Multiplying Mixed Numbers (J) Worksheet for 4th - 6th Grade ... - Free Printable

Let’s solve each multiplication problem step by step. Remember, to multiply mixed numbers:

1. Convert each mixed number to an improper fraction.
2. Multiply the numerators together and the denominators together.
3. Simplify the result if needed (convert back to a mixed number if it’s an improper fraction).

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Problem 1: 1⁴₇ × 4¹⁄₂

Step 1: Convert to improper fractions
1⁴⁄₇ = (7×1 + 4)/7 = 11/7
4¹⁄₂ = (2×4 + 1)/2 = 9/2

Step 2: Multiply
(11/7) × (9/2) = (11×9)/(7×2) = 99/14

Step 3: Convert to mixed number
99 ÷ 14 = 7 with remainder 1 → 7¹⁄₁₄

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Problem 2: 3¹⁄₂ × 1²⁄₅

Step 1: Convert
3¹⁄₂ = (2×3 + 1)/2 = 7/2
1²⁄₅ = (5×1 + 2)/5 = 7/5

Step 2: Multiply
(7/2) × (7/5) = 49/10

Step 3: Convert
49 ÷ 10 = 4 with remainder 9 → 4⁹⁄₁₀

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Problem 3: 6²⁄ × 4⁸⁄₉

Step 1: Convert
6²⁄₃ = (3×6 + 2)/3 = 20/3
4⁸⁄₉ = (9×4 + 8)/9 = 44/9

Step 2: Multiply
(20/3) × (44/9) = 880/27

Step 3: Convert
880 ÷ 27 = 32 with remainder 16 → 32¹⁶⁄₂₇

*(Check: 27×32 = 864; 880 - 864 = 16 → correct)*

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Problem 4: 8⁵⁄₆ × 5¹⁄₄

Step 1: Convert
8⁵⁄₆ = (6×8 + 5)/6 = 53/6
5¹⁄₄ = (4×5 + 1)/4 = 21/4

Step 2: Multiply
(53/6) × (21/4) = (53×21)/(6×4) = 1113/24

Simplify before converting? Let’s see if we can reduce first.

Note: 21 and 6 share a common factor of 3.

So: (53/6) × (21/4) = (53/2) × (7/4) after dividing 21÷3=7 and 6÷3=2 → now multiply: (53×7)/(2×4) = 371/8

Now convert: 371 ÷ 8 = 46 with remainder 3 → 46³⁄₈

*(Double-check original: 53×21 = 1113; 6×4=24; 1113÷24 = 46.375 → 46³⁄₈ is correct since 3/8=0.375)*

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Problem 5: 2⁵⁄₈ × 3¹⁄₃

Step 1: Convert
2⁵⁄₈ = (8×2 + 5)/8 = 21/8
3¹⁄₃ = (3×3 + 1)/3 = 10/3

Step 2: Multiply
(21/8) × (10/3) = (21×10)/(8×3) = 210/24

Simplify: divide numerator and denominator by 6 → 35/4

Convert: 35 ÷ 4 = 8 with remainder 3 → 8³⁄₄

*(Alternatively: 210 ÷ 24 = 8.75 → 8³⁄₄ is correct)*

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Problem 6: 7¹⁄₂ × 5¹⁄₃

Step 1: Convert
7¹⁄₂ = (2×7 + 1)/2 = 15/2
5¹⁄₃ = (3×5 + 1)/3 = 16/3

Step 2: Multiply
(15/2) × (16/3) = (15×16)/(2×3) = 240/6 = 40

→ 40 (whole number)

*(Nice simplification: 15/3 = 5, 16/2 = 8 → 5×8 = 40)*

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Problem 7: 7⁷⁄₉ × 4²⁄₅

Step 1: Convert
7⁷⁄₉ = (9×7 + 7)/9 = 70/9
4²⁄₅ = (5×4 + 2)/5 = 22/5

Step 2: Multiply
(70/9) × (22/5) = (70×22)/(9×5) = 1540/45

Simplify: Divide numerator and denominator by 5 → 308/9

Convert: 308 ÷ 9 = 34 with remainder 2 → 34²⁄₉

*(Check: 9×34 = 306; 308 - 306 = 2 → correct)*

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Problem 8: 1⁵⁄₇ × 3⁶⁄₇

Step 1: Convert
1⁵⁄₇ = (7×1 + 5)/7 = 12/7
3⁶⁄₇ = (7×3 + 6)/7 = 27/7

Step 2: Multiply
(12/7) × (27/7) = 324/49

Convert: 324 ÷ 49 = 6 with remainder 30 → 6³⁰⁄₄₉

*(Check: 49×6 = 294; 324 - 294 = 30 → correct)*

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Problem 9: 9³⁄₅ × 1⁴⁄₉

Step 1: Convert
9³⁄₅ = (5×9 + 3)/5 = 48/5
1⁴⁄₉ = (9×1 + 4)/9 = 13/9

Step 2: Multiply
(48/5) × (13/9) = (48×13)/(5×9) = 624/45

Simplify: Divide numerator and denominator by 3 → 208/15

Convert: 208 ÷ 15 = 13 with remainder 13 → 13¹³⁄₁₅

*(Check: 15×13 = 195; 208 - 195 = 13 → correct)*

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Problem 10: 9¹⁄₂ × 5³⁄₇

Step 1: Convert
9¹⁄₂ = (2×9 + 1)/2 = 19/2
5³⁄₇ = (7×5 + 3)/7 = 38/7

Step 2: Multiply
(19/2) × (38/7) = (19×38)/(2×7) = 722/14

Simplify: Divide numerator and denominator by 2 → 361/7

Convert: 361 ÷ 7 = 51 with remainder 4 → 51⁴⁄₇

*(Check: 7×51 = 357; 361 - 357 = 4 → correct)*

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Final Answer:
1. 7¹⁄₁₄
2. 4⁹⁄₁₀
3. 32¹⁶⁄₂₇
4. 46³⁄₈
5. 8³⁄₄
6. 40
7. 34²⁄₉
8. 6³⁰⁄₄₉
9. 13¹³⁄₁₅
10. 51⁴⁄