Divide fractions by whole numbers with this math worksheet.

Let's solve each of these problems step by step. The task is to divide a fraction by a whole number.

🔷 General Rule:

To divide a fraction by a whole number, you can follow this rule:

> Divide the fraction by the whole number by multiplying the fraction by the reciprocal of the whole number.

That is:
$$
\frac{a}{b} \div c = \frac{a}{b} \times \frac{1}{c}
$$

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1. $\frac{1}{3} \div 4$

$$
\frac{1}{3} \div 4 = \frac{1}{3} \times \frac{1}{4} = \frac{1 \times 1}{3 \times 4} = \frac{1}{12}
$$

✔ Answer: $\frac{1}{12}$

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2. $\frac{2}{5} \div 7$

$$
\frac{2}{5} \div 7 = \frac{2}{5} \times \frac{1}{7} = \frac{2 \times 1}{5 \times 7} = \frac{2}{35}
$$

✔ Answer: $\frac{2}{35}$

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3. $\frac{1}{2} \div 2$

$$
\frac{1}{2} \div 2 = \frac{1}{2} \times \frac{1}{2} = \frac{1 \times 1}{2 \times 2} = \frac{1}{4}
$$

✔ Answer: $\frac{1}{4}$

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4. $\frac{2}{5} \div 9$

$$
\frac{2}{5} \div 9 = \frac{2}{5} \times \frac{1}{9} = \frac{2 \times 1}{5 \times 9} = \frac{2}{45}
$$

✔ Answer: $\frac{2}{45}$

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5. $\frac{1}{2} \div 6$

$$
\frac{1}{2} \div 6 = \frac{1}{2} \times \frac{1}{6} = \frac{1 \times 1}{2 \times 6} = \frac{1}{12}
$$

✔ Answer: $\frac{1}{12}$

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6. $\frac{4}{10} \div 2$

First, simplify $\frac{4}{10}$:
$$
\frac{4}{10} = \frac{2}{5}
$$

Now divide:
$$
\frac{2}{5} \div 2 = \frac{2}{5} \times \frac{1}{2} = \frac{2 \times 1}{5 \times 2} = \frac{2}{10} = \frac{1}{5}
$$

✔ Answer: $\frac{1}{5}$

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✔ Final Answers:

1. $\frac{1}{3} \div 4 = \boxed{\frac{1}{12}}$
2. $\frac{2}{5} \div 7 = \boxed{\frac{2}{35}}$
3. $\frac{1}{2} \div 2 = \boxed{\frac{1}{4}}$
4. $\frac{2}{5} \div 9 = \boxed{\frac{2}{45}}$
5. $\frac{1}{2} \div 6 = \boxed{\frac{1}{12}}$
6. $\frac{4}{10} \div 2 = \boxed{\frac{1}{5}}$

Let me know if you'd like a visual explanation or help with word problems!