Learn · Grades 6–8

How to Solve Proportions (Ratios), Step by Step

A ratio compares two amounts, like 3 to 4. A proportion says two ratios are equal, such as 3/4 = x/20. Solving it means finding the missing number.

Try it with your own problem ↓

The steps

  1. Write both ratios as fractions with the same quantities in the same positions.
  2. Cross multiply: multiply the top of each fraction by the bottom of the other.
  3. Set the two products equal to each other.
  4. Solve for the unknown by dividing both sides by the number next to it.
  5. Check that both ratios simplify to the same fraction.

A worked example

Solve 3/4 = x/20.

  1. Cross multiply: 3 × 20 on one side and 4 × x on the other.
  2. That gives 60 = 4x.
  3. Divide both sides by 4: x = 60 ÷ 4 = 15.
  4. Check: 15/20 simplifies by 5 to 3/4. ✓

x = 15.

Why it works

Cross multiplying is a shortcut. Multiply both sides of 3/4 = x/20 by 4 and by 20, and the denominators clear, leaving 3 × 20 = 4 × x. Here is another way to see it: 4 × 5 = 20, so the top must also be multiplied by 5, and 3 × 5 = 15.

Try it with your own problem

Open the free The Ratio Table with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 3/4=x/20Opens The Ratio Table with this example

Or try these

Common mistakes

Questions people ask

What is the difference between a ratio and a proportion?

A ratio compares two quantities. A proportion is an equation that says two ratios are equal.

How do I simplify a ratio?

Divide both parts by their GCF, just like a fraction. 12:18 becomes 2:3.

How do I split an amount in a ratio?

Add the parts (2 + 3 = 5), divide the amount by that (60 ÷ 5 = 12), and multiply: 2 × 12 = 24 and 3 × 12 = 36.

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