How to Solve Ratio Problems

A ratio compares two quantities. Students use ratios for recipes, maps, speeds, mixtures, drawings, and probability.

Quick idea

Ratios stay equivalent when both parts are multiplied or divided by the same number.

Steps

1. Identify the two quantities being compared.
2. Write the ratio in the correct order.
3. Simplify by dividing both parts by the same common factor.
4. Scale up or down when the problem asks for an equivalent ratio.

Worked example

Solve a ratio where 3 to 5 equals 6 to x.

Full solution

Step-by-step walkthrough

Step 1

The first part doubled from 3 to 6.

Step 2

The second part must also double.

Step 3

Five doubled is 10, so x equals 10.

Common mistake

Keep the order consistent. A ratio of boys to girls is not the same as girls to boys.

Practice problems

1. Simplify 6:9.
2. If 2:3 = 8:x, find x.
3. A recipe uses 4 cups flour for 2 cups sugar. What is the simplified ratio?

Answers

1. 2:3
2. 12
3. 2:1

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