Lesson 6: Division of Unit Fractions by Whole Numbers

Property

To divide a unit fraction $\frac{1}{b}$ by a whole number $c$, partition the segment from $0$ to $\frac{1}{b}$ on a number line into $c$ equal parts. The length of one new part is the quotient.

Examples

Property

To divide a unit fraction by a whole number, you multiply the unit fraction by the reciprocal of the whole number. The reciprocal of a whole number $c$ is $\frac{1}{c}$.

Examples

• $\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$
• $\frac{1}{5} \div 4 = \frac{1}{5} \times \frac{1}{4} = \frac{1}{20}$
• $\frac{1}{8} \div 2 = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$

Explanation

Dividing a unit fraction by a whole number means splitting an already small piece into even smaller, equal parts. For example, dividing $\frac{1}{2}$ by $3$ is like cutting half a pizza into $3$ equal slices. The procedure for this is to change the division problem into a multiplication problem by using the reciprocal of the whole number. This method connects division and multiplication, showing they are inverse operations.