Skill: Interpret fractions as division

A fraction can be read as a division problem:

$$\frac{a}{b}=a\div b$$

• The numerator $a$ tells how many wholes are being shared.
• The denominator $b$ tells how many equal groups share them.

Example: Interpret $\frac{3}{4}$ as division

Rewrite the fraction as division:

$$\frac{3}{4}=3\div4$$

Now imagine sharing $3$ whole pizzas equally among $4$ groups.

1. Cut each pizza into $4$ equal pieces. Each piece is $\frac14$ of a pizza.
2. Give one piece from each pizza to every group.
3. Each group receives $3$ pieces, and each piece is $\frac14$ of a pizza.

So each group gets

$$\frac14+\frac14+\frac14=\frac34$$

Therefore,

$$3\div4=\frac34$$

Because $3$ is less than $4$, the answer is less than one whole. In general, the fraction $\frac{a}{b}$ tells the result of sharing $a$ wholes equally among $b$ groups.