Lesson 9: Divide Whole Numbers by Unit Fractions

Property

Dividing a whole number, $a$, by a unit fraction, $\frac{1}{b}$, is a way of asking: "How many groups of size $\frac{1}{b}$ are in $a$?"
This can be modeled visually to find the total number of fractional parts.

Examples

Property

To divide a whole number by a unit fraction, you can multiply the whole number by the denominator of the fraction. For a whole number $w$ and a unit fraction $\frac{1}{d}$:

Examples

• $6 \div \frac{1}{4} = 6 \times 4 = 24$
• $10 \div \frac{1}{2} = 10 \times 2 = 20$
• $3 \div \frac{1}{8} = 3 \times 8 = 24$

Explanation

Dividing by a unit fraction is like asking "how many of this fraction fit into the whole number?" For example, $6 \div \frac{1}{4}$ asks how many $\frac{1}{4}$-sized pieces are in 6 wholes. Since there are 4 fourths in 1 whole, there must be $6 \times 4$ fourths in 6 wholes. This shows that dividing by a unit fraction is the same as multiplying by its denominator.