Multiplying Mixed Numbers and Fractions worksheet - Free Printable

Let’s solve each problem step by step. We’ll multiply fractions and mixed numbers, then simplify the answer to its simplest form.

Remember:
- To multiply mixed numbers, first convert them to improper fractions.
- Multiply numerators together and denominators together.
- Simplify the result if needed (divide numerator and denominator by their greatest common factor).

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1. $ 1 \frac{1}{10} \times \frac{5}{8} = \frac{11}{16} $ ← already done for you!

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2. $ 2 \frac{2}{3} \times \frac{6}{12} $

Convert $ 2 \frac{2}{3} $ → $ \frac{8}{3} $

$ \frac{8}{3} \times \frac{6}{12} = \frac{48}{36} $

Simplify: divide numerator and denominator by 12 → $ \frac{4}{3} $ or $ 1 \frac{1}{3} $

✔ Final Answer: $ \frac{4}{3} $ or $ 1 \frac{1}{3} $

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3. $ 2 \frac{1}{2} \times \frac{9}{10} $

Convert $ 2 \frac{1}{2} $ → $ \frac{5}{2} $

$ \frac{5}{2} \times \frac{9}{10} = \frac{45}{20} $

Simplify: divide by 5 → $ \frac{9}{4} $ or $ 2 \frac{1}{4} $

✔ Final Answer: $ \frac{9}{4} $ or $ 2 \frac{1}{4} $

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4. $ 1 \frac{4}{6} \times \frac{4}{10} $

First, simplify $ \frac{4}{6} $ → $ \frac{2}{3} $, so $ 1 \frac{2}{3} = \frac{5}{3} $

$ \frac{5}{3} \times \frac{4}{10} = \frac{20}{30} $

Simplify: divide by 10 → $ \frac{2}{3} $

✔ Final Answer: $ \frac{2}{3} $

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5. $ 2 \frac{1}{3} \times \frac{1}{4} $

Convert $ 2 \frac{1}{3} $ → $ \frac{7}{3} $

$ \frac{7}{3} \times \frac{1}{4} = \frac{7}{12} $

Already simplified.

✔ Final Answer: $ \frac{7}{12} $

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6. $ 3 \frac{8}{12} \times \frac{1}{3} $

Simplify $ \frac{8}{12} $ → $ \frac{2}{3} $, so $ 3 \frac{2}{3} = \frac{11}{3} $

$ \frac{11}{3} \times \frac{1}{3} = \frac{11}{9} $ or $ 1 \frac{2}{9} $

✔ Final Answer: $ \frac{11}{9} $ or $ 1 \frac{2}{9} $

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7. $ 1 \frac{1}{2} \times 3 \frac{1}{2} $

Convert both:

$ 1 \frac{1}{2} = \frac{3}{2} $, $ 3 \frac{1}{2} = \frac{7}{2} $

$ \frac{3}{2} \times \frac{7}{2} = \frac{21}{4} $ or $ 5 \frac{1}{4} $

✔ Final Answer: $ \frac{21}{4} $ or $ 5 \frac{1}{4} $

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8. $ 1 \frac{8}{12} \times 3 \frac{2}{10} $

Simplify fractions first:

$ \frac{8}{12} = \frac{2}{3} $ → $ 1 \frac{2}{3} = \frac{5}{3} $

$ \frac{2}{10} = \frac{1}{5} $ → $ 3 \frac{1}{5} = \frac{16}{5} $

Now multiply: $ \frac{5}{3} \times \frac{16}{5} = \frac{80}{15} $

Simplify: divide by 5 → $ \frac{16}{3} $ or $ 5 \frac{1}{3} $

✔ Final Answer: $ \frac{16}{3} $ or $ 5 \frac{1}{3} $

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9. $ 3 \frac{2}{6} \times 3 \frac{2}{3} $

Simplify $ \frac{2}{6} = \frac{1}{3} $ → $ 3 \frac{1}{3} = \frac{10}{3} $

$ 3 \frac{2}{3} = \frac{11}{3} $

Multiply: $ \frac{10}{3} \times \frac{11}{3} = \frac{110}{9} $ or $ 12 \frac{2}{9} $

✔ Final Answer: $ \frac{110}{9} $ or $ 12 \frac{2}{9} $

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10. $ 3 \frac{4}{5} \times 2 \frac{3}{4} $

Convert:

$ 3 \frac{4}{5} = \frac{19}{5} $, $ 2 \frac{3}{4} = \frac{11}{4} $

Multiply: $ \frac{19}{5} \times \frac{11}{4} = \frac{209}{20} $ or $ 10 \frac{9}{20} $

✔ Final Answer: $ \frac{209}{20} $ or $ 10 \frac{9}{20} $

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11. $ 1 \frac{3}{4} \times 1 \frac{2}{4} $

Simplify $ \frac{2}{4} = \frac{1}{2} $ → $ 1 \frac{1}{2} = \frac{3}{2} $

$ 1 \frac{3}{4} = \frac{7}{4} $

Multiply: $ \frac{7}{4} \times \frac{3}{2} = \frac{21}{8} $ or $ 2 \frac{5}{8} $

✔ Final Answer: $ \frac{21}{8} $ or $ 2 \frac{5}{8} $

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12. $ 2 \frac{4}{5} \times 1 \frac{1}{12} $

Convert:

$ 2 \frac{4}{5} = \frac{14}{5} $, $ 1 \frac{1}{12} = \frac{13}{12} $

Multiply: $ \frac{14}{5} \times \frac{13}{12} = \frac{182}{60} $

Simplify: divide by 2 → $ \frac{91}{30} $ or $ 3 \frac{1}{30} $

✔ Final Answer: $ \frac{91}{30} $ or $ 3 \frac{1}{30} $

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13. $ 1 \frac{5}{8} \times 2 \frac{6}{8} $

Simplify $ \frac{6}{8} = \frac{3}{4} $ → $ 2 \frac{3}{4} = \frac{11}{4} $

$ 1 \frac{5}{8} = \frac{13}{8} $

Multiply: $ \frac{13}{8} \times \frac{11}{4} = \frac{143}{32} $ or $ 4 \frac{15}{32} $

✔ Final Answer: $ \frac{143}{32} $ or $ 4 \frac{15}{32} $

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14. $ 3 \frac{2}{3} \times 1 \frac{1}{2} $

Convert:

$ 3 \frac{2}{3} = \frac{11}{3} $, $ 1 \frac{1}{2} = \frac{3}{2} $

Multiply: $ \frac{11}{3} \times \frac{3}{2} = \frac{33}{6} $

Simplify: divide by 3 → $ \frac{11}{2} $ or $ 5 \frac{1}{2} $

✔ Final Answer: $ \frac{11}{2} $ or $ 5 \frac{1}{2} $

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Final Answer:
1. 11/16
2. 4/3 or 1 1/3
3. 9/4 or 2 1/4
4. 2/3
5. 7/12
6. 11/9 or 1 2/9
7. 21/4 or 5 1/4
8. 16/3 or 5 1/3
9. 110/9 or 12 2/9
10. 209/20 or 10 9/20
11. 21/8 or 2 5/8
12. 91/30 or 3 1/30
13. 143/32 or 4 15/32
14. 11/2 or 5 1/2