Long Division Worksheets - Free Printable
Educational worksheet: Long Division Worksheets. Download and print for classroom or home learning activities.
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Step-by-step solution for: Long Division Worksheets
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Show Answer Key & Explanations
Step-by-step solution for: Long Division Worksheets
The task involves solving division problems where the dividends are 3-digit numbers and the quotients are 2-digit numbers. We will solve each problem step by step using long division.
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1. Divide: How many times does 6 go into 12?
- \( 6 \times 2 = 12 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 12 - 12 = 0 \).
3. Bring down the next digit: Bring down the 6 to make it 6.
4. Divide: How many times does 6 go into 6?
- \( 6 \times 1 = 6 \). So, the second digit of the quotient is 1.
5. Multiply and Subtract:
- \( 6 - 6 = 0 \).
The quotient is 21 and the remainder is 0.
Answer for a: \( 21 \)
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1. Divide: How many times does 3 go into 15?
- \( 3 \times 5 = 15 \). So, the first digit of the quotient is 5.
2. Multiply and Subtract:
- \( 15 - 15 = 0 \).
3. Bring down the next digit: Bring down the 8 to make it 8.
4. Divide: How many times does 3 go into 8?
- \( 3 \times 2 = 6 \). So, the second digit of the quotient is 2.
5. Multiply and Subtract:
- \( 8 - 6 = 2 \).
The quotient is 52 and the remainder is 2.
Answer for b: \( 52 \) R \( 2 \)
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1. Divide: How many times does 2 go into 11?
- \( 2 \times 5 = 10 \). So, the first digit of the quotient is 5.
2. Multiply and Subtract:
- \( 11 - 10 = 1 \).
3. Bring down the next digit: Bring down the 3 to make it 13.
4. Divide: How many times does 2 go into 13?
- \( 2 \times 6 = 12 \). So, the second digit of the quotient is 6.
5. Multiply and Subtract:
- \( 13 - 12 = 1 \).
The quotient is 56 and the remainder is 1.
Answer for c: \( 56 \) R \( 1 \)
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1. Divide: How many times does 3 go into 26?
- \( 3 \times 8 = 24 \). So, the first digit of the quotient is 8.
2. Multiply and Subtract:
- \( 26 - 24 = 2 \).
3. Bring down the next digit: Bring down the 9 to make it 29.
4. Divide: How many times does 3 go into 29?
- \( 3 \times 9 = 27 \). So, the second digit of the quotient is 9.
5. Multiply and Subtract:
- \( 29 - 27 = 2 \).
The quotient is 89 and the remainder is 2.
Answer for d: \( 89 \) R \( 2 \)
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1. Divide: How many times does 4 go into 19?
- \( 4 \times 4 = 16 \). So, the first digit of the quotient is 4.
2. Multiply and Subtract:
- \( 19 - 16 = 3 \).
3. Bring down the next digit: Bring down the 5 to make it 35.
4. Divide: How many times does 4 go into 35?
- \( 4 \times 8 = 32 \). So, the second digit of the quotient is 8.
5. Multiply and Subtract:
- \( 35 - 32 = 3 \).
The quotient is 48 and the remainder is 3.
Answer for e: \( 48 \) R \( 3 \)
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1. Divide: How many times does 6 go into 24?
- \( 6 \times 4 = 24 \). So, the first digit of the quotient is 4.
2. Multiply and Subtract:
- \( 24 - 24 = 0 \).
3. Bring down the next digit: Bring down the 9 to make it 9.
4. Divide: How many times does 6 go into 9?
- \( 6 \times 1 = 6 \). So, the second digit of the quotient is 1.
5. Multiply and Subtract:
- \( 9 - 6 = 3 \).
The quotient is 41 and the remainder is 3.
Answer for f: \( 41 \) R \( 3 \)
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1. Divide: How many times does 7 go into 18?
- \( 7 \times 2 = 14 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 18 - 14 = 4 \).
