Ratio, fraction and percent
Three Year-6 ideas that belong together: ratio, fraction and percent. They are three ways of saying the same thing.
Example — a classroom
A class has 12 boys and 8 girls (20 children in total).
Ratio of boys to girls:Fraction of boys in the whole class:12 : 8 = 3 : 2 (simplified).
Percent of boys in the class:12/20 = 3/5.
3/5 = 60/100 = 60 %.
What we describe in three ways is the same phenomenon — the make-up of the class.
Ratio ↔ fraction
If the ratio is a : b, the parts make a + b equal slices, and each side's share is:
boys make up `a / (a + b)` of the whole, girls `b / (a + b)`.
For ratio 3 : 2 = total is 3 + 2 = 5 parts. Boys are 3/5, girls 2/5.
Fraction ↔ percent
Multiply by 100 and add the `%` sign.
- 3/5 = `3 · 100 ÷ 5 = 60` → 60 %.
- 1/4 = `1 · 100 ÷ 4 = 25` → 25 %.
- 2/3 = `2 · 100 ÷ 3 ≈ 66.67` → 66.67 %.
When to use which
- Ratio — comparing two quantities to each other ("boys to girls is 3 : 2").
- Fraction — talking about a part of the whole ("3/5 of the class are boys").
- Percent — scaling everything to 100 ("60 % of the class are boys").