Grade 5 long division worksheet focusing on single-digit division with no remainders.

Problem: Solve the long division problems by single-digit divisors (no remainder).

The worksheet asks us to find the quotient for each division problem. Let's solve each one step by step.

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#### 1. \( 4 \div 932 \)

- Dividend: 932
- Divisor: 4

Step-by-Step Solution:
1. Divide the first digit of the dividend (9) by the divisor (4).
\( 9 \div 4 = 2 \) (since \( 4 \times 2 = 8 \), which is the closest multiple of 4 less than 9).
2. Write 2 above the division bar.
3. Subtract \( 8 \) from \( 9 \):
\( 9 - 8 = 1 \).
4. Bring down the next digit (3). Now, we have 13.
5. Divide 13 by 4:
\( 13 \div 4 = 3 \) (since \( 4 \times 3 = 12 \)).
6. Write 3 above the division bar.
7. Subtract \( 12 \) from \( 13 \):
\( 13 - 12 = 1 \).
8. Bring down the next digit (2). Now, we have 12.
9. Divide 12 by 4:
\( 12 \div 4 = 3 \) (since \( 4 \times 3 = 12 \)).
10. Write 3 above the division bar.
11. Subtract \( 12 \) from \( 12 \):
\( 12 - 12 = 0 \).

The quotient is \( 233 \).

Answer: \( \boxed{233} \)

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#### 2. \( 8 \div 168 \)

- Dividend: 168
- Divisor: 8

Step-by-Step Solution:
1. Divide the first two digits of the dividend (16) by the divisor (8).
\( 16 \div 8 = 2 \) (since \( 8 \times 2 = 16 \)).
2. Write 2 above the division bar.
3. Subtract \( 16 \) from \( 16 \):
\( 16 - 16 = 0 \).
4. Bring down the next digit (8). Now, we have 8.
5. Divide 8 by 8:
\( 8 \div 8 = 1 \) (since \( 8 \times 1 = 8 \)).
6. Write 1 above the division bar.
7. Subtract \( 8 \) from \( 8 \):
\( 8 - 8 = 0 \).

The quotient is \( 21 \).

Answer: \( \boxed{21} \)

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#### 3. \( 7 \div 777 \)

- Dividend: 777
- Divisor: 7

Step-by-Step Solution:
1. Divide the first digit of the dividend (7) by the divisor (7).
\( 7 \div 7 = 1 \) (since \( 7 \times 1 = 7 \)).
2. Write 1 above the division bar.
3. Subtract \( 7 \) from \( 7 \):
\( 7 - 7 = 0 \).
4. Bring down the next digit (7). Now, we have 7.
5. Divide 7 by 7:
\( 7 \div 7 = 1 \) (since \( 7 \times 1 = 7 \)).
6. Write 1 above the division bar.
7. Subtract \( 7 \) from \( 7 \):
\( 7 - 7 = 0 \).
8. Bring down the next digit (7). Now, we have 7.
9. Divide 7 by 7:
\( 7 \div 7 = 1 \) (since \( 7 \times 1 = 7 \)).
10. Write 1 above the division bar.
11. Subtract \( 7 \) from \( 7 \):
\( 7 - 7 = 0 \).

The quotient is \( 111 \).

Answer: \( \boxed{111} \)

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#### 4. \( 9 \div 360 \)

- Dividend: 360
- Divisor: 9

Step-by-Step Solution:
1. Divide the first two digits of the dividend (36) by the divisor (9).
\( 36 \div 9 = 4 \) (since \( 9 \times 4 = 36 \)).
2. Write 4 above the division bar.
3. Subtract \( 36 \) from \( 36 \):
\( 36 - 36 = 0 \).
4. Bring down the next digit (0). Now, we have 0.
5. Divide 0 by 9:
\( 0 \div 9 = 0 \) (since \( 9 \times 0 = 0 \)).
6. Write 0 above the division bar.
7. Subtract \( 0 \) from \( 0 \):
\( 0 - 0 = 0 \).

The quotient is \( 40 \).

Answer: \( \boxed{40} \)

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#### 5. \( 6 \div 828 \)

- Dividend: 828
- Divisor: 6

Step-by-Step Solution:
1. Divide the first digit of the dividend (8) by the divisor (6).
\( 8 \div 6 = 1 \) (since \( 6 \times 1 = 6 \)).
2. Write 1 above the division bar.
3. Subtract \( 6 \) from \( 8 \):
\( 8 - 6 = 2 \).
4. Bring down the next digit (2). Now, we have 22.
5. Divide 22 by 6:
\( 22 \div 6 = 3 \) (since \( 6 \times 3 = 18 \)).
6. Write 3 above the division bar.
7. Subtract \( 18 \) from \( 22 \):
\( 22 - 18 = 4 \).
8. Bring down the next digit (8). Now, we have 48.
9. Divide 48 by 6:
\( 48 \div 6 = 8 \) (since \( 6 \times 8 = 48 \)).
10. Write 8 above the division bar.
11. Subtract \( 48 \) from \( 48 \):
\( 48 - 48 = 0 \).

