Ratios Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Ratios.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A ratio compares two or more quantities by showing how many times one contains the other, written as a:b or \frac{a}{b}. Unlike fractions, ratios can compare parts to parts, not just parts to wholes.

A recipe that uses 2 cups flour for every 1 cup sugar has a 2:1 ratio.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Ratios describe multiplicative relationships between quantities.

Common stuck point: Order always matters in a ratio: 3:5 (boys to girls) is different from 5:3 (girls to boys).

Sense of Study hint: Label each number with what it represents before writing the ratio, so the order matches the question being asked.

Common Mistakes to Watch For

Before you work through the examples, skim the mistake guide so you know which shortcuts and sign errors to avoid.

Fractions Mistakes

Worked Examples

Example 1

easy
A recipe calls for 3 cups of flour and 2 cups of sugar. What is the ratio of flour to sugar, and how much sugar is needed for 12 cups of flour?

Solution

  1. 1
    The ratio of flour to sugar is 3 : 2.
  2. 2
    Set up the proportion: \frac{3}{2} = \frac{12}{x}.
  3. 3
    Cross-multiply: 3x = 24, so x = 8.

Answer

8 \text{ cups of sugar}
A ratio compares two quantities. To scale a ratio, you can set up a proportion and cross-multiply to find the unknown value.

Example 2

medium
The ratio of boys to girls in a class is 5 : 3. If there are 40 students total, how many boys and how many girls are there?

Example 3

medium
A recipe uses flour and sugar in a 5:2 ratio. If you use 15 cups of flour, how much sugar do you need?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Simplify the ratio 18 : 24.

Example 2

hard
A map uses the scale 1 : 50{,}000. Two towns are 3.5 cm apart on the map. What is the actual distance in kilometres?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

fractionsdivision