Dividing Fractions Worksheets with Answer Key - Free Printable

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