What is a ratio?
A ratio compares two or more quantities of the same kind measured in the same unit. If a class has 12 boys and 18 girls, the ratio of boys to girls is written 12 : 18 and read "12 to 18". Order matters: 12 : 18 is not the same as 18 : 12. A ratio has no unit.
Key idea / Key idea
To simplify a ratio, divide every term by their HCF. 12 : 18 has HCF 6, so 12 : 18 = 2 : 3. An equivalent ratio is found by multiplying or dividing all terms by the same number.
Sharing in a given ratio
To share an amount in a ratio, add the parts to find the total number of parts, then find the value of one part.
Worked example / Worked example
Share RM60 between Ali and Bala in the ratio 2 : 3.
Total parts = 2 + 3 = 5.
One part = RM60 ÷ 5 = RM12.
Ali = 2 × RM12 = RM24.
Bala = 3 × RM12 = RM36.
Check: RM24 + RM36 = RM60. ✔
Before writing a ratio, make sure both quantities use the same unit. For example, 50 cm to 2 m must first become 50 cm to 200 cm, which is 50 : 200 = 1 : 4.
Remember / Remember
- A ratio has no unit and the order matters.
- Convert to the same unit before comparing.
- Simplest form: divide by the HCF.
- Ratios can have three terms, e.g. 1 : 2 : 3.