Simplifying ratios

What simplifying means

To simplify a ratio means to write it with the smallest possible whole numbers while keeping the same comparison. A ratio is in simplest form when its terms have no common factor except 1.

12:18 → 2:3

Method: divide by the GCF

1. Find the greatest common factor of all the terms.
2. Divide every term by it.

You can also divide in steps by any common factor until none is left.

Ratios with units: use common units first

Terms must use common units before you simplify.

Example: 50 cm to 2 m

• 2 m = 200 cm
• 50:200 → ÷ 50 → 1:4

Example: 45 minutes to 2 hours

• 2 h = 120 min
• 45:120 → ÷ 15 → 3:8

Ratios with decimals

Multiply by a power of 10 to get whole numbers, then simplify.

Example: 0.6:1.5

• × 10 → 6:15
• ÷ 3 → 2:5

Ratios with fractions

Multiply every term by the LCM of the denominators.

Example: 1/2 : 3/4

• × 4 → 2:3

Unit ratios

Sometimes it’s useful to make one term 1. This is a unit ratio.

• 4:10 → divide both by 4 → 1:2.5
• Screens: 16:9 ≈ 1.78:1

Unit ratios make comparisons easy. If one recipe is 1:2.5 and another is 1:3, the second has more of the second ingredient per unit of the first.

Worked examples

Example 1: Simplify 24:36.

GCF 12 → 2:3.

Example 2: Simplify 1.2 kg : 400 g.

1,200:400 → ÷ 400 → 3:1.

Example 3: Simplify 15:25:40.

GCF 5 → 3:5:8.

Common mistakes

• Simplifying with different units: 50 cm : 2 m is not 25:1.
• Stopping before simplest form: 12:18 → 6:9 is not done.
• Writing a ratio as a mixed number: 7:2 stays 7:2, not 3 1/2.

Try it yourself

1. Simplify 16:40.
2. Simplify 90 s : 3 min.
3. Simplify 2.4:3.6.
4. Simplify 18:27:45.
5. Write 5:8 as a unit ratio 1:?

Answers: 1) 2:5 2) 1:2 3) 2:3 4) 2:3:5 5) 1:1.6

Quick recap

• Simplify by dividing all terms by the greatest common factor.
• Convert to common units first.
• Clear decimals and fractions before simplifying.