# Equivalent ratios

Equivalent ratios are ratios that describe the same rate or make the same comparison. They are a result of the fact that ratios are scalable, meaning that they can be multiplied or divided by a constant to yield the same relationship, expressed in larger or smaller quantities.

Example

Samantha wants to buy and stock an aquarium. She saves $1 of each $5 she earns.

Saved | : | $1 | $2 | $3 | $4 | $5 |

Earned | : | $5 | $10 | $15 | $20 | $25 |

1:5, 2:10, 3:15, 4:20, and 5:25 are all equivalent ratios. These ratios can also be written as:

, , , , and .

Equivalent ratios are related to proportions in that proportions are a statement that two ratios are equal, making the ratios involved in any proportion, equivalent ratios.

Example

Given the ratios, 15:1 and 30:2, which represent how many miles you traveled on your bike in 1 and 2 hours, are proportional, test whether the ratios are equivalent ratios:

(15×2):(1×2) = 30:2

(30÷2):(2÷2) = 15:1

Since either of the ratios can be scaled by a factor of 2 to equal the other, they are equivalent fractions.