Fractions in ratio problems

WJEC Intermediate and Higher candidates must move fluently between ratios and fractions.

Ratio → fraction

If two quantities are in ratio a : b, the total has (a + b) parts.

• First quantity is a/(a + b) of the total.
• Second quantity is b/(a + b) of the total.

Example: chocolates split 3 : 5 between Anna and Ben.

• Anna has 3/8 of the chocolates.
• Ben has 5/8 of the chocolates.

Fraction → ratio

If 2/5 of a class are boys, then 3/5 are girls. Boys : girls = 2 : 3.

Three-part ratios

Ratio 2 : 3 : 4 has 9 parts in total. The quantities are 2/9, 3/9 = 1/3, and 4/9.

Sharing a known total

£200 is split in ratio 3 : 5.

• Anna: 3/8 × £200 = £75.
• Ben: 5/8 × £200 = £125.

Check: 75 + 125 = 200 ✓.

When one part is given

In a class of 30, boys : girls = 2 : 3. Boys = 2/5 × 30 = 12; girls = 18.

Combining ratios

A : B = 2 : 3 and B : C = 4 : 5. Make B common: scale first to 8 : 12 (×4) and second to 12 : 15 (×3). Now A : B : C = 8 : 12 : 15.

WJEC exam tip

Ratio questions worded as "what fraction is..." (Higher) test the bridge between ratio and fraction. Always write the total parts first as a sentence or working line — it earns the M1 even if a later arithmetic slip costs the A1.