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Defining and Identifying Equivalent Ratios

equivalent ratio: fractions in a pie chart

Equivalent ratios, sometimes known as equivalent fractions, are ratios that have the same proportion to each other when put in simplest form. Let's take the following ratios as a quick example.


We know each of these fractions has the same ratio between the numerators and the denominators. They all equal ½ when put in simplest form.

Equivalent ratios have the same unit rate or constant of proportionality. For example, when we compare the denominators of the fractions above to the numerators, we see that the unit rate or ratio is 2.

Building an Equivalent Ratio Table From a Given Ratio

Instead of relying on a ratio calculator or an online calculator, you can find equivalent ratios by multiplying numbers by the same ratio or unit rate.

Here’s an example: This table represents the above fractions. Can you fill in the missing numbers?

equivalent ratio: numerator and denominator table with question marks

The equivalent ratio from numerator to denominator here is 2. You can find each number on the right side by multiplying the left side number by 2.

Check your work!

numerator and denominator table with the answers

Where Can You Identify Equivalent Ratios?

Equivalent ratios on sixth-grade common core worksheets can show up as fractions or whole numbers separated by a colon, such as 2:3 or 4:6.

Equivalent ratios in word problems have a “unit rate,” such as $2.50 per gallon or traveling at 21.5 miles per hour. A constant unit rate, such as the cost of gas per gallon pumped, means that the two quantities will always be proportional.

Equivalent ratios compare two quantities and are not limited to only fractions and decimals. They can also be represented with mixed numbers, percentages, and even irrational numbers.

Identifying Equivalent Ratios in Real Life

Equivalent ratios demonstrate a proportional relationship between two quantities. A ratio simply compares one number to another. An equivalent ratio means that the proportional relationship stays the same.

You can calculate your own equivalent ratios by multiplying the first number by the same ratio, or unit of proportion, to get the second number.

Equivalent ratios are common in real life, whether it’s the cost of produce at the supermarket, miles per gallon for a car, or how much a job pays per hour.

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