Division between fractions and between fractions and whole numbers ... - Free Printable

Let's solve each of these division problems step by step. When dividing by a fraction, we multiply by its reciprocal. For dividing a whole number by a fraction or a fraction by a whole number, the same rule applies.

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a) $ 6 \div \frac{1}{4} $

To divide by a fraction, multiply by its reciprocal:

$$
6 \div \frac{1}{4} = 6 \times \frac{4}{1} = 24
$$

✔ Answer: 24

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b) $ \frac{1}{5} \div 8 $

Rewrite 8 as $ \frac{8}{1} $, then multiply by reciprocal:

$$
\frac{1}{5} \div 8 = \frac{1}{5} \div \frac{8}{1} = \frac{1}{5} \times \frac{1}{8} = \frac{1}{40}
$$

✔ Answer: $ \frac{1}{40} $

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c) $ 7 \div \frac{2}{3} $

Multiply by reciprocal of $ \frac{2}{3} $, which is $ \frac{3}{2} $:

$$
7 \div \frac{2}{3} = 7 \times \frac{3}{2} = \frac{21}{2} = 10\frac{1}{2}
$$

✔ Answer: $ \frac{21}{2} $ or $ 10\frac{1}{2} $

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d) $ 5 \div \frac{2}{5} $

Multiply by reciprocal of $ \frac{2}{5} $, which is $ \frac{5}{2} $:

$$
5 \div \frac{2}{5} = 5 \times \frac{5}{2} = \frac{25}{2} = 12\frac{1}{2}
$$

✔ Answer: $ \frac{25}{2} $ or $ 12\frac{1}{2} $

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e) $ \frac{3}{4} \div 15 $

Write 15 as $ \frac{15}{1} $, then:

$$
\frac{3}{4} \div 15 = \frac{3}{4} \times \frac{1}{15} = \frac{3}{60} = \frac{1}{20}
$$

✔ Answer: $ \frac{1}{20} $

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f) $ \frac{6}{7} \div 12 $

Write 12 as $ \frac{12}{1} $:

$$
\frac{6}{7} \div 12 = \frac{6}{7} \times \frac{1}{12} = \frac{6}{84} = \frac{1}{14}
$$

✔ Answer: $ \frac{1}{14} $

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g) $ \frac{5}{6} \div 5 $

Write 5 as $ \frac{5}{1} $:

$$
\frac{5}{6} \div 5 = \frac{5}{6} \times \frac{1}{5} = \frac{5}{30} = \frac{1}{6}
$$

✔ Answer: $ \frac{1}{6} $

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h) $ 4 \div \frac{2}{5} $

Multiply by reciprocal of $ \frac{2}{5} $, which is $ \frac{5}{2} $:

$$
4 \div \frac{2}{5} = 4 \times \frac{5}{2} = \frac{20}{2} = 10
$$

✔ Answer: 10

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i) $ \frac{2}{7} \div 7 $

Write 7 as $ \frac{7}{1} $:

$$
\frac{2}{7} \div 7 = \frac{2}{7} \times \frac{1}{7} = \frac{2}{49}
$$

✔ Answer: $ \frac{2}{49} $

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j) $ 10 \div \frac{3}{4} $

Multiply by reciprocal of $ \frac{3}{4} $, which is $ \frac{4}{3} $:

$$
10 \div \frac{3}{4} = 10 \times \frac{4}{3} = \frac{40}{3} = 13\frac{1}{3}
$$

✔ Answer: $ \frac{40}{3} $ or $ 13\frac{1}{3} $

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✔ Final Answers:

a) $ 24 $
b) $ \frac{1}{40} $
c) $ \frac{21}{2} $ or $ 10\frac{1}{2} $
d) $ \frac{25}{2} $ or $ 12\frac{1}{2} $
e) $ \frac{1}{20} $
f) $ \frac{1}{14} $
g) $ \frac{1}{6} $
h) $ 10 $
i) $ \frac{2}{49} $
j) $ \frac{40}{3} $ or $ 13\frac{1}{3} $

Let me know if you'd like these as decimals or in mixed numbers!