Dividing Fractions Worksheets with Answer Key - Free Printable
Educational worksheet: Dividing Fractions Worksheets with Answer Key. Download and print for classroom or home learning activities.
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Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
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Show Answer Key & Explanations
Step-by-step solution for: Dividing Fractions Worksheets with Answer Key
Let’s solve each problem step by step. We’ll convert mixed numbers to improper fractions, then divide by multiplying by the reciprocal, and simplify if needed.
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Problem 1: 3 ²⁄₃ ÷ 6 ¹⁄₆
Convert to improper fractions:
- 3 ²⁄₃ = (3×3 + 2)/3 = 11/3
- 6 ¹⁄₆ = (6×6 + 1)/6 = 37/6
Now divide:
11/3 ÷ 37/6 = 11/3 × 6/37 = (11×6)/(3×37) = 66/111
Simplify: Divide numerator and denominator by 3 → 22/37
✔ Final Answer for #1: 22/37
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Problem 2: 4 ⁵⁄₆ ÷ 2 ¹⁄₃
Convert:
- 4 ⁵⁄ = (4×6 + 5)/6 = 29/6
- 2 ¹⁄₃ = (2×3 + 1)/3 = 7/3
Divide:
29/6 ÷ 7/3 = 29/6 × 3/7 = (29×3)/(6×7) = 87/42
Simplify: Divide by 3 → 29/14 → or as mixed number: 2 ¹⁄₁₄
But since worksheet doesn’t specify format, we can leave as improper fraction unless asked. Let’s keep it simplified: 29/14
✔ Final Answer for #2: 29/14
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Problem 3: 7 ¹⁄₃ ⁵⁄
Convert:
- 7 ¹⁄₃ = (7×3 + 1)/3 = 22/3
Divide:
22/3 ÷ 5/6 = 22/3 × 6/5 = (22×6)/(3×5) = 132/15
Simplify: Divide by 3 → 44/5 → or 8 ⁴⁄₅
We’ll write as 44/5
✔ Final Answer for #3: 44/5
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Problem 4: 4 ³⁄₈ ÷ ¹⁴⁄₁₆
Convert:
- 4 ³⁄₈ = (4×8 + 3)/8 = 35/8
- 14/16 simplifies to 7/8 (but let’s keep as is for now)
Divide:
35/8 ÷ 14/16 = 35/8 × 16/14 = (35×16)/(8×14)
Simplify before multiplying:
- 16/8 = 2 → so becomes 35×2 / 14 = 70/14 = 5
✔ Final Answer for #4: 5
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Problem 5: ⁸⁄ ÷ ⁷²₈₄
First, simplify 72/84: divide numerator and denominator by 12 → 6/7
So: 8/9 ÷ 6/7 = 8/9 × 7/6 = (8×7)/(9×6) = 56/54
Simplify: divide by 2 → 28/27 → or 1 ¹⁄₂₇
We’ll write 28/27
✔ Final Answer for #5: 28/27
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Problem 6: ¹⁵⁄₁₆ ÷ ²⁄₂₁
Divide:
15/16 × 21/20 = (15×21)/(16×20) = 315/320
Simplify: divide by 5 → 63/64
✔ Final Answer for #6: 63/64
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Problem 7: ¹¹⁄₁₆ ÷ ⁴⁄
Divide:
11/16 × 5/4 = (11×5)/(16×4) = 55/64
Already simplified.
