Practice multiplying mixed numbers with this 20-problem worksheet that includes clear, step-by-step instructions at the top.

Let’s solve each problem step by step, following the 5 rules given:

1. Convert mixed numbers to improper fractions.
2. Multiply numerators.
3. Multiply denominators.
4. Simplify the fraction (if needed).
5. Convert back to a mixed number (if needed).

We’ll go one by one.

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Problem 1: 7½ × 8⁵⁄

Step 1: Convert to improper fractions
7½ = (7×2 + 1)/2 = 15/2
8⁵⁄₉ = (8×9 + 5)/9 = 77/9

Step 2: Multiply numerators → 15 × 77 = 1155
Step 3: Multiply denominators → 2 × 9 = 18
→ Fraction: 1155/18

Step 4: Simplify
Divide numerator and denominator by 3:
1155 ÷ 3 = 385
18 ÷ 3 = 6
→ 385/6

Step 5: Convert to mixed number
385 ÷ 6 = 64 with remainder 1 → 64¹⁄₆

✔ Final Answer for #1: 64¹⁄₆

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Problem 2: 4³⁄₉ × 1⁶⁄₈

First, simplify fractions if possible before multiplying!

4³⁄₉ → 3/9 = 1/3 → so 4¹⁄₃ = (4×3+1)/3 = 13/3
1⁶⁄ → 6/8 = 3/4 → so 1³⁄₄ = (1×4+3)/4 = 7/4

Now multiply:
Numerators: 13 × 7 = 91
Denominators: 3 × 4 = 12
→ 91/12

Convert to mixed number:
91 ÷ 12 = 7 with remainder 7 → 7⁷⁄₁₂

✔ Final Answer for #2: 7⁷⁄₁₂

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Problem 3: 7²⁄₅ × 2¹⁄₅

Convert:
7²⁄₅ = (7×5+2)/5 = 37/5
2¹⁄₅ = (2×5+1)/5 = 11/5

Multiply:
37 × 11 = 407
5 × 5 = 25
→ 407/25

Convert:
407 ÷ 25 = 16 with remainder 7 → 16⁷⁄₂₅

✔ Final Answer for #3: 16⁷⁄₂₅

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Problem 4: 3⁶⁄₉ × 4¹⁄₆

Simplify first:
3⁶⁄₉ → 6/9 = 2/3 → 3²⁄₃ = (3×3+2)/3 = 11/3
4¹⁄₆ stays as is → (4×6+1)/6 = 25/6

Multiply:
11 × 25 = 275
3 × 6 = 18
→ 275/18

Convert:
275 ÷ 18 = 15 with remainder 5 → 15⁵⁄₁₈

✔ Final Answer for #4: 15⁵⁄₁₈

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Problem 5: 6¹⁄₆ × 5²⁄₄

Simplify:
5²⁄₄ = 5¹⁄₂ = (5×2+1)/2 = 11/2
6¹⁄₆ = (6×6+1)/6 = 37/6

Multiply:
37 × 11 = 407
6 × 2 = 12
→ 407/12

Convert:
407 ÷ 12 = 33 with remainder 11 → 33¹¹⁄₁₂

✔ Final Answer for #5: 33¹¹⁄₁₂

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Problem 6: 7³⁄₈ × 5¹⁄₂

Convert:
7³⁄₈ = (7×8+3)/8 = 59/8
5¹⁄₂ = (5×2+1)/2 = 11/2

Multiply:
59 × 11 = 649
8 × 2 = 16
→ 649/16

Convert:
649 ÷ 16 = 40 with remainder 9 → 40⁹⁄₁₆

✔ Final Answer for #6: 40⁹₁₆

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Problem 7: 1³⁄₄ × 2¹⁄₂

Convert:
1³⁄₄ = 7/4
2¹⁄₂ = 5/2

Multiply:
7 × 5 = 35
4 × 2 = 8
→ 35/8

Convert:
35 ÷ 8 = 4 with remainder 3 → 4³⁄₈

✔ Final Answer for #7: 4³⁄₈

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Problem 8: 1⁴⁄₉ × 6⁴⁄₇

Convert:
1⁴⁄₉ = 13/9
6⁴⁄₇ = (6×7+4)/7 = 46/7

Multiply:
13 × 46 = let's compute:
10×46=460, 3×46=138 → total 598
9 × 7 = 63
→ 598/63

Check if simplifies? GCD of 598 and 63?
63 factors: 7×9
598 ÷ 7 = 85.4… no
598 ÷ 3 = 199.3… no → doesn’t simplify.

Convert:
598 ÷ 63 = 9 × 63 = 567 → remainder 31 → 9³¹⁄₆

Can we reduce 31/63? No, 31 is prime → leave it.

