How to Solve Proportions

A proportion is an equation that says two ratios are equal. Proportions are useful for maps, recipes, unit rates, similar triangles, and percent problems.

Quick idea

If two fractions are equal, their cross products are equal.

Steps

1. Write the two ratios as fractions.
2. Check whether simple scaling solves the problem.
3. If not, cross multiply.
4. Solve the resulting equation and check that the answer makes sense.

Worked example

Solve a proportion with an unknown numerator.

Full solution

Step-by-step walkthrough

Step 1

Cross multiply 3 times 20 and 5 times x.

Step 2

That gives 60 equals 5x.

Step 3

Divide by 5 to get x equals 12.

Common mistake

Cross multiplication is a tool, not magic. The two ratios must describe the same comparison in the same order.

Practice problems

1. Solve 1/4 = x/20.
2. Solve 2/3 = 10/x.
3. Solve 5/8 = x/40.

Answers

1. 5
2. 15
3. 25

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Solve Ratio Problems
• How to Solve Percent Word Problems
• Similar Triangles Explained