Multiplying Mixed Numbers worksheet with fraction multiplication problems.

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:

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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