✔ Final Answer for #8: 9³¹⁄₆

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Problem 9: 3⁵⁄₆ × 2⁴⁄₇

Convert:
3⁵⁄₆ = (3×6+5)/6 = 23/6
2⁴⁄₇ = (2×7+4)/7 = 18/7

Multiply:
23 × 18 = 414
6 × 7 = 42
→ 414/42

Simplify: divide numerator and denominator by 6
414 ÷ 6 = 69
42 ÷ 6 = 7
→ 69/7

Convert:
69 ÷ 7 = 9 with remainder 6 → 9⁶⁄₇

✔ Final Answer for #9: 9⁶⁄₇

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Problem 10: 2⁶₈ × 2¹⁄₅

Simplify:
2⁶₈ = 2³⁄₄ = (2×4+3)/4 = 11/4
2¹⁄₅ = 11/5

Multiply:
11 × 11 = 121
4 × 5 = 20
→ 121/20

Convert:
121 ÷ 20 = 6 with remainder 1 → 6¹⁄₂₀

✔ Final Answer for #10: 6¹⁄₂₀

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Problem 11: 6²⁄₈ × 1³⁄₄

Simplify:
6²⁄₈ = 6¹⁄₄ = (6×4+1)/4 = 25/4
1³⁄₄ = 7/4

Multiply:
25 × 7 = 175
4 × 4 = 16
→ 175/16

Convert:
175 ÷ 16 = 10 with remainder 15 → 10¹⁵⁄₁₆

✔ Final Answer for #11: 10¹⁵⁄₁₆

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Problem 12: 7²⁄₃ × 2¹⁄₂

Convert:
7²⁄₃ = (7×3+2)/3 = 23/3
2¹⁄₂ = 5/2

Multiply:
23 × 5 = 115
3 × 2 = 6
→ 115/6

Convert:
115 ÷ 6 = 19 with remainder 1 → 19¹⁄₆

✔ Final Answer for #12: 19¹⁄₆

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Problem 13: 4¹⁄₄ × 2²⁄₃

Convert:
4¹⁄₄ = 17/4
2²⁄₃ = 8/3

Multiply:
17 × 8 = 136
4 × 3 = 12
→ 136/12

Simplify: divide by 4 → 34/3

Convert:
34 ÷ 3 = 11 with remainder 1 → 11¹⁄₃

✔ Final Answer for #13: 11¹⁄₃

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Problem 14: 7¹⁄₇ × 5⁴⁄₅

Convert:
7¹⁄₇ = (7×7+1)/7 = 50/7
5⁴⁄₅ = (5×5+4)/5 = 29/5

Multiply:
50 × 29 = 1450
7 × 5 = 35
→ 1450/35

Simplify: divide numerator and denominator by 5 → 290/7

Convert:
290 ÷ 7 = 41 with remainder 3 → 41³⁄₇

✔ Final Answer for #14: 41³⁄₇

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Problem 15: 1²⁄₃ × 9²⁄₃

Convert:
1²⁄₃ = 5/3
9²⁄₃ = (9×3+2)/3 = 29/3

Multiply:
5 × 29 = 145
3 × 3 = 9
→ 145/9

Convert:
145 ÷ 9 = 16 with remainder 1 → 16¹⁄₉

✔ Final Answer for #15: 16¹⁄₉

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Problem 16: 7⁶⁄₈ × 9⁷⁄₉

Simplify:
7⁶⁄₈ = 7³⁄₄ = (7×4+3)/4 = 31/4
9⁷⁄ = (9×9+7)/9 = 88/9

Multiply:
31 × 88 = let’s compute:
30×88=2640, 1×88=88 → total 2728
4 × 9 = 36
→ 2728/36

Simplify: divide by 4 → 682/9

Convert:
682 ÷ 9 = 75 with remainder 7 → 75⁷⁄

✔ Final Answer for #16: 75⁷⁄₉

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Problem 17: 3⁴⁄₆ × 4⁶⁄₉

Simplify:
3⁴₆ = 3²⁄₃ = 11/3
4⁶⁄ = 4²⁄₃ = (4×3+2)/3 = 14/3

Multiply:
11 × 14 = 154
3 × 3 = 9
→ 154/9

Convert:
154 ÷ 9 = 17 with remainder 1 → 17¹⁄₉

✔ Final Answer for #17: 17¹⁄₉

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Problem 18: 5¹⁄₅ × 9¹⁄₂

Convert:
5¹⁄₅ = 26/5
9¹⁄₂ = 19/2

Multiply:
26 × 19 = 494
5 × 2 = 10
→ 494/10

Simplify: divide by 2 → 247/5

Convert:
247 ÷ 5 = 49 with remainder 2 → 49²⁄₅

✔ Final Answer for #18: 49²⁄₅

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Problem 19: 3⁷⁄₈ × 9³⁄₆

Simplify:
9³⁄₆ = 9¹⁄₂ = 19/2
3⁷⁄ = (3×8+7)/8 = 31/8

Multiply:
31 × 19 = 589
8 × 2 = 16
→ 589/16

Convert:
589 ÷ 16 = 36 with remainder 13 → 36¹³⁄₁₆

✔ Final Answer for #19: 36¹³⁄₁₆

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Problem 20: 1²⁄₅ × 2¹⁄₃

Convert:
1²⁄₅ = 7/5
2¹⁄₃ = 7/3

Multiply:
7 × 7 = 49
5 × 3 = 15
→ 49/15

Convert:
49 ÷ 15 = 3 with remainder 4 → 3⁴⁄₁₅

✔ Final Answer for #20: 3⁴⁄₁₅

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Final Answers:

1. 64¹⁄₆
2. 7⁷₁₂
3. 16⁷₂₅
4. 15⁵₁₈
5. 33¹¹⁄₁₂
6. 40⁹⁄₁₆
7. 4³⁄₈
8. 9³¹⁄₆₃
9. 9⁶₇
10. 6¹⁄₂₀
11. 10¹⁵⁄₁₆
12. 19¹⁄₆
13. 11¹⁄₃
14. 41³⁄₇
15. 16¹⁄₉
16. 75⁷₉
17. 17¹⁄₉
18. 49²⁄₅
19. 36¹³⁄₁₆
20. 3⁴⁄₁₅