Mathematics (Core)Exam code: 0580

Ratio and Proportion

Number

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

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

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, so decide which way round you are working before comparing

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