3-Digit by 1-Digit Long Division with Remainders with Grid ... - Free Printable

The task involves solving long division problems using a grid format. Below, I will solve each problem step by step and explain the process.

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Problem 1: \( 6 \div 311 \)

#### Step-by-Step Solution:
1. Divide: How many times does 6 go into 3? It doesn't, so we look at the first two digits, 31.
2. Divide: How many times does 6 go into 31? It goes 5 times (since \( 6 \times 5 = 30 \)).
3. Multiply: \( 6 \times 5 = 30 \).
4. Subtract: \( 31 - 30 = 1 \).
5. Bring down: Bring down the next digit, 1, making it 11.
6. Divide: How many times does 6 go into 11? It goes 1 time (since \( 6 \times 1 = 6 \)).
7. Multiply: \( 6 \times 1 = 6 \).
8. Subtract: \( 11 - 6 = 5 \).

The quotient is 51 with a remainder of 5.

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Problem 2: \( 4 \div 888 \)

#### Step-by-Step Solution:
1. Divide: How many times does 4 go into 8? It goes 2 times (since \( 4 \times 2 = 8 \)).
2. Multiply: \( 4 \times 2 = 8 \).
3. Subtract: \( 8 - 8 = 0 \).
4. Bring down: Bring down the next digit, 8, making it 08.
5. Divide: How many times does 4 go into 8? It goes 2 times (since \( 4 \times 2 = 8 \)).
6. Multiply: \( 4 \times 2 = 8 \).
7. Subtract: \( 8 - 8 = 0 \).
8. Bring down: Bring down the next digit, 8, making it 08.
9. Divide: How many times does 4 go into 8? It goes 2 times (since \( 4 \times 2 = 8 \)).
10. Multiply: \( 4 \times 2 = 8 \).
11. Subtract: \( 8 - 8 = 0 \).

The quotient is 222 with no remainder.

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Problem 3: \( 5 \div 676 \)

#### Step-by-Step Solution:
1. Divide: How many times does 5 go into 6? It goes 1 time (since \( 5 \times 1 = 5 \)).
2. Multiply: \( 5 \times 1 = 5 \).
3. Subtract: \( 6 - 5 = 1 \).
4. Bring down: Bring down the next digit, 7, making it 17.
5. Divide: How many times does 5 go into 17? It goes 3 times (since \( 5 \times 3 = 15 \)).
6. Multiply: \( 5 \times 3 = 15 \).
7. Subtract: \( 17 - 15 = 2 \).
8. Bring down: Bring down the next digit, 6, making it 26.
9. Divide: How many times does 5 go into 26? It goes 5 times (since \( 5 \times 5 = 25 \)).
10. Multiply: \( 5 \times 5 = 25 \).
11. Subtract: \( 26 - 25 = 1 \).

The quotient is 135 with a remainder of 1.

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Problem 4: \( 2 \div 668 \)

#### Step-by-Step Solution:
1. Divide: How many times does 2 go into 6? It goes 3 times (since \( 2 \times 3 = 6 \)).
2. Multiply: \( 2 \times 3 = 6 \).
3. Subtract: \( 6 - 6 = 0 \).
4. Bring down: Bring down the next digit, 6, making it 06.
5. Divide: How many times does 2 go into 6? It goes 3 times (since \( 2 \times 3 = 6 \)).
6. Multiply: \( 2 \times 3 = 6 \).
7. Subtract: \( 6 - 6 = 0 \).
8. Bring down: Bring down the next digit, 8, making it 08.
9. Divide: How many times does 2 go into 8? It goes 4 times (since \( 2 \times 4 = 8 \)).
10. Multiply: \( 2 \times 4 = 8 \).
11. Subtract: \( 8 - 8 = 0 \).

The quotient is 334 with no remainder.

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Problem 5: \( 4 \div 556 \)

#### Step-by-Step Solution:
1. Divide: How many times does 4 go into 5? It goes 1 time (since \( 4 \times 1 = 4 \)).
2. Multiply: \( 4 \times 1 = 4 \).
3. Subtract: \( 5 - 4 = 1 \).
4. Bring down: Bring down the next digit, 5, making it 15.
5. Divide: How many times does 4 go into 15? It goes 3 times (since \( 4 \times 3 = 12 \)).
6. Multiply: \( 4 \times 3 = 12 \).
7. Subtract: \( 15 - 12 = 3 \).
8. Bring down: Bring down the next digit, 6, making it 36.
9. Divide: How many times does 4 go into 36? It goes 9 times (since \( 4 \times 9 = 36 \)).
10. Multiply: \( 4 \times 9 = 36 \).
11. Subtract: \( 36 - 36 = 0 \).

The quotient is 139 with no remainder.

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Problem 6: \( 3 \div 563 \)

#### Step-by-Step Solution:
1. Divide: How many times does 3 go into 5? It goes 1 time (since \( 3 \times 1 = 3 \)).
2. Multiply: \( 3 \times 1 = 3 \).
3. Subtract: \( 5 - 3 = 2 \).
4. Bring down: Bring down the next digit, 6, making it 26.
5. Divide: How many times does 3 go into 26? It goes 8 times (since \( 3 \times 8 = 24 \)).
6. Multiply: \( 3 \times 8 = 24 \).
7. Subtract: \( 26 - 24 = 2 \).
8. Bring down: Bring down the next digit, 3, making it 23.
9. Divide: How many times does 3 go into 23? It goes 7 times (since \( 3 \times 7 = 21 \)).
10. Multiply: \( 3 \times 7 = 21 \).
11. Subtract: \( 23 - 21 = 2 \).

The quotient is 187 with a remainder of 2.

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Problem 7: \( 3 \div 434 \)

#### Step-by-Step Solution:
1. Divide: How many times does 3 go into 4? It goes 1 time (since \( 3 \times 1 = 3 \)).
2. Multiply: \( 3 \times 1 = 3 \).
3. Subtract: \( 4 - 3 = 1 \).
4. Bring down: Bring down the next digit, 3, making it 13.
5. Divide: How many times does 3 go into 13? It goes 4 times (since \( 3 \times 4 = 12 \)).
6. Multiply: \( 3 \times 4 = 12 \).
7. Subtract: \( 13 - 12 = 1 \).
8. Bring down: Bring down the next digit, 4, making it 14.
9. Divide: How many times does 3 go into 14? It goes 4 times (since \( 3 \times 4 = 12 \)).
10. Multiply: \( 3 \times 4 = 12 \).
11. Subtract: \( 14 - 12 = 2 \).

The quotient is 144 with a remainder of 2.

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Problem 8: \( 5 \div 151 \)

#### Step-by-Step Solution:
1. Divide: How many times does 5 go into 1? It doesn't, so we look at the first two digits, 15.
2. Divide: How many times does 5 go into 15? It goes 3 times (since \( 5 \times 3 = 15 \)).
3. Multiply: \( 5 \times 3 = 15 \).
4. Subtract: \( 15 - 15 = 0 \).
5. Bring down: Bring down the next digit, 1, making it 01.
6. Divide: How many times does 5 go into 1? It doesn't go any times.

The quotient is 30 with a remainder of 1.

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Final Answers:

1. \( 6 \div 311 = 51 \) R5
2. \( 4 \div 888 = 222 \)
3. \( 5 \div 676 = 135 \) R1
4. \( 2 \div 668 = 334 \)
5. \( 4 \div 556 = 139 \)
6. \( 3 \div 563 = 187 \) R2
7. \( 3 \div 434 = 144 \) R2
8. \( 5 \div 151 = 30 \) R1

\[
\boxed{51, 222, 135, 334, 139, 187, 144, 30}
\]