Multiplying mixed fractions by proper fractions worksheets - Math ... - Free Printable

Let's solve each of these fraction multiplication problems step by step. The key steps are:

1. Convert mixed numbers to improper fractions.
2. Multiply the numerators together and the denominators together.
3. Simplify the resulting fraction, if needed.
4. Convert back to a mixed number if required.

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1. $ 2\frac{3}{6} \times \frac{3}{7} $

- Simplify $ 2\frac{3}{6} $:
$ \frac{3}{6} = \frac{1}{2} $, so $ 2\frac{1}{2} $
- Convert to improper fraction:
$ 2\frac{1}{2} = \frac{5}{2} $
- Multiply:
$ \frac{5}{2} \times \frac{3}{7} = \frac{15}{14} $
- Convert to mixed number:
$ \frac{15}{14} = 1\frac{1}{14} $

✔ Answer: $ 1\frac{1}{14} $

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

- Convert $ 2\frac{1}{7} $:
$ = \frac{15}{7} $
- Multiply:
$ \frac{15}{7} \times \frac{1}{2} = \frac{15}{14} $
- Convert:
$ \frac{15}{14} = 1\frac{1}{14} $

✔ Answer: $ 1\frac{1}{14} $

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3. $ 4\frac{6}{9} \times \frac{2}{10} $

- Simplify $ \frac{6}{9} = \frac{2}{3} $, so $ 4\frac{2}{3} $
- Convert: $ 4\frac{2}{3} = \frac{14}{3} $
- Simplify $ \frac{2}{10} = \frac{1}{5} $
- Multiply:
$ \frac{14}{3} \times \frac{1}{5} = \frac{14}{15} $

✔ Answer: $ \frac{14}{15} $

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4. $ 4\frac{5}{11} \times \frac{1}{9} $

- Convert $ 4\frac{5}{11} = \frac{49}{11} $
- Multiply:
$ \frac{49}{11} \times \frac{1}{9} = \frac{49}{99} $

✔ Answer: $ \frac{49}{99} $

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

- Simplify $ \frac{4}{12} = \frac{1}{3} $, so $ 4\frac{1}{3} $
- Convert: $ 4\frac{1}{3} = \frac{13}{3} $
- Simplify $ \frac{4}{12} = \frac{1}{3} $
- Multiply:
$ \frac{13}{3} \times \frac{1}{3} = \frac{13}{9} $
- Convert: $ \frac{13}{9} = 1\frac{4}{9} $

✔ Answer: $ 1\frac{4}{9} $

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6. $ 6\frac{1}{8} \times \frac{9}{12} $

- Convert $ 6\frac{1}{8} = \frac{49}{8} $
- Simplify $ \frac{9}{12} = \frac{3}{4} $
- Multiply:
$ \frac{49}{8} \times \frac{3}{4} = \frac{147}{32} $
- Convert: $ \frac{147}{32} = 4\frac{19}{32} $

✔ Answer: $ 4\frac{19}{32} $

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7. $ 4\frac{5}{9} \times \frac{1}{2} $

- Convert $ 4\frac{5}{9} = \frac{41}{9} $
- Multiply:
$ \frac{41}{9} \times \frac{1}{2} = \frac{41}{18} $
- Convert: $ \frac{41}{18} = 2\frac{5}{18} $

✔ Answer: $ 2\frac{5}{18} $

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8. $ 10\frac{5}{12} \times \frac{2}{4} $

- Simplify $ \frac{2}{4} = \frac{1}{2} $
- Convert $ 10\frac{5}{12} = \frac{125}{12} $
- Multiply:
$ \frac{125}{12} \times \frac{1}{2} = \frac{125}{24} $
- Convert: $ \frac{125}{24} = 5\frac{5}{24} $

✔ Answer: $ 5\frac{5}{24} $

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9. $ 1\frac{4}{5} \times \frac{4}{7} $

- Convert $ 1\frac{4}{5} = \frac{9}{5} $
- Multiply:
$ \frac{9}{5} \times \frac{4}{7} = \frac{36}{35} $
- Convert: $ \frac{36}{35} = 1\frac{1}{35} $

✔ Answer: $ 1\frac{1}{35} $

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

- Convert $ 9\frac{1}{2} = \frac{19}{2} $
- Multiply:
$ \frac{19}{2} \times \frac{3}{5} = \frac{57}{10} $
- Convert: $ \frac{57}{10} = 5\frac{7}{10} $

✔ Answer: $ 5\frac{7}{10} $

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✔ Final Answers:

1. $ 1\frac{1}{14} $
2. $ 1\frac{1}{14} $
3. $ \frac{14}{15} $
4. $ \frac{49}{99} $
5. $ 1\frac{4}{9} $
6. $ 4\frac{19}{32} $
7. $ 2\frac{5}{18} $
8. $ 5\frac{5}{24} $
9. $ 1\frac{1}{35} $
10. $ 5\frac{7}{10} $

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