**Definition of Equivalent Ratios**

- If two ratios have the same value when simplified, then they are called Equivalent Ratios.

**More about Equivalent Ratios**

- Equivalent ratios can be obtained by multiplying or dividing both sides by the same non-zero number.

**Examples of Equivalent Ratios**

- andare equivalent ratios since they represent the same fraction.
- The two ratios 8 : 24 and 4 : 12 are equivalent.
- There are 10 dolls for every 40 children in a preschool. Then the ratio of the number of children to that of the dolls = 40:10=4:1.

**Solved Example on Equivalent Ratios**

A carnival game has 3 winners for every 7 losers. Find two ratios equal to the ratio of winners to losers.

Choices:

A.,

B.,

C.,

D.,

Correct Answer: D

Solution:

Step 1:The ratio of winners to losers =

Step 2:= = [Multiply both the numerator and the denominator by 2.]

Step 3:= = [Multiply both the numerator and the denominator by 3.]

Step 4:The two ratios equal to the ratio of winners to the losers are and .

**Related Terms for Equivalent Ratios**

- Equal Fraction
- Equal Value