Division with Unit Fractions

A unit fraction is a fraction where the numerator is 1 and the denominator is a positive integer, such as $$\frac{1}{2}$$ or $$\frac{1}{5}$$ .

To divide a whole number by a unit fraction, multiply the whole number by the denominator of the fraction. For example, $$6 \div \frac{1}{3} = 6 \times 3 = 18$$ .

The result is 15, because $$5 \div \frac{1}{3} = 5 \times 3 = 15$$ .

Each part represents $$\frac{1}{4}$$ .

The equation is $$\frac{a}{b} \div c = \frac{a}{b \times c}$$ .

There are 8 $$\frac{1}{4}$$ cups in 2 cups, because $$2 \div \frac{1}{4} = 2 \times 4 = 8$$ .

The result is $$\frac{1}{6}$$ , because $$\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$$ .

You need 1 cup of sugar, because $$\frac{1}{3} \times 3 = 1$$ .

Division by a fraction is the same as multiplying by its reciprocal. For example, $$a \div \frac{b}{c} = a \times \frac{c}{b}$$ .

To find the fraction of a whole when dividing a unit fraction, multiply the whole by the reciprocal of the unit fraction.