Ratios

What are Ratios?

A ratio is a comparison of two or more quantities. It shows how much of one thing there is compared to another thing.

Ways to Write Ratios

Using a colon

3:2

Using the word "to"

3 to 2

As a fraction

3/2

Ratios are used in many real-world situations, such as recipes, maps, and comparing prices.

Equivalent Ratios

Equivalent ratios are ratios that express the same relationship between numbers. You can find equivalent ratios by multiplying or dividing both terms by the same number.

Example: Equivalent Ratios for 3:2

3:2

Original

6:4

× 2

9:6

× 3

12:8

× 4

Simplifying Ratios

To simplify a ratio, divide both terms by their greatest common factor (GCF).

Simplify 12:8

GCF = 4

12 ÷ 4 : 8 ÷ 4

3:2

Ratio Word Problems

Example 1: Recipe Scaling

A recipe calls for 2 cups of flour and 3 cups of sugar. If you want to use 6 cups of flour, how much sugar will you need?

Original ratio: 2 cups flour : 3 cups sugar

New amount of flour: 6 cups

Set up proportion: 2/3 = 6/x

Cross multiply: 2x = 6 × 3

2x = 18

x = 9

You need 9 cups of sugar.

Example 2: Map Scale

On a map, 1 inch represents 50 miles. If two cities are 3.5 inches apart on the map, what is the actual distance between them?

Scale ratio: 1 inch : 50 miles

Distance on map: 3.5 inches

Set up proportion: 1/50 = 3.5/x

Cross multiply: x = 3.5 × 50

x = 175

The actual distance is 175 miles.

Practice Ratios

Test your knowledge with our interactive ratio practice exercises.

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Ratio Calculator

Use our calculator to simplify ratios and solve ratio problems.

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