Zeros in Division worksheet - Free Printable

Problem Overview:

The task involves solving division problems and identifying the quotient and remainder for each. The worksheet is titled "Zeros in Division," which suggests that some of the divisions may involve zeros in the quotient or remainder.

Solution Approach:

We will solve each division problem step by step, following the standard long division method. For each problem, we will:
1. Divide the dividend by the divisor.
2. Write down the quotient.
3. Determine the remainder (if any).

Step-by-Step Solutions:

#### Section 1:
1. \( 3 \overline{)927} \)
- Divide: \( 9 \div 3 = 3 \)
- Multiply: \( 3 \times 3 = 9 \)
- Subtract: \( 9 - 9 = 0 \)
- Bring down: 2
- Divide: \( 2 \div 3 \) (not possible, so bring down 7)
- Divide: \( 27 \div 3 = 9 \)
- Multiply: \( 9 \times 3 = 27 \)
- Subtract: \( 27 - 27 = 0 \)
- Quotient: 309, Remainder: 0

2. \( 8 \overline{)872} \)
- Divide: \( 8 \div 8 = 1 \)
- Multiply: \( 1 \times 8 = 8 \)
- Subtract: \( 8 - 8 = 0 \)
- Bring down: 7
- Divide: \( 7 \div 8 \) (not possible, so bring down 2)
- Divide: \( 72 \div 8 = 9 \)
- Multiply: \( 9 \times 8 = 72 \)
- Subtract: \( 72 - 72 = 0 \)
- Quotient: 109, Remainder: 0

3. \( 5 \overline{)542} \)
- Divide: \( 5 \div 5 = 1 \)
- Multiply: \( 1 \times 5 = 5 \)
- Subtract: \( 5 - 5 = 0 \)
- Bring down: 4
- Divide: \( 4 \div 5 \) (not possible, so bring down 2)
- Divide: \( 42 \div 5 = 8 \)
- Multiply: \( 8 \times 5 = 40 \)
- Subtract: \( 42 - 40 = 2 \)
- Quotient: 108, Remainder: 2

4. \( 6 \overline{)608} \)
- Divide: \( 6 \div 6 = 1 \)
- Multiply: \( 1 \times 6 = 6 \)
- Subtract: \( 6 - 6 = 0 \)
- Bring down: 0
- Divide: \( 0 \div 6 = 0 \)
- Multiply: \( 0 \times 6 = 0 \)
- Subtract: \( 0 - 0 = 0 \)
- Bring down: 8
- Divide: \( 8 \div 6 = 1 \)
- Multiply: \( 1 \times 6 = 6 \)
- Subtract: \( 8 - 6 = 2 \)
- Quotient: 101, Remainder: 2

#### Section 2:
5. \( 3 \overline{)624} \)
- Divide: \( 6 \div 3 = 2 \)
- Multiply: \( 2 \times 3 = 6 \)
- Subtract: \( 6 - 6 = 0 \)
- Bring down: 2
- Divide: \( 2 \div 3 \) (not possible, so bring down 4)
- Divide: \( 24 \div 3 = 8 \)
- Multiply: \( 8 \times 3 = 24 \)
- Subtract: \( 24 - 24 = 0 \)
- Quotient: 208, Remainder: 0

6. \( 2 \overline{)807} \)
- Divide: \( 8 \div 2 = 4 \)
- Multiply: \( 4 \times 2 = 8 \)
- Subtract: \( 8 - 8 = 0 \)
- Bring down: 0
- Divide: \( 0 \div 2 = 0 \)
- Multiply: \( 0 \times 2 = 0 \)
- Subtract: \( 0 - 0 = 0 \)
- Bring down: 7
- Divide: \( 7 \div 2 = 3 \)
- Multiply: \( 3 \times 2 = 6 \)
- Subtract: \( 7 - 6 = 1 \)
- Quotient: 403, Remainder: 1