The quotient is \( 138 \).

Answer: \( \boxed{138} \)

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#### 6. \( 3 \div 363 \)

- Dividend: 363
- Divisor: 3

Step-by-Step Solution:
1. Divide the first digit of the dividend (3) by the divisor (3).
\( 3 \div 3 = 1 \) (since \( 3 \times 1 = 3 \)).
2. Write 1 above the division bar.
3. Subtract \( 3 \) from \( 3 \):
\( 3 - 3 = 0 \).
4. Bring down the next digit (6). Now, we have 6.
5. Divide 6 by 3:
\( 6 \div 3 = 2 \) (since \( 3 \times 2 = 6 \)).
6. Write 2 above the division bar.
7. Subtract \( 6 \) from \( 6 \):
\( 6 - 6 = 0 \).
8. Bring down the next digit (3). Now, we have 3.
9. Divide 3 by 3:
\( 3 \div 3 = 1 \) (since \( 3 \times 1 = 3 \)).
10. Write 1 above the division bar.
11. Subtract \( 3 \) from \( 3 \):
\( 3 - 3 = 0 \).

The quotient is \( 121 \).

Answer: \( \boxed{121} \)

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#### 7. \( 9 \div 243 \)

- Dividend: 243
- Divisor: 9

Step-by-Step Solution:
1. Divide the first two digits of the dividend (24) by the divisor (9).
\( 24 \div 9 = 2 \) (since \( 9 \times 2 = 18 \)).
2. Write 2 above the division bar.
3. Subtract \( 18 \) from \( 24 \):
\( 24 - 18 = 6 \).
4. Bring down the next digit (3). Now, we have 63.
5. Divide 63 by 9:
\( 63 \div 9 = 7 \) (since \( 9 \times 7 = 63 \)).
6. Write 7 above the division bar.
7. Subtract \( 63 \) from \( 63 \):
\( 63 - 63 = 0 \).

The quotient is \( 27 \).

Answer: \( \boxed{27} \)

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#### 8. \( 5 \div 355 \)

- Dividend: 355
- Divisor: 5

Step-by-Step Solution:
1. Divide the first digit of the dividend (3) by the divisor (5). Since 3 is less than 5, consider the first two digits (35).
2. Divide 35 by 5:
\( 35 \div 5 = 7 \) (since \( 5 \times 7 = 35 \)).
3. Write 7 above the division bar.
4. Subtract \( 35 \) from \( 35 \):
\( 35 - 35 = 0 \).
5. Bring down the next digit (5). Now, we have 5.
6. Divide 5 by 5:
\( 5 \div 5 = 1 \) (since \( 5 \times 1 = 5 \)).
7. Write 1 above the division bar.
8. Subtract \( 5 \) from \( 5 \):
\( 5 - 5 = 0 \).

The quotient is \( 71 \).

Answer: \( \boxed{71} \)

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#### 9. \( 2 \div 782 \)

- Dividend: 782
- Divisor: 2

Step-by-Step Solution:
1. Divide the first digit of the dividend (7) by the divisor (2).
\( 7 \div 2 = 3 \) (since \( 2 \times 3 = 6 \)).
2. Write 3 above the division bar.
3. Subtract \( 6 \) from \( 7 \):
\( 7 - 6 = 1 \).
4. Bring down the next digit (8). Now, we have 18.
5. Divide 18 by 2:
\( 18 \div 2 = 9 \) (since \( 2 \times 9 = 18 \)).
6. Write 9 above the division bar.
7. Subtract \( 18 \) from \( 18 \):
\( 18 - 18 = 0 \).
8. Bring down the next digit (2). Now, we have 2.
9. Divide 2 by 2:
\( 2 \div 2 = 1 \) (since \( 2 \times 1 = 2 \)).
10. Write 1 above the division bar.
11. Subtract \( 2 \) from \( 2 \):
\( 2 - 2 = 0 \).

The quotient is \( 391 \).

Answer: \( \boxed{391} \)

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Final Answers:

1. \( \boxed{233} \)
2. \( \boxed{21} \)
3. \( \boxed{111} \)
4. \( \boxed{40} \)
5. \( \boxed{138} \)
6. \( \boxed{121} \)
7. \( \boxed{27} \)
8. \( \boxed{71} \)
9. \( \boxed{391} \)