Proportions

What are Proportions?

A proportion is an equation that states that two ratios are equal. It can be written in the form a/b = c/d.

This proportion states that the ratio 3:2 is equal to the ratio 9:6.

We can verify this: 3 ÷ 2 = 1.5 and 9 ÷ 6 = 1.5

Cross Multiplication

Cross multiplication is a method used to solve proportions. If a/b = c/d, then a × d = b × c.

Cross Multiplication Method

Solving Proportions

Example 1: Find the Missing Value

Solve for x in the proportion: 3/4 = x/20

3/4 = x/20

Cross multiply: 3 × 20 = 4 × x

60 = 4x

x = 60 ÷ 4

x = 15

Example 2: Recipe Scaling

A recipe calls for 2 cups of flour to make 3 dozen cookies. How many cups of flour are needed to make 5 dozen cookies?

2 cups / 3 dozen = x cups / 5 dozen

Cross multiply: 2 × 5 = 3 × x

10 = 3x

x = 10 ÷ 3

x = 3.33 cups

Example 3: Similar Triangles

Two triangles are similar. If the first triangle has sides of lengths 6 cm, 8 cm, and 10 cm, and the second triangle has one side of length 15 cm corresponding to the 10 cm side, find the lengths of the other two sides of the second triangle.

Set up the proportion: 10/15 = 6/a = 8/b

10/15 = 6/a

Cross multiply: 10 × a = 15 × 6

10a = 90

a = 9 cm

10/15 = 8/b

Cross multiply: 10 × b = 15 × 8

10b = 120

b = 12 cm

Practice Proportions

Test your knowledge with our interactive proportion practice exercises.

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Proportion Calculator

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