Dividing Unit Fractions by Whole Numbers worksheet - Free Printable

Let's solve each problem step by step using the visual models provided. The task is to divide unit fractions by whole numbers, and the models show how the original fraction is divided into smaller equal parts.

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1) $\frac{1}{9} \div 2$

Model:
- A bar labeled $\frac{1}{9}$ is split into two equal parts, each labeled $\frac{1}{18}$.

This means:
$$
\frac{1}{9} \div 2 = \frac{1}{18}
$$

✔ Answer: $\frac{1}{18}$

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

Model:
- A bar labeled $\frac{1}{5}$ is divided into 6 equal parts, each labeled $\frac{1}{30}$.

So:
$$
\frac{1}{5} \div 6 = \frac{1}{30}
$$

✔ Answer: $\frac{1}{30}$

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3) $\frac{1}{2} \div 8$

Model:
- A bar labeled $\frac{1}{2}$ is split into 8 equal parts, each labeled $\frac{1}{16}$.

So:
$$
\frac{1}{2} \div 8 = \frac{1}{16}
$$

✔ Answer: $\frac{1}{16}$

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4) $\frac{1}{4} \div 5$

Model:
- A bar labeled $\frac{1}{4}$ is divided into 5 equal parts, each labeled $\frac{1}{20}$.

So:
$$
\frac{1}{4} \div 5 = \frac{1}{20}
$$

✔ Answer: $\frac{1}{20}$

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5) $\frac{1}{6} \div 9$

Model:
- A bar labeled $\frac{1}{6}$ is split into 9 equal parts, each labeled $\frac{1}{54}$.

So:
$$
\frac{1}{6} \div 9 = \frac{1}{54}
$$

✔ Answer: $\frac{1}{54}$

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6) $\frac{1}{3} \div 3$

Model:
- A bar labeled $\frac{1}{3}$ is divided into 3 equal parts, each labeled $\frac{1}{9}$.

So:
$$
\frac{1}{3} \div 3 = \frac{1}{9}
$$

✔ Answer: $\frac{1}{9}$

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✔ Final Answers:

1) $\frac{1}{18}$
2) $\frac{1}{30}$
3) $\frac{1}{16}$
4) $\frac{1}{20}$
5) $\frac{1}{54}$
6) $\frac{1}{9}$

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🔍 Explanation (General Rule):

When dividing a unit fraction ($\frac{1}{n}$) by a whole number ($m$), you can think of it as:
$$
\frac{1}{n} \div m = \frac{1}{n \times m}
$$

This matches all the answers above:
- Example: $\frac{1}{9} \div 2 = \frac{1}{9 \times 2} = \frac{1}{18}$

The models visually represent this idea — splitting a portion into more equal pieces, making each piece smaller.

Let me know if you'd like a printable version or further explanation!