RATIO AND PROPORTION

Simplifying Ratios

Learn the reliable method for simplifying ratios, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A ratio is simplest when all its terms have no common factor greater than one.

Picture itCompare each group in the same order
Bowls, fruit, scales and a measuring jug showing ratio and measurement in baking
2 · THE METHOD

Follow these steps

  1. Find the highest common factor of every term.
  2. Divide every term by that same factor.
  3. Keep the terms in their original order.
one share = total ÷ sum of ratio parts
3 · WORKED EXAMPLES

See the method in action

Example 1

Simplify the ratio 8:12.

  1. Divide both parts by their highest common factor, 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
  2. The simplest ratio is 2:3.
Answer: 2:3
Example 2

There are 42 red beads and 56 blue beads. 7 more red beads are added. What is the new red-to-blue ratio in its simplest form?

  1. There are now 49 red and 56 blue beads.
  2. Divide both by 7: 7:8.
Answer: 7:8
4 · ELEVENSPRINT TIP

A useful shortcut

Keep the terms in their original order.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.