Ratios, fractions and linear functions

Ratios are tested across Foundation and Higher Edexcel papers. The Higher tier specifically links ratio language to fractions and linear function form.

Ratio as a fraction

If the ratio of A to B is a:b, then A/B = a/b. Equivalently, A is a/(a+b) of the total and B is b/(a+b) of the total.

Example: ratio of pens to pencils is 3:5 in a box of 80 items.

• Pens = 3/8 × 80 = 30.
• Pencils = 5/8 × 80 = 50.
• Pens/pencils = 3/5 (the ratio expressed as a fraction).

Ratio as a linear function

If y = kx, then y:x is constant in the ratio k:1 — this is direct proportion. The line passes through the origin with gradient k.

Example: petrol costs £1.40 per litre. Cost (y) and litres (x) satisfy y = 1.4x. Ratio cost:litres = 1.4:1 = 7:5.

Sharing in a ratio

To share £240 in the ratio 2:3:5:

• Total parts = 2 + 3 + 5 = 10.
• One part = £240 / 10 = £24.
• Shares = £48, £72, £120.

Ratio change problems (Higher focus)

If A:B = 3:5 originally and A increases by 4 to make A:B = 7:10, find the original A.

Let A = 3k, B = 5k. (3k + 4) / 5k = 7/10 10(3k + 4) = 35k 30k + 40 = 35k 40 = 5k k = 8

So A = 24, B = 40. Check: (24 + 4):40 = 28:40 = 7:10 ✓

Ratio and gradients (linking algebra and geometry)

A line y = mx + c has gradient m. The ratio of vertical change to horizontal change is m:1. This is how Edexcel tests "ratios as linear functions" on Higher Paper 2H or 3H.

Common Edexcel exam tip

Always check whether the question asks for a ratio (e.g. 2:5), a fraction (e.g. 2/5) or a quantity (e.g. £24). Mis-formatted answers lose A1 marks regularly.