7. \( 4 \overline{)826} \)
- Divide: \( 8 \div 4 = 2 \)
- Multiply: \( 2 \times 4 = 8 \)
- Subtract: \( 8 - 8 = 0 \)
- Bring down: 2
- Divide: \( 2 \div 4 \) (not possible, so bring down 6)
- Divide: \( 26 \div 4 = 6 \)
- Multiply: \( 6 \times 4 = 24 \)
- Subtract: \( 26 - 24 = 2 \)
- Quotient: 206, Remainder: 2

8. \( 7 \overline{)843} \)
- Divide: \( 8 \div 7 = 1 \)
- Multiply: \( 1 \times 7 = 7 \)
- Subtract: \( 8 - 7 = 1 \)
- Bring down: 4
- Divide: \( 14 \div 7 = 2 \)
- Multiply: \( 2 \times 7 = 14 \)
- Subtract: \( 14 - 14 = 0 \)
- Bring down: 3
- Divide: \( 3 \div 7 \) (not possible)
- Quotient: 120, Remainder: 3

#### Section 3:
1. \( 8 \overline{)330} \)
- Divide: \( 3 \div 8 \) (not possible, so bring down 3)
- Divide: \( 33 \div 8 = 4 \)
- Multiply: \( 4 \times 8 = 32 \)
- Subtract: \( 33 - 32 = 1 \)
- Bring down: 0
- Divide: \( 10 \div 8 = 1 \)
- Multiply: \( 1 \times 8 = 8 \)
- Subtract: \( 10 - 8 = 2 \)
- Quotient: 41, Remainder: 2

2. \( 6 \overline{)371} \)
- Divide: \( 3 \div 6 \) (not possible, so bring down 7)
- Divide: \( 37 \div 6 = 6 \)
- Multiply: \( 6 \times 6 = 36 \)
- Subtract: \( 37 - 36 = 1 \)
- Bring down: 1
- Divide: \( 11 \div 6 = 1 \)
- Multiply: \( 1 \times 6 = 6 \)
- Subtract: \( 11 - 6 = 5 \)
- Quotient: 61, Remainder: 5

3. \( 2 \overline{)813} \)
- Divide: \( 8 \div 2 = 4 \)
- Multiply: \( 4 \times 2 = 8 \)
- Subtract: \( 8 - 8 = 0 \)
- Bring down: 1
- Divide: \( 1 \div 2 \) (not possible, so bring down 3)
- Divide: \( 13 \div 2 = 6 \)
- Multiply: \( 6 \times 2 = 12 \)
- Subtract: \( 13 - 12 = 1 \)
- Quotient: 406, Remainder: 1

4. \( 9 \overline{)625} \)
- Divide: \( 6 \div 9 \) (not possible, so bring down 2)
- Divide: \( 62 \div 9 = 6 \)
- Multiply: \( 6 \times 9 = 54 \)
- Subtract: \( 62 - 54 = 8 \)
- Bring down: 5
- Divide: \( 85 \div 9 = 9 \)
- Multiply: \( 9 \times 9 = 81 \)
- Subtract: \( 85 - 81 = 4 \)
- Quotient: 69, Remainder: 4

#### Section 4:
5. \( 5 \overline{)535} \)
- Divide: \( 5 \div 5 = 1 \)
- Multiply: \( 1 \times 5 = 5 \)
- Subtract: \( 5 - 5 = 0 \)
- Bring down: 3
- Divide: \( 3 \div 5 \) (not possible, so bring down 5)
- Divide: \( 35 \div 5 = 7 \)
- Multiply: \( 7 \times 5 = 35 \)
- Subtract: \( 35 - 35 = 0 \)
- Quotient: 107, Remainder: 0

