Multiplicative relationships: ratio and fraction

WJEC tests this on every paper from Foundation to Higher — translating between ratio language and fraction language.

Ratio basics

A ratio compares parts. Written a : b (read "a to b"). Order matters — boys to girls = 3 : 5 means for every 3 boys there are 5 girls.

Ratio ↔ fraction conversion

If a class is split boys : girls = 3 : 5, total parts = 3 + 5 = 8.

• Fraction that are boys = 3/8.
• Fraction that are girls = 5/8.
• Boys as a fraction OF girls = 3/5 (NOT of the total).

Reverse: if 3/8 of the class are boys, then ratio of boys to girls = 3 : 5 (since 5/8 are girls).

WJEC trap: "What fraction are boys?" wants 3/8. "What is the ratio of boys to girls?" wants 3 : 5. Read the question.

Simplifying ratios

Divide all parts by the highest common factor.

• 12 : 18 → divide both by 6 → 2 : 3.
• 30 : 45 : 75 → divide by 15 → 2 : 3 : 5.

For ratios with units, convert to a single common unit first.

• 50 cm : 2 m → 50 cm : 200 cm → 1 : 4.

Sharing in a ratio

To share £240 in the ratio 3 : 5:

• Total parts = 8.
• One part = 240 ÷ 8 = £30.
• Each share = 3 × 30 = £90 and 5 × 30 = £150.

Ratio as a "rate" / 1 : n form

Sometimes WJEC wants 1 : n form — divide both parts by the first.

• 8 : 36 → 1 : 4.5.

Multiplicative comparison

"x is 1.5 times y" can be written ratio x : y = 3 : 2 (multiplying through by 2 to clear the decimal).

WJEC exam tip

Always show the total parts line for a ratio question. Writing "Total parts = 3 + 5 = 8" earns the M1 even if a later arithmetic slip costs the A1.