3. Bring down the next digit: Bring down the 6 to make it 46.
4. Divide: How many times does 7 go into 46?
- \( 7 \times 6 = 42 \). So, the second digit of the quotient is 6.
5. Multiply and Subtract:
- \( 46 - 42 = 4 \).
The quotient is 26 and the remainder is 4.
Answer for g: \( 26 \) R \( 4 \)
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1. Divide: How many times does 9 go into 19?
- \( 9 \times 2 = 18 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 19 - 18 = 1 \).
3. Bring down the next digit: Bring down the 8 to make it 18.
4. Divide: How many times does 9 go into 18?
- \( 9 \times 2 = 18 \). So, the second digit of the quotient is 2.
5. Multiply and Subtract:
- \( 18 - 18 = 0 \).
The quotient is 22 and the remainder is 0.
Answer for h: \( 22 \)
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1. Divide: How many times does 3 go into 20?
- \( 3 \times 6 = 18 \). So, the first digit of the quotient is 6.
2. Multiply and Subtract:
- \( 20 - 18 = 2 \).
3. Bring down the next digit: Bring down the 8 to make it 28.
4. Divide: How many times does 3 go into 28?
- \( 3 \times 9 = 27 \). So, the second digit of the quotient is 9.
5. Multiply and Subtract:
- \( 28 - 27 = 1 \).
The quotient is 69 and the remainder is 1.
Answer for i: \( 69 \) R \( 1 \)
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\[
\boxed{
\begin{array}{ll}
a. & 21 \\
b. & 52 \text{ R } 2 \\
c. & 56 \text{ R } 1 \\
d. & 89 \text{ R } 2 \\
e. & 48 \text{ R } 3 \\
f. & 41 \text{ R } 3 \\
g. & 26 \text{ R } 4 \\
h. & 22 \\
i. & 69 \text{ R } 1 \\
\end{array}
}
\]
---
Problem a: \( 6 \longdiv{126} \)
1. Divide: How many times does 6 go into 12?
- \( 6 \times 2 = 12 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 12 - 12 = 0 \).
3. Bring down the next digit: Bring down the 6 to make it 6.
4. Divide: How many times does 6 go into 6?
- \( 6 \times 1 = 6 \). So, the second digit of the quotient is 1.
5. Multiply and Subtract:
- \( 6 - 6 = 0 \).
The quotient is 21 and the remainder is 0.
Answer for a: \( 21 \)
---
Problem b: \( 3 \longdiv{158} \)
1. Divide: How many times does 3 go into 15?
- \( 3 \times 5 = 15 \). So, the first digit of the quotient is 5.
2. Multiply and Subtract:
- \( 15 - 15 = 0 \).
3. Bring down the next digit: Bring down the 8 to make it 8.
4. Divide: How many times does 3 go into 8?
- \( 3 \times 2 = 6 \). So, the second digit of the quotient is 2.
5. Multiply and Subtract:
- \( 8 - 6 = 2 \).
The quotient is 52 and the remainder is 2.
Answer for b: \( 52 \) R \( 2 \)
---
Problem c: \( 2 \longdiv{113} \)
1. Divide: How many times does 2 go into 11?
- \( 2 \times 5 = 10 \). So, the first digit of the quotient is 5.
2. Multiply and Subtract:
- \( 11 - 10 = 1 \).
3. Bring down the next digit: Bring down the 3 to make it 13.
4. Divide: How many times does 2 go into 13?
- \( 2 \times 6 = 12 \). So, the second digit of the quotient is 6.
5. Multiply and Subtract:
- \( 13 - 12 = 1 \).
The quotient is 56 and the remainder is 1.
Answer for c: \( 56 \) R \( 1 \)
---
Problem d: \( 3 \longdiv{269} \)
1. Divide: How many times does 3 go into 26?
- \( 3 \times 8 = 24 \). So, the first digit of the quotient is 8.
2. Multiply and Subtract:
- \( 26 - 24 = 2 \).
