How It Works

A proportion states that two ratios are equal. To solve for an unknown value, cross multiply the two ratios and isolate the missing variable. For example, if a/b = c/d, multiplying both sides by d gives a × d = b × c, which can then be rearranged to solve for the unknown value.

For a/b = c/d, cross multiplication gives a × d = b × c. If a is unknown, a = (b × c) ÷ d. If d is unknown, d = (b × c) ÷ a.

Example

For example, if 2/4 = 3/d, cross multiplication gives 2d = 4 × 3. Solving for d gives d = 6, so the completed proportion is 2/4 = 3/6.

Frequently Asked Questions

How do you solve a proportion?

Set the two ratios equal to each other, cross multiply, and solve for the missing value. For example, in 2/4 = 3/x, cross multiplication gives 2x = 12, so x = 6.

What is cross multiplication?

Cross multiplication multiplies the numerator of one fraction by the denominator of the other. For a/b = c/d, it produces the equation a × d = b × c.

What is the missing value in 2/4 = 3/x?

The missing value is 6. Cross multiplication gives 2x = 12, and dividing by 2 gives x = 6.

What are proportions used for?

Proportions are used to compare equivalent ratios and solve scaling problems in areas such as recipes, maps, measurements, rates, and other situations involving proportional relationships.

What is the difference between a ratio and a proportion?

A ratio compares two quantities, while a proportion states that two ratios are equal. For example, 2:4 is a ratio, while 2/4 = 3/6 is a proportion.