Multiplying Mixed Numbers Worksheets - 15 Worksheets Library - Free Printable

Let's solve each problem step by step. The task is to multiply mixed numbers by fractions. To do this, we follow these steps:

Steps:

1. Convert the mixed number to an improper fraction.
2. Multiply the improper fraction by the given fraction.
3. Simplify the result and convert back to a mixed number if needed.

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We’ll go through each question one by one.

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1. What is $ \frac{1}{15} $ of $ 1\frac{2}{5} $?

- Convert $ 1\frac{2}{5} $ to improper fraction:
$ 1\frac{2}{5} = \frac{5 \times 1 + 2}{5} = \frac{7}{5} $
- Multiply:
$ \frac{1}{15} \times \frac{7}{5} = \frac{7}{75} $

✔ Answer: $ \frac{7}{75} $

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2. What is one-seventh of $ 3\frac{2}{7} $?

- Convert $ 3\frac{2}{7} $:
$ 3\frac{2}{7} = \frac{7 \times 3 + 2}{7} = \frac{23}{7} $
- Multiply:
$ \frac{1}{7} \times \frac{23}{7} = \frac{23}{49} $

✔ Answer: $ \frac{23}{49} $

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3. What is one-third of $ 3\frac{7}{9} $?

- Convert $ 3\frac{7}{9} $:
$ 3\frac{7}{9} = \frac{9 \times 3 + 7}{9} = \frac{34}{9} $
- Multiply:
$ \frac{1}{3} \times \frac{34}{9} = \frac{34}{27} $
- Convert to mixed number:
$ \frac{34}{27} = 1\frac{7}{27} $

✔ Answer: $ 1\frac{7}{27} $

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4. What is $ \frac{1}{15} $ of $ 2\frac{5}{18} $?

- Convert $ 2\frac{5}{18} $:
$ 2\frac{5}{18} = \frac{18 \times 2 + 5}{18} = \frac{41}{18} $
- Multiply:
$ \frac{1}{15} \times \frac{41}{18} = \frac{41}{270} $

✔ Answer: $ \frac{41}{270} $

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5. What is $ \frac{6}{7} $ of $ 2\frac{3}{14} $?

- Convert $ 2\frac{3}{14} $:
$ 2\frac{3}{14} = \frac{14 \times 2 + 3}{14} = \frac{31}{14} $
- Multiply:
$ \frac{6}{7} \times \frac{31}{14} = \frac{186}{98} $
- Simplify: divide numerator and denominator by 2 → $ \frac{93}{49} $
- Convert to mixed number:
$ \frac{93}{49} = 1\frac{44}{49} $

✔ Answer: $ 1\frac{44}{49} $

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6. What is $ \frac{3}{5} $ of $ 1\frac{2}{5} $?

- Convert $ 1\frac{2}{5} $:
$ 1\frac{2}{5} = \frac{7}{5} $
- Multiply:
$ \frac{3}{5} \times \frac{7}{5} = \frac{21}{25} $

✔ Answer: $ \frac{21}{25} $

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7. What is two-fifths of $ 2\frac{1}{6} $?

- Convert $ 2\frac{1}{6} $:
$ 2\frac{1}{6} = \frac{13}{6} $
- Multiply:
$ \frac{2}{5} \times \frac{13}{6} = \frac{26}{30} $
- Simplify: $ \frac{13}{15} $

✔ Answer: $ \frac{13}{15} $

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8. What is $ \frac{7}{10} $ of $ 2\frac{5}{12} $?

- Convert $ 2\frac{5}{12} $:
$ 2\frac{5}{12} = \frac{29}{12} $
- Multiply:
$ \frac{7}{10} \times \frac{29}{12} = \frac{203}{120} $
- Convert to mixed number:
$ \frac{203}{120} = 1\frac{83}{120} $

✔ Answer: $ 1\frac{83}{120} $

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9. What is $ \frac{3}{10} $ of $ 2\frac{3}{7} $?

- Convert $ 2\frac{3}{7} $:
$ 2\frac{3}{7} = \frac{17}{7} $
- Multiply:
$ \frac{3}{10} \times \frac{17}{7} = \frac{51}{70} $

✔ Answer: $ \frac{51}{70} $

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10. What is one fifth of $ 1\frac{2}{15} $?

- Convert $ 1\frac{2}{15} $:
$ 1\frac{2}{15} = \frac{17}{15} $
- Multiply:
$ \frac{1}{5} \times \frac{17}{15} = \frac{17}{75} $

✔ Answer: $ \frac{17}{75} $

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | $ \frac{7}{75} $ |
| 2 | $ \frac{23}{49} $ |
| 3 | $ 1\frac{7}{27} $ |
| 4 | $ \frac{41}{270} $ |
| 5 | $ 1\frac{44}{49} $ |
| 6 | $ \frac{21}{25} $ |
| 7 | $ \frac{13}{15} $ |
| 8 | $ 1\frac{83}{120} $ |
| 9 | $ \frac{51}{70} $ |
| 10 | $ \frac{17}{75} $ |

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