Math worksheet for practicing addition and subtraction of mixed fractions.

Here's the step-by-step solution to all 12 problems involving adding and subtracting mixed fractions.

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🔢 General Strategy:

To add or subtract mixed numbers:
1. Convert mixed numbers to improper fractions (optional, but helpful for some).
2. Find a common denominator for the fractional parts.
3. Add or subtract the whole numbers separately, and the fractions separately.
4. If needed, borrow (for subtraction) or carry over (for addition) when fractions exceed 1 or go negative.
5. Simplify the result and convert back to a mixed number if needed.

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## ✔ Problem 1:
7½ + 1⅞

- Convert to improper fractions:
- 7½ = 15/2
- 1⅞ = 15/8

- Common denominator of 2 and 8 is 8.
- 15/2 = 60/8
- 15/8 = 15/8

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

- Convert to mixed number:
75 ÷ 8 = 9 with remainder 3 → 9 3/8

✔ Answer: 9 3/8

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## ✔ Problem 2:
9⅙ - 4½

- Convert:
- 9⅙ = 55/6
- 4½ = 9/2

- Common denominator of 6 and 2 is 6.
- 55/6 stays same
- 9/2 = 27/6

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

- Simplify: 28/6 = 14/3 = 4 2/3

✔ Answer: 4 2/3

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## ✔ Problem 3:
6⅓ + 2⅚

- Whole numbers: 6 + 2 = 8
- Fractions: ⅓ + ⅚ → common denominator 6
- ⅓ = 2/6, ⅚ = 5/6 → 2/6 + 5/6 = 7/6 = 1 1/6

- Add whole parts: 8 + 1 = 9, plus 1/6 → 9 1/6

✔ Answer: 9 1/6

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## ✔ Problem 4:
4⁴⁄₅ - 3¹⁄₆

- Whole numbers: 4 - 3 = 1
- Fractions: ⁴⁄₅ - ¹⁄₆ → common denominator 30
- ⁴⁄₅ = 24/30, ¹⁄₆ = 5/30 → 24/30 - 5/30 = 19/30

- Combine: 1 + 19/30 = 1 19/30

✔ Answer: 1 19/30

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## ✔ Problem 5:
2½ + 3¼

- Whole numbers: 2 + 3 = 5
- Fractions: ½ + ¼ → common denominator 4
- ½ = 2/4, ¼ = 1/4 → 3/4

- Total: 5 3/4

✔ Answer: 5 3/4

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## ✔ Problem 6:
4⁴⁄₇ - 2²⁄₅

- Whole numbers: 4 - 2 = 2
- Fractions: ⁴⁄₇ - ²⁄₅ → common denominator 35
- ⁴⁄₇ = 20/35, ²⁄₅ = 14/35 → 20/35 - 14/35 = 6/35

- Total: 2 6/35

✔ Answer: 2 6/35

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## ✔ Problem 7:
3⁷⁄₁₂ + 2¹⁄₈

- Whole numbers: 3 + 2 = 5
- Fractions: ⁷⁄₁₂ + ¹⁄₈ → common denominator 24
- ⁷⁄₁₂ = 14/24, ¹⁄₈ = 3/24 → 17/24

- Total: 5 17/24

✔ Answer: 5 17/24

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## ✔ Problem 8:
5⅕ - 3⁵⁄₇

- Whole numbers: 5 - 3 = 2
- Fractions: ⅕ - ⁵⁄₇ → common denominator 35
- ⅕ = 7/35, ⁵⁄₇ = 25/35 → 7/35 - 25/35 = -18/35

→ Since fraction is negative, borrow 1 from whole number:

- 2 becomes 1, and add 35/35 to -18/35 → 35/35 - 18/35 = 17/35

→ So total: 1 17/35

✔ Answer: 1 17/35

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## ✔ Problem 9:
4²⁄₅ + 3⁵⁄₆

- Whole numbers: 4 + 3 = 7
- Fractions: ²⁄₅ + ⁵⁄₆ → common denominator 30
- ²⁄₅ = 12/30, ⁵⁄₆ = 25/30 → 37/30 = 1 7/30

- Add to whole: 7 + 1 = 8, plus 7/30 → 8 7/30

✔ Answer: 8 7/30

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## ✔ Problem 10:
3¹⁄₁₀ - 1⁶⁄₈

First, simplify ⁶⁄₈ = ¾

So: 3¹⁄₁₀ - 1¾

- Whole numbers: 3 - 1 = 2
- Fractions: ¹⁄₁₀ - ¾ → common denominator 20
- ¹⁄₁₀ = 2/20, ¾ = 15/20 → 2/20 - 15/20 = -13/20

→ Borrow 1 from 2 → becomes 1, add 20/20 → 20/20 - 13/20 = 7/20

→ Total: 1 7/20

✔ Answer: 1 7/20

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## ✔ Problem 11:
6⁷⁄₈ + 9³⁄₉

Simplify ³⁄₉ = ⅓

So: 6⁷⁄₈ + 9⅓

- Whole numbers: 6 + 9 = 15
- Fractions: ⁷⁄₈ + ⅓ → common denominator 24
- ⁷⁄₈ = 21/24, ⅓ = 8/24 → 29/24 = 1 5/24

- Add to whole: 15 + 1 = 16, plus 5/24 → 16 5/24

✔ Answer: 16 5/24

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## ✔ Problem 12:
7½ - 4⁷⁄₈

- Whole numbers: 7 - 4 = 3
- Fractions: ½ - ⁷⁄₈ → common denominator 8
- ½ = 4/8, ⁷⁄₈ = 7/8 → 4/8 - 7/8 = -3/8

→ Borrow 1 from 3 → becomes 2, add 8/8 → 8/8 - 3/8 = 5/8

→ Total: 2 5/8

✔ Answer: 2 5/8

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## 🧾 Final Answers Summary:

1. 9 3/8
2. 4 2/3
3. 9 1/6
4. 1 19/30
5. 5 3/4
6. 2 6/35
7. 5 17/24
8. 1 17/35
9. 8 7/30
10. 1 7/20
11. 16 5/24
12. 2 5/8

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