Dividing Unit Fractions by Whole Numbers and Vice Versa

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 unit fraction by a whole number, multiply the denominator of the fraction by the whole number. For example, $$\frac{1}{4} \div 2 = \frac{1}{4 \times 2} = \frac{1}{8}$$ .

Dividing a whole number by a unit fraction is the same as multiplying the whole number by the reciprocal of the unit fraction. For example, $$3 \div \frac{1}{4} = 3 \times 4 = 12$$ .

Mrs. Beverly can serve 24 students.

Scarlett can make 30 pillows.

It takes 6 scoops to fill the bowl.

Each friend gets $$\frac{5}{8}$$ of an apple.

Each friend will receive $$2 \frac{1}{4}$$ pies.

The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, the reciprocal of $$\frac{3}{4}$$ is $$\frac{4}{3}$$ .

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that over the original denominator. For example, $$2 \frac{1}{4} = \frac{(2 \times 4) + 1}{4} = \frac{9}{4}$$ .