Learn · Numeracy · 4 min

Fractions, from scratch

A fraction is a part of a whole — two numbers, each with a job:

343 of 4 equal parts
tophow many parts you have (the numerator)
bottomhow many equal parts the whole is split into (the denominator)

See it: a fraction is parts of a whole

Parts shaded — the top number: 3

Equal parts in the whole — the bottom number: 4

34 = 0.75 = 75%

Bottom = how many equal parts. Top = how many you take.

Now — a fraction OF an amount

What’s 34 of 20 lollies? Split the whole into the bottom number of equal parts, then take the top number of them.

The one move: ÷ bottom, × top

① Split 20 into 4 equal parts → 20 ÷ 4 = 5
② Take 3 of them → 5 × 3 = 15
So 34 of 20 = 15.

Tips & tricks

Simplify — divide top & bottom by the same number

68 = 34 (both ÷ 2)

To compare or add — give them the same bottom

12 = 36, so it beats 26 (i.e. 13)

Fraction OF an amount — ÷ bottom, × top

23 of 30 = 30 ÷ 3 × 2 = 20

Fraction → percentage — × 100

34 × 100 = 75%

Compare two fractions — cross-multiply

Bigger: 34 or 57? 3 × 7 = 21 vs 5 × 4 = 20 → 34 wins.

Now you try — 0/3

1. What is 34 of 20?

2. Simplify 68.

3. Which is bigger?

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