Dividing Fractions

Study Sheet

Dividing Fractions

Multiply by the reciprocal

Why Flip and Multiply

Concept
The Big Idea
1 of 2 parts shaded

Dividing asks “how many of these fit?” Dividing by cd\dfrac{c}{d} is the same as multiplying by dc\dfrac{d}{c}, because that undoes the division.

Example
Finding 12÷14\dfrac{1}{2} \div \dfrac{1}{4}

Flip and multiply: 12×41=2\dfrac{1}{2} \times \dfrac{4}{1} = 2. And indeed two quarters fit inside a half.

In Plain Terms & More Examples

Concept
In plain terms

To divide by a fraction, flip it (its reciprocal) and multiply. Dividing asks how many of the second fraction fit inside the first.

Example
Finding 34÷12\dfrac{3}{4} \div \dfrac{1}{2}

Flip and multiply: 34×21=64=32\dfrac{3}{4} \times \dfrac{2}{1} = \dfrac{6}{4} = \dfrac{3}{2}.

Example
Finding 23÷16\dfrac{2}{3} \div \dfrac{1}{6}

Flip and multiply: 23×61=123=4\dfrac{2}{3} \times \dfrac{6}{1} = \dfrac{12}{3} = 4.