Long Division Worksheets -Worksheets Library - Free Printable
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Step-by-step solution for: Long Division Worksheets -Worksheets Library
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Show Answer Key & Explanations
Step-by-step solution for: Long Division Worksheets -Worksheets Library
Let’s solve each long division problem step by step. We’re dividing decimals by whole numbers, so we’ll treat the decimal point carefully — it stays in the same place in the answer as it is in the dividend (the number being divided).
We’ll go one by one:
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1. 14.37 ÷ 6
6 goes into 14 two times → 2 × 6 = 12
Subtract: 14 - 12 = 2
Bring down 3 → 23
6 goes into 23 three times → 3 × 6 = 18
Subtract: 23 - 18 = 5
Bring down 7 → 57
6 goes into 57 nine times → 9 × 6 = 54
Subtract: 57 - 54 = 3 → add a zero → 30
6 goes into 30 five times → 5 × 6 = 30
Subtract: 0
So: 2.395
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2. 62.91 ÷ 9
9 into 62 → 6 times → 6×9=54
62-54=8
Bring down 9 → 89
9 into 89 → 9 times → 9×9=81
89-81=8
Bring down 1 → 81
9 into 81 → 9 times → 9×9=81
Subtract: 0
So: 6.99
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3. 34.51 ÷ 7
7 into 34 → 4 times → 4×7=28
34-28=6
Bring down 5 → 65
7 into 65 → 9 times → 9×7=63
65-63=2
Bring down 1 → 21
7 into 21 → 3 times → 3×7=21
Subtract: 0
So: 4.93
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4. 76.98 ÷ 3
3 into 7 → 2 times → 2×3=6
7-6=1
Bring down 6 → 16
3 into 16 → 5 times → 5×3=15
16-15=1
Bring down 9 → 19
3 into 19 → 6 times → 6×3=18
19-18=1
Bring down 8 → 18
3 into 18 → 6 times → 6×3=18
Subtract: 0
So: 25.66
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5. 23.82 ÷ 5
5 into 23 → 4 times → 4×5=20
23-20=3
Bring down 8 → 38
5 into 38 → 7 times → 7×5=35
38-35=3
Bring down 2 → 32
5 into 32 → 6 times → 6×5=30
32-30=2 → add zero → 20
5 into 20 → 4 times → 4×5=20
Subtract: 0
So: 4.764
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6. 23.82 ÷ 4
4 into 23 → 5 times → 5×4=20
23-20=3
Bring down 8 → 38
4 into 38 → 9 times → 9×4=36
38-36=2
Bring down 2 → 22
4 into 22 → 5 times → 5×4=20
22-20=2 → add zero → 20
4 into 20 → 5 times → 5×4=20
Subtract: 0
So: 5.955
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7. 32.67 ÷ 2
2 into 3 → 1 time → 1×2=2
3-2=1
Bring down 2 → 12
2 into 12 → 6 times → 6×2=12
Subtract: 0
Bring down 6 → 6
2 into 6 → 3 times → 3×2=6
Subtract: 0
Bring down 7 → 7
2 into 7 → 3 times → 3×2=6
7-6=1 → add zero → 10
2 into 10 → 5 times → 5×2=10
Subtract: 0
So: 16.335
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8. 54.96 ÷ 6
6 into 54 → 9 times → 9×6=54
Subtract: 0
Bring down 9 → 9
6 into 9 → 1 time → 1×6=6
9-6=3
Bring down 6 → 36
6 into 36 → 6 times → 6×6=36
Subtract: 0
So: 9.16
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9. 56.34 ÷ 5
5 into 56 → 11 times? Wait — let’s do digit by digit.
5 into 5 → 1 → 1×5=5
Subtract: 0
Bring down 6 → 6
5 into 6 → 1 → 1×5=5
6-5=1
Bring down 3 → 13
5 into 13 → 2 → 2×5=10
13-10=3
Bring down 4 → 34
5 into 34 → 6 → 6×5=30
34-30=4 → add zero → 40
5 into 40 → 8 → 8×5=40
Subtract: 0
So: 11.268
Wait — actually, 5 into 56 is 11 with remainder 1? Let me redo this properly.
Actually, better to think:
5 into 56 → 11 times? But we do one digit at a time.
Start over:
Dividend: 56.34
5 into 5 → 1 → write 1 above first 5
1×5=5 → subtract → 0
Bring down 6 → 6
5 into 6 → 1 → write 1 above 6
1×5=5 → subtract → 1
Decimal point now — bring down 3 → 13
5 into 13 → 2 → write 2 after decimal
2×5=10 → subtract → 3
Bring down 4 → 34
5 into 34 → 6 → write 6
6×5=30 → subtract → 4
Add zero → 40
5 into 40 → 8 → write 8
8×5=40 → subtract → 0
So: 11.268
Yes.