✔ Final Answer for #7: 55/64
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Problem 8: 8 ²⁄₃ 2 ¹₃
Convert:
- 8 ²⁄₃ = (8×3 + 2)/3 = 26/3
- 2 ¹⁄₃ = (2×3 + 1)/3 = 7/3
Divide:
26/3 ÷ 7/3 = 26/3 × 3/7 = (26×3)/(3×7) = 78/21 → cancel 3s → 26/7
Or 3 ⁵⁄ — but we’ll write 26/7
✔ Final Answer for #8: 26/7
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Problem 9: ²⁹⁄₅ 3 ²⁄₉
Convert:
- 3 ²⁄₉ = (3×9 + 2)/9 = 29/9
Divide:
29/5 ÷ 29/9 = 29/5 × 9/29 = (29×9)/(5×29) = 9/5 (29 cancels out)
✔ Final Answer for #9: 9/5
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Problem 10: ³⁄₄ ÷ 7 ³⁄₈
Convert:
- 7 ³⁄₈ = (7×8 + 3)/8 = 59/8
Divide:
3/4 ÷ 59/8 = 3/4 × 8/59 = (3×8)/(4×59) = 24/236
Simplify: divide by 4 → 6/59
✔ Final Answer for #10: 6/59
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Problem 11: ¹⁷⁄₂ ÷ ¹⁴⁄₄
Note: 14/4 = 7/2 (simplified)
So: 17/2 ÷ 7/2 = 17/2 × 2/7 = (17×2)/(2×7) = 34/14 → cancel 2s → 17/7
✔ Final Answer for #11: 17/7
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Problem 12: ¹⁷⁄₃ ÷ ³⁴⁄₄
Simplify 34/4 = 17/2
So: 17/3 ÷ 17/2 = 17/3 × 2/17 = (17×2)/(3×17) = 2/3 (17 cancels)
✔ Final Answer for #12: 2/3
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Problem 13: 6 ¹⁄₂ ÷ ³⁴⁄₄
Convert:
- 6 ¹⁄₂ = 13/2
- 34/4 = 17/2
Divide:
13/2 ÷ 17/2 = 13/2 × 2/17 = (13×2)/(2×17) = 26/34 → simplify by 2 → 13/17
✔ Final Answer for #13: 13/17
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Problem 14: ²⁴⁄₃ 6 ²⁄₅
Simplify 24/3 = 8
Convert 6 ²⁄₅ = (6×5 + 2)/5 = 32/5
So: 8 ÷ 32/5 = 8/1 × 5/32 = 40/32 = 5/4 (divide by 8)
✔ Final Answer for #14: 5/4
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Final Answers:
1. 22/37
2. 29/14
3. 44/5
4. 5
5. 28/27
6. 63/64
7. 55/64
8. 26/7
9. 9/5
10. 6/59
11. 17/7
12. 2/3
13. 13/17
14. 5/4
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Problem 1: 3 ²⁄₃ ÷ 6 ¹⁄₆
Convert to improper fractions:
- 3 ²⁄₃ = (3×3 + 2)/3 = 11/3
- 6 ¹⁄₆ = (6×6 + 1)/6 = 37/6
Now divide:
11/3 ÷ 37/6 = 11/3 × 6/37 = (11×6)/(3×37) = 66/111
Simplify: Divide numerator and denominator by 3 → 22/37
✔ Final Answer for #1: 22/37
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Problem 2: 4 ⁵⁄₆ ÷ 2 ¹⁄₃
Convert:
- 4 ⁵⁄ = (4×6 + 5)/6 = 29/6
- 2 ¹⁄₃ = (2×3 + 1)/3 = 7/3
Divide:
29/6 ÷ 7/3 = 29/6 × 3/7 = (29×3)/(6×7) = 87/42
Simplify: Divide by 3 → 29/14 → or as mixed number: 2 ¹⁄₁₄
But since worksheet doesn’t specify format, we can leave as improper fraction unless asked. Let’s keep it simplified: 29/14
✔ Final Answer for #2: 29/14
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Problem 3: 7 ¹⁄₃ ⁵⁄
Convert:
- 7 ¹⁄₃ = (7×3 + 1)/3 = 22/3
Divide:
22/3 ÷ 5/6 = 22/3 × 6/5 = (22×6)/(3×5) = 132/15
Simplify: Divide by 3 → 44/5 → or 8 ⁴⁄₅
We’ll write as 44/5
✔ Final Answer for #3: 44/5
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Problem 4: 4 ³⁄₈ ÷ ¹⁴⁄₁₆
Convert:
- 4 ³⁄₈ = (4×8 + 3)/8 = 35/8
- 14/16 simplifies to 7/8 (but let’s keep as is for now)
Divide:
35/8 ÷ 14/16 = 35/8 × 16/14 = (35×16)/(8×14)
Simplify before multiplying:
- 16/8 = 2 → so becomes 35×2 / 14 = 70/14 = 5
✔ Final Answer for #4: 5
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Problem 5: ⁸⁄ ÷ ⁷²₈₄
First, simplify 72/84: divide numerator and denominator by 12 → 6/7
So: 8/9 ÷ 6/7 = 8/9 × 7/6 = (8×7)/(9×6) = 56/54
Simplify: divide by 2 → 28/27 → or 1 ¹⁄₂₇
We’ll write 28/27
✔ Final Answer for #5: 28/27
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Problem 6: ¹⁵⁄₁₆ ÷ ²⁄₂₁
Divide:
15/16 × 21/20 = (15×21)/(16×20) = 315/320
Simplify: divide by 5 → 63/64
✔ Final Answer for #6: 63/64
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Problem 7: ¹¹⁄₁₆ ÷ ⁴⁄
Divide:
11/16 × 5/4 = (11×5)/(16×4) = 55/64
Already simplified.
