Let’s solve each problem step by step. We’ll convert mixed fractions to improper fractions when needed, find common denominators for addition or subtraction, then simplify back to mixed numbers if necessary.
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Problem 1: 7½ + 1⅞
Convert to improper fractions:
- 7½ = 15/2
- 1⅞ = 15/8
Find LCD of 2 and 8 → 8
- 15/2 = 60/8
- 15/8 stays same
Add: 60/8 + 15/8 = 75/8
Convert back: 75 ÷ 8 = 9 remainder 3 →
9⅜
✔ Check: 7.5 + 1.875 = 9.375 → 9⅜ ✔️
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Problem 2: 9⅙ - 4½
Convert:
- 9⅙ = 55/6
- 4½ = 9/2 = 27/6
Subtract: 55/6 - 27/6 = 28/6 = 14/3 =
4⅔
✔ Check: 9.166... - 4.5 = 4.666... → 4⅔ ✔️
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Problem 3: 6⅓ + 2⅚
Convert:
- 6⅓ = 19/3 = 38/6
- 2⅚ = 17/6
Add: 38/6 + 17/6 = 55/6 =
9⅙
✔ Check: 6.333... + 2.833... = 9.166... → 9⅙ ✔️
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Problem 4: 4⁴₅ - 3⅙
Convert:
- 4⁴⁄₅ = 24/5
- 3⅙ = 19/6
LCD of 5 and 6 → 30
- 24/5 = 144/30
- 19/6 = 95/30
Subtract: 144/30 - 95/30 = 49/30 =
1¹⁹⁄₃₀
✔ Check: 4.8 - 3.166... ≈ 1.633... → 1¹⁹⁄₃₀ (since 19÷30≈0.633) ✔️
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Problem 5: 2½ + 3¼
Convert:
- 2½ = 5/2 = 10/4
- 3¼ = 13/4
Add: 10/4 + 13/4 = 23/4 =
5¾
✔ Check: 2.5 + 3.25 = 5.75 → 5¾ ✔️
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Problem 6: 4⁴⁄₇ - 2⅖
Convert:
- 4⁴⁄ = 32/7
- 2⅖ = 12/5
LCD of 7 and 5 → 35
- 32/7 = 160/35
- 12/5 = 84/35
Subtract: 160/35 - 84/35 = 76/35 =
2⁶⁄₅
✔ Check: ~4.571 - 2.4 = ~2.171 → 76÷35≈2.171 ✔️
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Problem 7: 3⁷⁄₁₂ + 2⅛
Convert:
- 3⁷⁄₁₂ = 43/12
- 2⅛ = 17/8
LCD of 12 and 8 → 24
- 43/12 = 86/24
- 17/8 = 51/24
Add: 86/24 + 51/24 = 137/24 =
5¹⁷⁄₂₄
✔ Check: ~3.583 + 2.125 = ~5.708 → 137÷24≈5.708 ✔️
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Problem 8: 5⅕ - 3⁵⁄
Convert:
- 5⅕ = 26/5
- 3⁵⁄₇ = 26/7
LCD of 5 and 7 → 35
- 26/5 = 182/35
- 26/7 = 130/35
Subtract: 182/35 - 130/35 = 52/35 =
1¹⁷⁄₃
✔ Check: 5.2 - 3.714 ≈ 1.486 → 52÷35≈1.486 ✔️
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Problem 9: 4⅖ + 3⅚
Convert:
- 4⅖ = 22/5
- 3⅚ = 23/6
LCD of 5 and 6 → 30
- 22/5 = 132/30
- 23/6 = 115/30
Add: 132/30 + 115/30 = 247/30 =
8⁷⁄₀
✔ Check: 4.4 + 3.833 ≈ 8.233 → 247÷30≈8.233 ✔️
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Problem 10: 3¹⁄₁₀ - 1⁶⁄₈
First, simplify 6/8 → 3/4, so 1⁶⁄ = 1¾
Convert:
- 3¹⁄₁₀ = 31/10
- 1¾ = 7/4
LCD of 10 and 4 → 20
- 31/10 = 62/20
- 7/4 = 35/20
Subtract: 62/20 - 35/20 = 27/20 =
1⁷⁄₂₀
✔ Check: 3.1 - 1.75 = 1.35 → 27÷20=1.35 ✔️
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Problem 11: 6⁷⁄₈ + 9³⁄₉
Simplify 3/9 → 1/3, so 9³⁄₉ = 9⅓
Convert:
- 6⁷⁄₈ = 55/8
- 9⅓ = 28/3
LCD of 8 and 3 → 24
- 55/8 = 165/24
- 28/3 = 224/24
Add: 165/24 + 224/24 = 389/24 =
16⁵⁄₂₄
✔ Check: 6.875 + 9.333 ≈ 16.208 → 389÷24≈16.208 ✔️
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Problem 12: 7½ - 4⁷⁄₈
Convert:
- 7½ = 15/2 = 60/8
- 4⁷⁄ = 39/8
Subtract: 60/8 - 39/8 = 21/8 =
2⁵⁄
✔ Check: 7.5 - 4.875 = 2.625 → 21÷8=2.625 ✔️
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Final Answer:
1. 9⅜
2. 4⅔
3. 9⅙
4. 1¹⁹⁄₃₀
5. 5¾
6. 2⁶⁄₃₅
7. 5¹⁷⁄₂₄
8. 1¹⁷⁄₅
9. 8⁷⁄₃₀
10. 1⁷⁄₂₀
11. 16⁵⁄₂₄
12. 2⁵⁄
Parent Tip: Review the logic above to help your child master the concept of add and subtract fractions and mixed numbers worksheet.