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10. 79.56 ÷ 8
8 into 79 → 9 times → 9×8=72
79-72=7
Bring down 5 → 75
8 into 75 → 9 times → 9×8=72
75-72=3
Bring down 6 → 36
8 into 36 → 4 times → 4×8=32
36-32=4 → add zero → 40
8 into 40 → 5 times → 5×8=40
Subtract: 0
So: 9.945
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11. 45.29 ÷ 7
7 into 45 → 6 times → 6×7=42
45-42=3
Bring down 2 → 32
7 into 32 → 4 times → 4×7=28
32-28=4
Bring down 9 → 49
7 into 49 → 7 times → 7×7=49
Subtract: 0
So: 6.47
Wait — 45.29 ÷ 7
After 45 - 42 = 3, bring down 2 → 32 → 4×7=28 → remainder 4
Bring down 9 → 49 → 7×7=49 → done.
But what about the decimal? The 2 and 9 are after decimal, so answer should be 6.47 exactly? Let's check:
7 × 6.47 = 7×6 + 7×0.4 + 7×0.07 = 42 + 2.8 + 0.49 = 45.29 → yes!
So: 6.47
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12. 52.89 ÷ 3
3 into 5 → 1 → 1×3=3
5-3=2
Bring down 2 → 22
3 into 22 → 7 → 7×3=21
22-21=1
Bring down 8 → 18
3 into 18 → 6 → 6×3=18
Subtract: 0
Bring down 9 → 9
3 into 9 → 3 → 3×3=9
Subtract: 0
So: 17.63
Wait — 52.89 ÷ 3
Step-by-step:
3 into 5 → 1 → remainder 2
Bring down 2 → 22 → 7×3=21 → remainder 1
Bring down 8 → 18 → 6×3=18 → remainder 0
Bring down 9 → 9 → 3×3=9 → remainder 0
So digits: 1 (tens), 7 (ones), then decimal, then 6 (tenths), 3 (hundredths) → 17.63
Check: 3 × 17.63 = 3×17 + 3×0.63 = 51 + 1.89 = 52.89 → correct.
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Now, compiling all answers:
1. 2.395
2. 6.99
3. 4.93
4. 25.66
5. 4.764
6. 5.955
7. 16.335
8. 9.16
9. 11.268
10. 9.945
11. 6.47
12. 17.63
Final Answer:
1. 2.395
2. 6.99
3. 4.93
4. 25.66
5. 4.764
6. 5.955
7. 16.335
8. 9.16
9. 11.268
10. 9.945
11. 6.47
12. 17.63
We’ll go one by one:
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1. 14.37 ÷ 6
6 goes into 14 two times → 2 × 6 = 12
Subtract: 14 - 12 = 2
Bring down 3 → 23
6 goes into 23 three times → 3 × 6 = 18
Subtract: 23 - 18 = 5
Bring down 7 → 57
6 goes into 57 nine times → 9 × 6 = 54
Subtract: 57 - 54 = 3 → add a zero → 30
6 goes into 30 five times → 5 × 6 = 30
Subtract: 0
So: 2.395
---
2. 62.91 ÷ 9
9 into 62 → 6 times → 6×9=54
62-54=8
Bring down 9 → 89
9 into 89 → 9 times → 9×9=81
89-81=8
Bring down 1 → 81
9 into 81 → 9 times → 9×9=81
Subtract: 0
So: 6.99
---
3. 34.51 ÷ 7
7 into 34 → 4 times → 4×7=28
34-28=6
Bring down 5 → 65
7 into 65 → 9 times → 9×7=63
65-63=2
Bring down 1 → 21
7 into 21 → 3 times → 3×7=21
Subtract: 0
So: 4.93
---
4. 76.98 ÷ 3
3 into 7 → 2 times → 2×3=6
7-6=1
Bring down 6 → 16
3 into 16 → 5 times → 5×3=15
16-15=1
Bring down 9 → 19
3 into 19 → 6 times → 6×3=18
19-18=1
Bring down 8 → 18
3 into 18 → 6 times → 6×3=18
Subtract: 0
So: 25.66
---
5. 23.82 ÷ 5
5 into 23 → 4 times → 4×5=20
23-20=3
Bring down 8 → 38
5 into 38 → 7 times → 7×5=35
38-35=3
Bring down 2 → 32
5 into 32 → 6 times → 6×5=30
32-30=2 → add zero → 20
5 into 20 → 4 times → 4×5=20
Subtract: 0
So: 4.764
---
6. 23.82 ÷ 4
4 into 23 → 5 times → 5×4=20
23-20=3
Bring down 8 → 38
4 into 38 → 9 times → 9×4=36
38-36=2
Bring down 2 → 22
4 into 22 → 5 times → 5×4=20
22-20=2 → add zero → 20
4 into 20 → 5 times → 5×4=20
Subtract: 0
So: 5.955
---
7. 32.67 ÷ 2
2 into 3 → 1 time → 1×2=2
3-2=1
Bring down 2 → 12
2 into 12 → 6 times → 6×2=12
Subtract: 0
Bring down 6 → 6
2 into 6 → 3 times → 3×2=6
Subtract: 0
Bring down 7 → 7
2 into 7 → 3 times → 3×2=6
7-6=1 → add zero → 10
2 into 10 → 5 times → 5×2=10
Subtract: 0
So: 16.335
---
8. 54.96 ÷ 6
6 into 54 → 9 times → 9×6=54
Subtract: 0
Bring down 9 → 9
6 into 9 → 1 time → 1×6=6
9-6=3
Bring down 6 → 36
6 into 36 → 6 times → 6×6=36
Subtract: 0
So: 9.16
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9. 56.34 ÷ 5
5 into 56 → 11 times? Wait — let’s do digit by digit.
