1.3 Using ratios
Time conversions are also ratios. The ratio of time measured in minutes to time measured in seconds is one to sixty (1:60), as there are sixty seconds in a minute.
Adam's grandfather ran a mile in minutes. Adam took 260 seconds. Which is greater, 260 seconds or minutes? Did Adam run faster than his grandfather?
minutes is equivalent to × 60 seconds.
is equivalent to . So this is × 60 = 270 seconds.
So minutes is just a bit longer than 260 seconds. Therefore Adam has run faster than his grandfather.
When shopping for a bargain, the ratio of price to quantity is often a useful way of comparing prices of different sized packets.
A local shop sells ready-made custard at £1.45 for a special offer pack of three 425 g tins. It also sells the same brand of custard in 1 kg cartons costing £1.29 each. Which is the better bargain?
To compare the prices it would be best to compare the ratio of prices to amounts (measuring amounts in the same units) i.e. prices per kg.
Three 425 g tins will contain 3 × 425 g = 1275 g or 1.275 kg.
£1.45 for 1.275 kg is
≈ £1.14 per kg.
The 1 kg carton costs £1.29 per kg.
The three tins are 15 p cheaper per kg. So the three-tin pack is the better bargain.