Math worksheet for practicing addition and subtraction of mixed fractions.

Let’s solve each problem step by step. We’ll convert mixed fractions to improper fractions, find common denominators when needed, add or subtract, then simplify back to a mixed fraction if necessary.

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Problem 1: 7½ + 1⁷⁄₈

Convert to improper fractions:
- 7½ = (7×2 + 1)/2 = 15/2
- 1⁷⁄₈ = (1×8 + 7)/8 = 15/8

Find common denominator of 2 and 8 → LCD is 8.
- 15/2 = (15×4)/(2×4) = 60/8
- 15/8 stays as is

Add: 60/8 + 15/8 = 75/8

Convert back to mixed number: 75 ÷ 8 = 9 remainder 3 → 9³⁄₈

✔ Final Answer for #1: 9³⁄₈

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Problem 2: 9¹⁄₆ - 4¹⁄₂

Convert:
- 9¹⁄₆ = (9×6 + 1)/6 = 55/6
- 4¹⁄₂ = (4×2 + 1)/2 = 9/2

LCD of 6 and 2 is 6.
- 9/2 = (9×3)/(2×3) = 27/6

Subtract: 55/6 - 27/6 = 28/6

Simplify: 28÷2 / 6÷2 = 14/3 → Convert to mixed: 14÷3 = 4 remainder 2 → 4²⁄₃

✔ Final Answer for #2: 4²⁄₃

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Problem 3: 6¹⁄₃ + 2⁵⁄₆

Convert:
- 6¹⁄₃ = (6×3 + 1)/3 = 19/3
- 2⁵⁄₆ = (2×6 + 5)/6 = 17/6

LCD of 3 and 6 is 6.
- 19/3 = (19×2)/(3×2) = 38/6

Add: 38/6 + 17/6 = 55/6

Mixed: 55÷6 = 9 remainder 1 → 9¹⁄₆

✔ Final Answer for #3: 9¹⁄₆

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Problem 4: 4⁴⁄₅ - 3¹⁄₆

Convert:
- 4⁴⁄₅ = (4×5 + 4)/5 = 24/5
- 3¹⁄₆ = (3×6 + 1)/6 = 19/6

LCD of 5 and 6 is 30.
- 24/5 = (24×6)/(5×6) = 144/30
- 19/6 = (19×5)/(6×5) = 95/30

Subtract: 144/30 - 95/30 = 49/30

Mixed: 49÷30 = 1 remainder 19 → 1¹⁹⁄₃₀

✔ Final Answer for #4: 1¹⁹⁄₀

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Problem 5: 2½ + 3¼

Convert:
- 2½ = 5/2
- 3¼ = 13/4

LCD of 2 and 4 is 4.
- 5/2 = 10/4

Add: 10/4 + 13/4 = 23/4

Mixed: 23÷4 = 5 remainder 3 → 5³⁄₄

✔ Final Answer for #5: 5³⁄₄

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Problem 6: 4⁴⁄₇ - 2²⁄₅

Convert:
- 4⁴⁄₇ = (4×7 + 4)/7 = 32/7
- 2²⁄₅ = (2×5 + 2)/5 = 12/5

LCD of 7 and 5 is 35.
- 32/7 = (32×5)/(7×5) = 160/35
- 12/5 = (12×7)/(5×7) = 84/35

Subtract: 160/35 - 84/35 = 76/35

Mixed: 76÷35 = 2 remainder 6 → 2⁶⁄₃₅

✔ Final Answer for #6: 2⁶⁄₅

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Problem 7: 3⁷⁄₁₂ + 2¹⁄₈

Convert:
- 3⁷⁄₁₂ = (3×12 + 7)/12 = 43/12
- 2¹⁄₈ = (2×8 + 1)/8 = 17/8

LCD of 12 and 8 is 24.
- 43/12 = (43×2)/(12×2) = 86/24
- 17/8 = (17×3)/(8×3) = 51/24

Add: 86/24 + 51/24 = 137/24

Mixed: 137÷24 = 5 remainder 17 → 5¹⁷⁄₂₄

✔ Final Answer for #7: 5¹⁷⁄₂₄

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Problem 8: 5¹⁄₅ - 3⁵⁄₇

Convert:
- 5¹⁄₅ = (5×5 + 1)/5 = 26/5
- 3⁵⁄₇ = (3×7 + 5)/7 = 26/7

LCD of 5 and 7 is 35.
- 26/5 = (26×7)/(5×7) = 182/35
- 26/7 = (26×5)/(7×5) = 130/35

Subtract: 182/35 - 130/35 = 52/35

Mixed: 52÷35 = 1 remainder 17 → 1¹⁷⁄₃

✔ Final Answer for #8: 1¹⁷⁄₃

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Problem 9: 4²⁄₅ + 3⁵⁄₆

Convert:
- 4²⁄₅ = (4×5 + 2)/5 = 22/5
- 3⁵⁄ = (3×6 + 5)/6 = 23/6

LCD of 5 and 6 is 30.
- 22/5 = (22×6)/(5×6) = 132/30
- 23/6 = (23×5)/(6×5) = 115/30

Add: 132/30 + 115/30 = 247/30

Mixed: 247÷30 = 8 remainder 7 → 8⁷⁄₃₀

✔ Final Answer for #9: 8⁷⁄₃₀

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Problem 10: 3¹⁄₁₀ - 1⁶⁄₈

First, simplify 6/8 → 3/4, so 1⁶⁄ = 1³⁄

Convert:
- 3¹⁄₁₀ = (3×10 + 1)/10 = 31/10
- 1³⁄₄ = (1×4 + 3)/4 = 7/4

LCD of 10 and 4 is 20.
- 31/10 = (31×2)/(10×2) = 62/20
- 7/4 = (7×5)/(4×5) = 35/20

Subtract: 62/20 - 35/20 = 27/20

Mixed: 27÷20 = 1 remainder 7 → 1⁷⁄₂₀

✔ Final Answer for #10: 1⁷⁄₂₀

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Problem 11: 6⁷⁄₈ + 9³⁄₉

Simplify 3/9 → 1/3, so 9³⁄₉ = 9¹⁄₃

Convert:
- 6⁷⁄ = (6×8 + 7)/8 = 55/8
- 9¹⁄₃ = (9×3 + 1)/3 = 28/3

LCD of 8 and 3 is 24.
- 55/8 = (55×3)/(8×3) = 165/24
- 28/3 = (28×8)/(3×8) = 224/24

Add: 165/24 + 224/24 = 389/24

Mixed: 389÷24 = 16 remainder 5 → 16⁵⁄₂₄

✔ Final Answer for #11: 16⁵⁄₂₄

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Problem 12: 7½ - 4⁷⁄₈

Convert:
- 7½ = 15/2
- 4⁷⁄₈ = (4×8 + 7)/8 = 39/8

LCD of 2 and 8 is 8.
- 15/2 = (15×4)/(2×4) = 60/8

Subtract: 60/8 - 39/8 = 21/8

Mixed: 21÷8 = 2 remainder 5 → 2⁵⁄

✔ Final Answer for #12: 2⁵⁄₈

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Final Answer:
1. 9³⁄₈
2. 4²⁄₃
3. 9¹⁄₆
4. 1¹⁹⁄₀
5. 5³⁄₄
6. 2⁶⁄₃
7. 5¹⁄₂₄
8. 1¹⁷⁄₃₅
9. 8⁷⁄₃₀
10. 1⁷⁄₂₀
11. 16⁵⁄₂₄
12. 2⁵⁄₈