Grade 6 Fraction Worksheet: Multiplying Mixed Numbers

I'll solve these multiplication problems with mixed numbers step by step.

Let me work through each problem carefully:

Problem 1: 3⅜ × 6⅔
- Convert to improper fractions: 3⅜ = 27/8, 6⅔ = 20/3
- Multiply: (27/8) × (20/3) = 540/24
- Simplify: 540 ÷ 24 = 22.5 = 22½

Problem 2: 1½ × 11⅘
- Convert: 1½ = 3/2, 11⅘ = 59/5
- Multiply: (3/2) × (59/5) = 177/10
- Convert back: 177 ÷ 10 = 17 remainder 7 = 17⁷/₁₀

Problem 3: 8¹⁰/₁₁ × 1¼
- Convert: 8¹⁰/₁₁ = 98/11, 1¼ = 5/4
- Multiply: (98/11) × (5/4) = 490/44
- Simplify: 490 ÷ 44 = 11 remainder 6 = 11⁶/₄₄ = 11³/₂₂

Problem 4: 8⅓ × 3⅓
- Convert: 8 = 25/3, 3 = 10/3
- Multiply: (25/3) × (10/3) = 250/9
- Convert back: 250 ÷ 9 = 27 remainder 7 = 27/₉

Problem 5: 3²/₅ × 12/₁₂
- Convert: 3²/₅ = 17/5, 12⁵/₁₂ = 149/12
- Multiply: (17/5) × (149/12) = 2533/60
- Convert back: 2533 ÷ 60 = 42 remainder 13 = 42¹³/₆₀

Problem 6: 7²/₃ × 10²/₃
- Convert: 7²/₃ = 23/3, 10²/₃ = 32/3
- Multiply: (23/3) × (32/3) = 736/9
- Convert back: 736 ÷ 9 = 81 remainder 7 = 81⁷/₉

Problem 7: 10/₁₂ × 12/₈
- Convert: 10⁵/₁₂ = 125/12, 12⁵/₈ = 101/8
- Multiply: (125/12) × (101/8) = 12625/96
- Convert back: 12625 ÷ 96 = 131 remainder 49 = 131⁴⁹/₉

Problem 8: 9⁵/₈ × 8⁵/
- Convert: 9⁵/₈ = 77/8, 8⁵/₈ = 69/8
- Multiply: (77/8) × (69/8) = 5313/64
- Convert back: 5313 ÷ 64 = 83 remainder 1 = 83¹/₆₄

Problem 9: 4/₅ × 1³/₁₁
- Convert: 4⁴/₅ = 24/5, 1³/₁₁ = 14/11
- Multiply: (24/5) × (14/11) = 336/55
- Convert back: 336 ÷ 55 = 6 remainder 6 = 6⁶/₅

Problem 10: 6¹/₁₀ × 12½
- Convert: 6¹/₁₀ = 61/10, 12½ = 25/2
- Multiply: (61/10) × (25/2) = 1525/20
- Simplify: 1525 ÷ 20 = 76.25 = 76¼

Final Answer:
1. 22½
2. 17⁷/₁₀
3. 11³/₂₂
4. 27⁷/₉
5. 42¹³/₆₀
6. 81⁷/₉
7. 131⁴⁹/₉₆
8. 83¹/₆₄
9. 6⁶/₅
10. 76¼