Multiplying Two Mixed Fractions with All Simplification (Fillable) (A) - Free Printable

Let’s solve each problem step by step. We’re multiplying mixed numbers, so we’ll follow these steps for each:

1. Convert each mixed number to an improper fraction.
2. Multiply the two improper fractions (numerator × numerator, denominator × denominator).
3. Simplify the result if possible.
4. Convert back to a mixed number if needed.

We’ll go one by one.

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Problem 1: 5⁴⁄ × 2⁄₇

Step 1: Convert
5⁴⁄₉ = (5×9 + 4)/9 = 49/9
2⁵⁄₇ = (2×7 + 5)/7 = 19/7

Step 2: Multiply
(49/9) × (19/7) = (49×19)/(9×7) = 931 / 63

Step 3: Simplify
Check if 931 and 63 have common factors.
63 = 7×9
931 ÷ 7 = 133 → yes!
So divide numerator and denominator by 7:
931 ÷ 7 = 133
63 ÷ 7 = 9
→ 133/9

Step 4: Convert to mixed number
133 ÷ 9 = 14 remainder 7 → 14⁷⁄₉

✔ Final Answer for #1: 14⁷₉

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Problem 2: 3¹⁄₇ × 3¹⁄₄

Step 1: Convert
3¹⁄₇ = (3×7 + 1)/7 = 22/7
3¹⁄₄ = (3×4 + 1)/4 = 13/4

Step 2: Multiply
(22/7) × (13/4) = (22×13)/(7×4) = 286 / 28

Step 3: Simplify
Divide numerator and denominator by 2:
286 ÷ 2 = 143
28 ÷ 2 = 14
→ 143/14

Step 4: Convert
143 ÷ 14 = 10 remainder 3 → 10³⁄₁₄

✔ Final Answer for #2: 10³⁄₁₄

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Problem 3: 5²⁄₃ × 1¹⁄₅

Step 1: Convert
5²⁄₃ = (5×3 + 2)/3 = 17/3
1¹⁄₅ = (1×5 + 1)/5 = 6/5

Step 2: Multiply
(17/3) × (6/5) = (17×6)/(3×5) = 102 / 15

Step 3: Simplify
Divide by 3:
102 ÷ 3 = 34
15 ÷ 3 = 5
→ 34/5

Step 4: Convert
34 ÷ 5 = 6 remainder 4 → 6⁴₅

✔ Final Answer for #3: 6⁴⁄₅

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Problem 4: 1²⁄₃ × 4²⁄₅

Step 1: Convert
1²⁄₃ = (1×3 + 2)/3 = 5/3
4²⁄₅ = (4×5 + 2)/5 = 22/5

Step 2: Multiply
(5/3) × (22/5) = (5×22)/(3×5) = 110 / 15

Step 3: Simplify
Cancel 5 top and bottom:
110 ÷ 5 = 22
15 ÷ 5 = 3
→ 22/3

Step 4: Convert
22 ÷ 3 = 7 remainder 1 → 7¹⁄₃

✔ Final Answer for #4: 7¹⁄₃

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Problem 5: 1¹⁄₆ × 3³⁄₄

Step 1: Convert
1¹⁄₆ = (1×6 + 1)/6 = 7/6
3³⁄₄ = (3×4 + 3)/4 = 15/4

Step 2: Multiply
(7/6) × (15/4) = (7×15)/(6×4) = 105 / 24

Step 3: Simplify
Divide by 3:
105 ÷ 3 = 35
24 ÷ 3 = 8
→ 35/8

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

✔ Final Answer for #5: 4³⁄₈

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Problem 6: 3¹⁄₈ × 3¹⁄₃

Step 1: Convert
3¹⁄₈ = (3×8 + 1)/8 = 25/8
3¹⁄₃ = (3×3 + 1)/3 = 10/3

Step 2: Multiply
(25/8) × (10/3) = (25×10)/(8×3) = 250 / 24

Step 3: Simplify
Divide by 2:
250 ÷ 2 = 125
24 ÷ 2 = 12
→ 125/12

Step 4: Convert
125 ÷ 12 = 10 remainder 5 → 10⁵₁₂

✔ Final Answer for #6: 10⁵⁄₁₂

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Problem 7: 3²⁄₃ × 3³⁄₇

Step 1: Convert
3²⁄₃ = (3×3 + 2)/3 = 11/3
3³⁄₇ = (3×7 + 3)/7 = 24/7

Step 2: Multiply
(11/3) × (24/7) = (11×24)/(3×7) = 264 / 21

Step 3: Simplify
Divide by 3:
264 ÷ 3 = 88
21 ÷ 3 = 7
→ 88/7

Step 4: Convert
88 ÷ 7 = 12 remainder 4 → 12⁴⁄₇

✔ Final Answer for #7: 12⁴⁄₇

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Problem 8: 3⁴⁄₅ × 3¹⁄₃

Step 1: Convert
3⁴⁄₅ = (3×5 + 4)/5 = 19/5
3¹⁄₃ = (3×3 + 1)/3 = 10/3

Step 2: Multiply
(19/5) × (10/3) = (19×10)/(5×3) = 190 / 15

Step 3: Simplify
Divide by 5:
190 ÷ 5 = 38
15 ÷ 5 = 3
→ 38/3

Step 4: Convert
38 ÷ 3 = 12 remainder 2 → 12²⁄₃

✔ Final Answer for #8: 12²⁄₃

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Problem 9: 4²⁄₃ × 4¹⁄₅

Step 1: Convert
4²⁄₃ = (4×3 + 2)/3 = 14/3
4¹⁄₅ = (4×5 + 1)/5 = 21/5

Step 2: Multiply
(14/3) × (21/5) = (14×21)/(3×5) = 294 / 15

Step 3: Simplify
Divide by 3:
294 ÷ 3 = 98
15 ÷ 3 = 5
→ 98/5

Step 4: Convert
98 ÷ 5 = 19 remainder 3 → 19³⁄₅

✔ Final Answer for #9: 19³⁄₅

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Problem 10: 5²⁄₇ × 3¹⁄₂

Step 1: Convert
5²⁄₇ = (5×7 + 2)/7 = 37/7
3¹⁄₂ = (3×2 + 1)/2 = 7/2

Step 2: Multiply
(37/7) × (7/2) = (37×7)/(7×2) = 259 / 14

Step 3: Simplify
Cancel 7 top and bottom:
259 ÷ 7 = 37
14 ÷ 7 = 2
→ 37/2

Step 4: Convert
37 ÷ 2 = 18 remainder 1 → 18¹⁄₂

✔ Final Answer for #10: 18¹⁄₂

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Final Answer:
1. 14⁷⁄₉
2. 10³⁄₁₄
3. 6⁴⁄₅
4. 7¹⁄₃
5. 4³⁄₈
6. 10⁵₁₂
7. 12⁴⁄₇
8. 12²⁄₃
9. 19³⁄₅
10. 18¹⁄₂