6. \( 3 \overline{)924} \)
- Divide: \( 9 \div 3 = 3 \)
- Multiply: \( 3 \times 3 = 9 \)
- Subtract: \( 9 - 9 = 0 \)
- Bring down: 2
- Divide: \( 2 \div 3 \) (not possible, so bring down 4)
- Divide: \( 24 \div 3 = 8 \)
- Multiply: \( 8 \times 3 = 24 \)
- Subtract: \( 24 - 24 = 0 \)
- Quotient: 308, Remainder: 0

7. \( 4 \overline{)836} \)
- Divide: \( 8 \div 4 = 2 \)
- Multiply: \( 2 \times 4 = 8 \)
- Subtract: \( 8 - 8 = 0 \)
- Bring down: 3
- Divide: \( 3 \div 4 \) (not possible, so bring down 6)
- Divide: \( 36 \div 4 = 9 \)
- Multiply: \( 9 \times 4 = 36 \)
- Subtract: \( 36 - 36 = 0 \)
- Quotient: 209, Remainder: 0

8. \( 6 \overline{)615} \)
- Divide: \( 6 \div 6 = 1 \)
- Multiply: \( 1 \times 6 = 6 \)
- Subtract: \( 6 - 6 = 0 \)
- Bring down: 1
- Divide: \( 1 \div 6 \) (not possible, so bring down 5)
- Divide: \( 15 \div 6 = 2 \)
- Multiply: \( 2 \times 6 = 12 \)
- Subtract: \( 15 - 12 = 3 \)
- Quotient: 102, Remainder: 3

#### Section 5:
9. \( 2 \overline{)610} \)
- Divide: \( 6 \div 2 = 3 \)
- Multiply: \( 3 \times 2 = 6 \)
- Subtract: \( 6 - 6 = 0 \)
- Bring down: 1
- Divide: \( 1 \div 2 \) (not possible, so bring down 0)
- Divide: \( 10 \div 2 = 5 \)
- Multiply: \( 5 \times 2 = 10 \)
- Subtract: \( 10 - 10 = 0 \)
- Quotient: 305, Remainder: 0

10. \( 9 \overline{)960} \)
- Divide: \( 9 \div 9 = 1 \)
- Multiply: \( 1 \times 9 = 9 \)
- Subtract: \( 9 - 9 = 0 \)
- Bring down: 6
- Divide: \( 6 \div 9 \) (not possible, so bring down 0)
- Divide: \( 60 \div 9 = 6 \)
- Multiply: \( 6 \times 9 = 54 \)
- Subtract: \( 60 - 54 = 6 \)
- Quotient: 106, Remainder: 6

11. \( 7 \overline{)423} \)
- Divide: \( 4 \div 7 \) (not possible, so bring down 2)
- Divide: \( 42 \div 7 = 6 \)
- Multiply: \( 6 \times 7 = 42 \)
- Subtract: \( 42 - 42 = 0 \)
- Bring down: 3
- Divide: \( 3 \div 7 \) (not possible)
- Quotient: 60, Remainder: 3

12. \( 8 \overline{)647} \)
- Divide: \( 6 \div 8 \) (not possible, so bring down 4)
- Divide: \( 64 \div 8 = 8 \)
- Multiply: \( 8 \times 8 = 64 \)
- Subtract: \( 64 - 64 = 0 \)
- Bring down: 7
- Divide: \( 7 \div 8 \) (not possible)
- Quotient: 80, Remainder: 7

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & 309, 0 \\
2. & 109, 0 \\
3. & 108, 2 \\
4. & 101, 2 \\
5. & 208, 0 \\
6. & 403, 1 \\
7. & 206, 2 \\
8. & 120, 3 \\
9. & 41, 2 \\
10. & 61, 5 \\
11. & 406, 1 \\
12. & 69, 4 \\
13. & 107, 0 \\
14. & 308, 0 \\
15. & 209, 0 \\
16. & 102, 3 \\
17. & 305, 0 \\
18. & 106, 6 \\
19. & 60, 3 \\
20. & 80, 7 \\
\end{array}
}
\]