✔ Final Answer for #7: 55/64
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Problem 8: 8 ²⁄₃ 2 ¹₃
Convert:
- 8 ²⁄₃ = (8×3 + 2)/3 = 26/3
- 2 ¹⁄₃ = (2×3 + 1)/3 = 7/3
Divide:
26/3 ÷ 7/3 = 26/3 × 3/7 = (26×3)/(3×7) = 78/21 → cancel 3s → 26/7
Or 3 ⁵⁄ — but we’ll write 26/7
✔ Final Answer for #8: 26/7
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Problem 9: ²⁹⁄₅ 3 ²⁄₉
Convert:
- 3 ²⁄₉ = (3×9 + 2)/9 = 29/9
Divide:
29/5 ÷ 29/9 = 29/5 × 9/29 = (29×9)/(5×29) = 9/5 (29 cancels out)
✔ Final Answer for #9: 9/5
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Problem 10: ³⁄₄ ÷ 7 ³⁄₈
Convert:
- 7 ³⁄₈ = (7×8 + 3)/8 = 59/8
Divide:
3/4 ÷ 59/8 = 3/4 × 8/59 = (3×8)/(4×59) = 24/236
Simplify: divide by 4 → 6/59
✔ Final Answer for #10: 6/59
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Problem 11: ¹⁷⁄₂ ÷ ¹⁴⁄₄
Note: 14/4 = 7/2 (simplified)
So: 17/2 ÷ 7/2 = 17/2 × 2/7 = (17×2)/(2×7) = 34/14 → cancel 2s → 17/7
✔ Final Answer for #11: 17/7
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Problem 12: ¹⁷⁄₃ ÷ ³⁴⁄₄
Simplify 34/4 = 17/2
So: 17/3 ÷ 17/2 = 17/3 × 2/17 = (17×2)/(3×17) = 2/3 (17 cancels)
✔ Final Answer for #12: 2/3
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Problem 13: 6 ¹⁄₂ ÷ ³⁴⁄₄
Convert:
- 6 ¹⁄₂ = 13/2
- 34/4 = 17/2
Divide:
13/2 ÷ 17/2 = 13/2 × 2/17 = (13×2)/(2×17) = 26/34 → simplify by 2 → 13/17
✔ Final Answer for #13: 13/17
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Problem 14: ²⁴⁄₃ 6 ²⁄₅
Simplify 24/3 = 8
Convert 6 ²⁄₅ = (6×5 + 2)/5 = 32/5
So: 8 ÷ 32/5 = 8/1 × 5/32 = 40/32 = 5/4 (divide by 8)
✔ Final Answer for #14: 5/4
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Final Answers:
1. 22/37
2. 29/14
3. 44/5
4. 5
5. 28/27
6. 63/64
7. 55/64
8. 26/7
9. 9/5
10. 6/59
11. 17/7
12. 2/3
13. 13/17
14. 5/4
Parent Tip: Review the logic above to help your child master the concept of fraction division worksheet.