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Ratios and Fractions
A ratio is similar to a fraction. In the above example the length of the shortest
line is three-fifths (
3
5
) of the longest line. If a boy weighs 100lbs and a man
weighs 150lbs, then the boy weighs a fraction
100
150
of the man. The ratio is
100:150 . The fraction can be simplified (cancelled) to give:
100
150
=
2
3
Similarly, the ratio is simplified giving:
100:150 = 2:3
So, remember that if the two numbers have a common factor the ratio should be
simplified. In the above example the common factor is 50, so that both sides of
the ratio (the 100 and the 150) are divided by 50.
Ratios and fractions aren’t just similar - they are really the same thing. Saying
that the boy weighs ‘two-thirds of the man’ is an alternative way of saying that
‘the ratio of their weights is 2 to 3’.
Example 2
Calculate the ratio of 80p to £1 and express the answer in its simplest form.
This time the units are different, so convert to the same unit. It is easier to
change to the smaller unit and so convert the £s to pence.
£1 = 100p. The ratio of 80p to 100p is 80:100. The numbers have a common
factor of 20 and so can be cancelled giving:
80:100 = 4:5
Note: in a ratio the order of the two numbers is important. The ratio of 80p to
£1 is written 4:5 but the ratio of £1 to 80p is 5:4 .
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