Lesson 2: Equivalent Ratios

Property

Two ratios, $a : b$ and $c : d$, are equivalent ratios if there is a positive number $p$ such that

Examples

• The ratio 3:7 is equivalent to 9:21 because both parts were multiplied by 3. ($3 \times 3 = 9$ and $7 \times 3 = 21$).
• To simplify the ratio 20:15, find the greatest common factor, which is 5. Dividing both parts by 5 gives the equivalent ratio 4:3.
• A map scale is 1 inch to 5 miles (1:5). An equivalent ratio shows that 4 inches on the map represents 20 miles, since both parts are multiplied by 4.

Explanation

Equivalent ratios are like different-sized versions of the same recipe. The proportions stay the same whether you're making a small snack or a giant feast. You create them by multiplying or dividing both numbers in the ratio by the same amount.

Property

To find a ratio equivalent to $a:b$, multiply or divide both terms by the same non-zero number, $c$.

Examples