3. Bring down the next digit: Bring down the 9 to make it 29.
4. Divide: How many times does 3 go into 29?
- \( 3 \times 9 = 27 \). So, the second digit of the quotient is 9.
5. Multiply and Subtract:
- \( 29 - 27 = 2 \).
The quotient is 89 and the remainder is 2.
Answer for d: \( 89 \) R \( 2 \)
---
Problem e: \( 4 \longdiv{195} \)
1. Divide: How many times does 4 go into 19?
- \( 4 \times 4 = 16 \). So, the first digit of the quotient is 4.
2. Multiply and Subtract:
- \( 19 - 16 = 3 \).
3. Bring down the next digit: Bring down the 5 to make it 35.
4. Divide: How many times does 4 go into 35?
- \( 4 \times 8 = 32 \). So, the second digit of the quotient is 8.
5. Multiply and Subtract:
- \( 35 - 32 = 3 \).
The quotient is 48 and the remainder is 3.
Answer for e: \( 48 \) R \( 3 \)
---
Problem f: \( 6 \longdiv{249} \)
1. Divide: How many times does 6 go into 24?
- \( 6 \times 4 = 24 \). So, the first digit of the quotient is 4.
2. Multiply and Subtract:
- \( 24 - 24 = 0 \).
3. Bring down the next digit: Bring down the 9 to make it 9.
4. Divide: How many times does 6 go into 9?
- \( 6 \times 1 = 6 \). So, the second digit of the quotient is 1.
5. Multiply and Subtract:
- \( 9 - 6 = 3 \).
The quotient is 41 and the remainder is 3.
Answer for f: \( 41 \) R \( 3 \)
---
Problem g: \( 7 \longdiv{186} \)
1. Divide: How many times does 7 go into 18?
- \( 7 \times 2 = 14 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 18 - 14 = 4 \).
3. Bring down the next digit: Bring down the 6 to make it 46.
4. Divide: How many times does 7 go into 46?
- \( 7 \times 6 = 42 \). So, the second digit of the quotient is 6.
5. Multiply and Subtract:
- \( 46 - 42 = 4 \).
The quotient is 26 and the remainder is 4.
Answer for g: \( 26 \) R \( 4 \)
---
Problem h: \( 9 \longdiv{198} \)
1. Divide: How many times does 9 go into 19?
- \( 9 \times 2 = 18 \). So, the first digit of the quotient is 2.
2. Multiply and Subtract:
- \( 19 - 18 = 1 \).
3. Bring down the next digit: Bring down the 8 to make it 18.
4. Divide: How many times does 9 go into 18?
- \( 9 \times 2 = 18 \). So, the second digit of the quotient is 2.
5. Multiply and Subtract:
- \( 18 - 18 = 0 \).
The quotient is 22 and the remainder is 0.
Answer for h: \( 22 \)
---
Problem i: \( 3 \longdiv{208} \)
1. Divide: How many times does 3 go into 20?
- \( 3 \times 6 = 18 \). So, the first digit of the quotient is 6.
2. Multiply and Subtract:
- \( 20 - 18 = 2 \).
3. Bring down the next digit: Bring down the 8 to make it 28.
4. Divide: How many times does 3 go into 28?
- \( 3 \times 9 = 27 \). So, the second digit of the quotient is 9.
5. Multiply and Subtract:
- \( 28 - 27 = 1 \).
The quotient is 69 and the remainder is 1.
Answer for i: \( 69 \) R \( 1 \)
---
Final Answers
\[
\boxed{
\begin{array}{ll}
a. & 21 \\
b. & 52 \text{ R } 2 \\
c. & 56 \text{ R } 1 \\
d. & 89 \text{ R } 2 \\
e. & 48 \text{ R } 3 \\
f. & 41 \text{ R } 3 \\
g. & 26 \text{ R } 4 \\
h. & 22 \\
i. & 69 \text{ R } 1 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of free printable long division worksheets on graph paper.
