Fraction multiplication worksheet for students to solve and reduce to lowest terms.

Let’s solve each problem step by step. We’re multiplying mixed numbers, so first we’ll turn them into improper fractions, multiply, then simplify and convert back to a mixed number if needed.

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Problem 1: 2⁵₆ × 6²⁄₅

Step 1: Convert to improper fractions
2⁵⁄₆ = (2×6 + 5)/6 = 17/6
6²⁄₅ = (6×5 + 2)/5 = 32/5

Step 2: Multiply numerators and denominators
(17 × 32) / (6 × 5) = 544 / 30

Step 3: Simplify
Divide numerator and denominator by 2 → 272 / 15

Step 4: Convert to mixed number
15 goes into 272 eighteen times (15×18=270), remainder 2 → 18²⁄₁₅

✔ Final Answer for #1: 18²⁄₁₅

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Problem 2: 2¹⁄₉ × 7¹⁄₉

Convert:
2¹⁄₉ = 19/9
7¹⁄₉ = 64/9

Multiply: (19 × 64) / (9 × 9) = 1216 / 81

Simplify? 1216 ÷ 81 = 15 with remainder 1 → 15¹⁄₈₁

✔ Final Answer for #2: 15¹⁄₈₁

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Problem 3: 4³⁄₄ × 9⁴⁄₉

Convert:
4³⁄₄ = 19/4
9⁴⁄ = 85/9

Multiply: (19 × 85) / (4 × 9) = 1615 / 36

Divide: 36 × 44 = 1584, remainder 31 → 44³¹⁄₃₆

✔ Final Answer for #3: 44³¹⁄₃₆

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Problem 4: 3³⁄₆ × 1¹⁄₆

First, simplify 3³⁄₆ → 3½ = 7/2
1¹⁄₆ = 7/6

Multiply: (7 × 7) / (2 × 6) = 49 / 12 → 4¹⁄₁₂

✔ Final Answer for #4: 4¹⁄₁₂

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Problem 5: 4⁵⁄ × 4⁄₉

Same number twice → square it.
4⁵⁄ = 41/9
(41/9)² = 1681 / 81

Divide: 81 × 20 = 1620, remainder 61 → 20⁶¹⁄₈₁

✔ Final Answer for #5: 20⁶¹⁄₈₁

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Problem 6: 1¹⁄₈ × 6²⁄₃

Convert:
1¹⁄₈ = 9/8
6²⁄₃ = 20/3

Multiply: (9 × 20) / (8 × 3) = 180 / 24

Simplify: divide by 12 → 15/2 → 7½

✔ Final Answer for #6: 7½

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Problem 7: 2⁶₉ × 2²⁄₃

Simplify first: 2⁶₉ = 2²⁄₃ = 8/3
So: (8/3) × (8/3) = 64/9 → 7¹⁄₉

✔ Final Answer for #7: 7¹⁄₉

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Problem 8: 4²⁄₈ × 6⁵⁄

Simplify 4²⁄₈ = 4¼ = 17/4
6⁵⁄ = 53/8

Multiply: (17 × 53) / (4 × 8) = 901 / 32

Divide: 32 × 28 = 896, remainder 5 → 28⁵⁄₂

✔ Final Answer for #8: 28⁵⁄₂

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Problem 9: 5³⁄₉ × 7²⁄₃

Simplify 5³⁄₉ = 5⅓ = 16/3
7²⁄₃ = 23/3

Multiply: (16 × 23) / (3 × 3) = 368 / 9 → 40⁸⁄

✔ Final Answer for #9: 40⁸⁄₉

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Problem 10: 3²⁄₃ × 7¹⁄₃

Convert:
3²⁄₃ = 11/3
7¹⁄₃ = 22/3

Multiply: (11 × 22) / (3 × 3) = 242 / 9 → 26⁸⁄₉

✔ Final Answer for #10: 26⁸⁄₉

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Problem 11: 6⁷₈ × 8¹⁄₃

Convert:
6⁷₈ = 55/8
8¹⁄₃ = 25/3

Multiply: (55 × 25) / (8 × 3) = 1375 / 24

Divide: 24 × 57 = 1368, remainder 7 → 57⁷⁄₂₄

✔ Final Answer for #11: 57⁷₂₄

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Problem 12: 7¹⁄₆ × 9²⁄₄

Simplify 9²⁄₄ = 9½ = 19/2
7¹⁄₆ = 43/6

Multiply: (43 × 19) / (6 × 2) = 817 / 12 → 68¹⁄₁₂

✔ Final Answer for #12: 68¹⁄₁₂

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Problem 13: 4³⁄₈ × 6¹⁄₄

Convert:
4³⁄₈ = 35/8
6¹⁄₄ = 25/4

Multiply: (35 × 25) / (8 × 4) = 875 / 32 → 27¹¹⁄₃₂

✔ Final Answer for #13: 27¹¹⁄₃₂

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Problem 14: 1³⁄₄ × 7²⁄₃

Convert:
1³⁄₄ = 7/4
7²⁄₃ = 23/3

Multiply: (7 × 23) / (4 × 3) = 161 / 12 → 13⁵⁄₁₂

✔ Final Answer for #14: 13⁵⁄₁₂

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Problem 15: 5²⁄₆ × 2¹⁄₇

Simplify 5²⁄₆ = 5⅓ = 16/3
2¹⁄₇ = 15/7

Multiply: (16 × 15) / (3 × 7) = 240 / 21 → simplify by 3 → 80/7 → 11³⁄₇

✔ Final Answer for #15: 11³⁄₇

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Final Answer:
1. 18²⁄₁₅
2. 15¹⁄₈₁
3. 44³¹⁄₃₆
4. 4¹⁄₁₂
5. 20⁶¹⁄₈₁
6. 7½
7. 7¹⁄₉
8. 28⁵₃₂
9. 40⁸⁄₉
10. 26⁸⁄
11. 57⁷₂₄
12. 68¹⁄₁₂
13. 27¹¹⁄₃₂
14. 13⁵⁄₁₂
15. 11³⁄₇