5 into 5 → 1 → 1×5=5
Subtract: 0
Bring down 6 → 6
5 into 6 → 1 → 1×5=5
6-5=1
Bring down 3 → 13
5 into 13 → 2 → 2×5=10
13-10=3
Bring down 4 → 34
5 into 34 → 6 → 6×5=30
34-30=4 → add zero → 40
5 into 40 → 8 → 8×5=40
Subtract: 0
So: 11.268
Wait — actually, 5 into 56 is 11 with remainder 1? Let me redo this properly.
Actually, better to think:
5 into 56 → 11 times? But we do one digit at a time.
Start over:
Dividend: 56.34
5 into 5 → 1 → write 1 above first 5
1×5=5 → subtract → 0
Bring down 6 → 6
5 into 6 → 1 → write 1 above 6
1×5=5 → subtract → 1
Decimal point now — bring down 3 → 13
5 into 13 → 2 → write 2 after decimal
2×5=10 → subtract → 3
Bring down 4 → 34
5 into 34 → 6 → write 6
6×5=30 → subtract → 4
Add zero → 40
5 into 40 → 8 → write 8
8×5=40 → subtract → 0
So: 11.268
Yes.
---
10. 79.56 ÷ 8
8 into 79 → 9 times → 9×8=72
79-72=7
Bring down 5 → 75
8 into 75 → 9 times → 9×8=72
75-72=3
Bring down 6 → 36
8 into 36 → 4 times → 4×8=32
36-32=4 → add zero → 40
8 into 40 → 5 times → 5×8=40
Subtract: 0
So: 9.945
---
11. 45.29 ÷ 7
7 into 45 → 6 times → 6×7=42
45-42=3
Bring down 2 → 32
7 into 32 → 4 times → 4×7=28
32-28=4
Bring down 9 → 49
7 into 49 → 7 times → 7×7=49
Subtract: 0
So: 6.47
Wait — 45.29 ÷ 7
After 45 - 42 = 3, bring down 2 → 32 → 4×7=28 → remainder 4
Bring down 9 → 49 → 7×7=49 → done.
But what about the decimal? The 2 and 9 are after decimal, so answer should be 6.47 exactly? Let's check:
7 × 6.47 = 7×6 + 7×0.4 + 7×0.07 = 42 + 2.8 + 0.49 = 45.29 → yes!
So: 6.47
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12. 52.89 ÷ 3
3 into 5 → 1 → 1×3=3
5-3=2
Bring down 2 → 22
3 into 22 → 7 → 7×3=21
22-21=1
Bring down 8 → 18
3 into 18 → 6 → 6×3=18
Subtract: 0
Bring down 9 → 9
3 into 9 → 3 → 3×3=9
Subtract: 0
So: 17.63
Wait — 52.89 ÷ 3
Step-by-step:
3 into 5 → 1 → remainder 2
Bring down 2 → 22 → 7×3=21 → remainder 1
Bring down 8 → 18 → 6×3=18 → remainder 0
Bring down 9 → 9 → 3×3=9 → remainder 0
So digits: 1 (tens), 7 (ones), then decimal, then 6 (tenths), 3 (hundredths) → 17.63
Check: 3 × 17.63 = 3×17 + 3×0.63 = 51 + 1.89 = 52.89 → correct.
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Now, compiling all answers:
1. 2.395
2. 6.99
3. 4.93
4. 25.66
5. 4.764
6. 5.955
7. 16.335
8. 9.16
9. 11.268
10. 9.945
11. 6.47
12. 17.63
Final Answer:
1. 2.395
2. 6.99
3. 4.93
4. 25.66
5. 4.764
6. 5.955
7. 16.335
8. 9.16
9. 11.268
10. 9.945
11. 6.47
12. 17.63
Parent Tip: Review the logic above to help your child master the concept of 5th grade long division worksheet.