0580

Working with Ratios

Number

Map scales

  • A scale written as a ratio has no units, so both sides are measured the same way
  • A scale of 1 : 50 000 means one centimetre on the map is 50 000 cm on the ground
  • Convert to sensible units at the end: 50 000 cm is 500 m, or 0.5 km

Comparing value

  • To decide which of two sizes is better value, reduce both to the same fixed amount
  • Either compare the cost of one unit, or compare how much is obtained per unit of currency
  • Whichever is chosen, the same comparison must be applied to both options
Exam tip

State what one unit is worth on its own line before scaling up: that line carries the method mark when the final figure is wrong. Judge any rounding by the situation rather than the halfway rule — 4.2 minibuses means 5 — and answer in the terms the question used.

Worked example

Deciding which pack is better value

A 750 g pack costs £2.40 and a 1.2 kg pack costs £3.72. Determine which is better value.

Solution:

  • Two quantities can only be compared once they are measured the same way, so fix the units first
  • 1.2 kg = 1200 g, and working in pence avoids decimals: £2.40 is 240p and £3.72 is 372p
  • Then reduce both to the same single unit — here, the cost of one gram
  • Smaller pack: 240 ÷ 750 = 0.32p per gram
  • Larger pack: 372 ÷ 1200 = 0.31p per gram
  • The larger pack costs less for the same gram, so the 1.2 kg pack is better value
  • Say which one and why, because "0.31 < 0.32" alone does not answer the question asked
  • Grams per penny works equally well as the comparison, but then the larger figure is the better value — decide which way round you are working before comparing