 \) once (write \( 1 \)).
- \( 1 \times 4 = 4 \), subtract: \( 4 - 4 = 0 \).
- Quotient: \( 171 \), Remainder: \( 0 \).
- Answer: \( 171 \)
3. Problem: \( 481 \div 8 \)
- Perform long division:
- \( 8 \) goes into \( 48 \) six times (write \( 6 \)).
- \( 6 \times 8 = 48 \), subtract: \( 48 - 48 = 0 \).
- Bring down \( 1 \): \( 1 \).
- Quotient: \( 60 \), Remainder: \( 1 \).
- Answer: \( 60 \text{ R } 1 \)
---
#### Column 3:
1. Problem: \( 330 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 3 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 3 - 3 = 0 \).
- Bring down \( 3 \): \( 3 \).
- \( 3 \) goes into \( 3 \) once (write \( 1 \)).
- \( 1 \times 3 = 3 \), subtract: \( 3 - 3 = 0 \).
- Bring down \( 0 \): \( 0 \).
- \( 3 \) goes into \( 0 \) zero times (write \( 0 \)).
- \( 0 \times 3 = 0 \), subtract: \( 0 - 0 = 0 \).
- Quotient: \( 110 \), Remainder: \( 0 \).
- Answer: \( 110 \)
2. Problem: \( 675 \div 3 \)
- Perform long division:
- \( 3 \) goes into \( 6 \) twice (write \( 2 \)).
- \( 2 \times 3 = 6 \), subtract: \( 6 - 6 = 0 \).
- Bring down \( 7 \): \( 7 \).
- \( 3 \) goes into \( 7 \) twice (write \( 2 \)).
- \( 2 \times 3 = 6 \), subtract: \( 7 - 6 = 1 \).
- Bring down \( 5 \): \( 15 \).
- \( 3 \) goes into \( 15 \) five times (write \( 5 \)).
- \( 5 \times 3 = 15 \), subtract: \( 15 - 15 = 0 \).
- Quotient: \( 225 \), Remainder: \( 0 \).
- Answer: \( 225 \)
3. Problem: \( 778 \div 7 \)
- Perform long division:
- \( 7 \) goes into \( 7 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 7 - 7 = 0 \).
- Bring down \( 7 \): \( 7 \).
- \( 7 \) goes into \( 7 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 7 - 7 = 0 \).
- Bring down \( 8 \): \( 8 \).
- \( 7 \) goes into \( 8 \) once (write \( 1 \)).
- \( 1 \times 7 = 7 \), subtract: \( 8 - 7 = 1 \).
- Quotient: \( 111 \), Remainder: \( 1 \).
- Answer: \( 111 \text{ R } 1 \)
---
Final Answer Key
Here are the answers for all the problems:
| Column 1 | Column 2 | Column 3 |
|-----------------|-----------------|-----------------|
| \( 168 \text{ R } 2 \) | \( 49 \text{ R } 2 \) | \( 110 \) |
| \( 23 \text{ R } 4 \) | \( 171 \) | \( 225 \) |
| \( 487 \text{ R } 1 \) | \( 60 \text{ R } 1 \) | \( 111 \text{ R } 1 \) |
Boxed Final Answer:
\[
\boxed{
\begin{array}{ccc}
168 \text{ R } 2 & 49 \text{ R } 2 & 110 \\
23 \text{ R } 4 & 171 & 225 \\
487 \text{ R } 1 & 60 \text{ R } 1 & 111 \text{ R } 1
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of division with decimal remainders worksheet.