Multiply and Divide Fractions Worksheets | Worsheets library - Free Printable

Let's solve each problem on the "Multiplying fractions and mixed numbers" worksheet step by step.

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General Rules to Remember:

1. Convert mixed numbers to improper fractions.
2. Multiply numerators together and denominators together.
3. Simplify the result (reduce fraction) and convert back to a mixed number if needed.

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We’ll go through each problem:

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1. $ 3\frac{2}{5} \times \frac{9}{10} $

- Convert $ 3\frac{2}{5} $ → $ \frac{3 \times 5 + 2}{5} = \frac{17}{5} $
- Multiply: $ \frac{17}{5} \times \frac{9}{10} = \frac{153}{50} $
- Simplify: $ \frac{153}{50} = 3\frac{3}{50} $

✔ Answer: $ 3\frac{3}{50} $

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

- $ 1\frac{1}{4} = \frac{5}{4} $
- $ \frac{5}{4} \times \frac{4}{5} = \frac{20}{20} = 1 $

✔ Answer: $ 1 $

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

- Simplify $ 2\frac{4}{10} = 2\frac{2}{5} $ → $ \frac{12}{5} $
- $ \frac{12}{5} \times \frac{4}{5} = \frac{48}{25} $
- $ \frac{48}{25} = 1\frac{23}{25} $

✔ Answer: $ 1\frac{23}{25} $

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4. $ 1\frac{4}{5} \times \frac{6}{7} $

- $ 1\frac{4}{5} = \frac{9}{5} $
- $ \frac{9}{5} \times \frac{6}{7} = \frac{54}{35} $
- $ \frac{54}{35} = 1\frac{19}{35} $

✔ Answer: $ 1\frac{19}{35} $

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

- $ 1\frac{1}{3} = \frac{4}{3} $
- $ \frac{4}{3} \times \frac{2}{5} = \frac{8}{15} $

✔ Answer: $ \frac{8}{15} $

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6. $ 3\frac{1}{4} \times \frac{1}{4} $

- $ 3\frac{1}{4} = \frac{13}{4} $
- $ \frac{13}{4} \times \frac{1}{4} = \frac{13}{16} $

✔ Answer: $ \frac{13}{16} $

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7. $ 3\frac{1}{5} \times \frac{5}{6} $

- $ 3\frac{1}{5} = \frac{16}{5} $
- $ \frac{16}{5} \times \frac{5}{6} = \frac{80}{30} = \frac{8}{3} $
- $ \frac{8}{3} = 2\frac{2}{3} $

✔ Answer: $ 2\frac{2}{3} $

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8. $ 3\frac{1}{4} \times \frac{4}{5} $

- $ 3\frac{1}{4} = \frac{13}{4} $
- $ \frac{13}{4} \times \frac{4}{5} = \frac{52}{20} = \frac{13}{5} $
- $ \frac{13}{5} = 2\frac{3}{5} $

✔ Answer: $ 2\frac{3}{5} $

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9. $ 2\frac{1}{2} \times \frac{3}{5} $

- $ 2\frac{1}{2} = \frac{5}{2} $
- $ \frac{5}{2} \times \frac{3}{5} = \frac{15}{10} = \frac{3}{2} $
- $ \frac{3}{2} = 1\frac{1}{2} $

✔ Answer: $ 1\frac{1}{2} $

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10. $ 3\frac{1}{5} \times \frac{1}{2} $

- $ 3\frac{1}{5} = \frac{16}{5} $
- $ \frac{16}{5} \times \frac{1}{2} = \frac{16}{10} = \frac{8}{5} $
- $ \frac{8}{5} = 1\frac{3}{5} $

✔ Answer: $ 1\frac{3}{5} $

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

- $ 1\frac{1}{4} = \frac{5}{4} $
- $ \frac{5}{4} \times \frac{1}{4} = \frac{5}{16} $

✔ Answer: $ \frac{5}{16} $

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12. $ 3\frac{5}{12} \times \frac{1}{12} $

- $ 3\frac{5}{12} = \frac{41}{12} $
- $ \frac{41}{12} \times \frac{1}{12} = \frac{41}{144} $

✔ Answer: $ \frac{41}{144} $

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13. $ 3\frac{1}{3} \times \frac{4}{5} $

- $ 3\frac{1}{3} = \frac{10}{3} $
- $ \frac{10}{3} \times \frac{4}{5} = \frac{40}{15} = \frac{8}{3} $
- $ \frac{8}{3} = 2\frac{2}{3} $

✔ Answer: $ 2\frac{2}{3} $

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14. $ 2\frac{1}{2} \times \frac{1}{4} $

- $ 2\frac{1}{2} = \frac{5}{2} $
- $ \frac{5}{2} \times \frac{1}{4} = \frac{5}{8} $

✔ Answer: $ \frac{5}{8} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ 3\frac{3}{50} $ |
| 2 | $ 1 $ |
| 3 | $ 1\frac{23}{25} $ |
| 4 | $ 1\frac{19}{35} $ |
| 5 | $ \frac{8}{15} $ |
| 6 | $ \frac{13}{16} $ |
| 7 | $ 2\frac{2}{3} $ |
| 8 | $ 2\frac{3}{5} $ |
| 9 | $ 1\frac{1}{2} $ |
| 10 | $ 1\frac{3}{5} $ |
| 11 | $ \frac{5}{16} $ |
| 12 | $ \frac{41}{144} $ |
| 13 | $ 2\frac{2}{3} $ |
| 14 | $ \frac{5}{8} $ |

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Let me know if you'd like this as a downloadable PDF or need explanations for any specific problem!