Percentages Worksheet printable pdf download

Percentages Worksheet

Worksheet 1.5 Percentages

Section 1

Proportions

A pie is cut into twelve pieces. John eats ﬁve pieces, Peter eats one piece and Chris and

Michael eat three pieces each. If we ask what proportion of the pie John ate we are asking

what fraction of the total pie he ate. The proportion John ate is

Proportions are comparisons, usually between part of something and the whole of it. Chris

and Michael each had

of the pie.

For the proportion of pie John ate you could instead say that he ate 5 in 12 parts of the pie.

This means for every twelve pieces of pie John ate ﬁve. To write it this way instead of the

fractional way we write 5:12 and say ﬁve in twelve. Proportions can be simpliﬁed in the same

way as fractions, i.e. by canceling common factors.

Example 1 : For every hundred students enrolled in ﬁrst-year Maths at a univer-

sity 55 of them are males. What proportion of ﬁrst-year Maths students at the

university are female?

100

55 = 45 females in every 100

proportion of females =

100

9× 5

100

20× 5

So the proportion of females in ﬁrst-year Maths is

or 9:20. Hence we could say

that for every 20 students enrolled in the ﬁrst year maths course, 9 of them are

female.

Example 2 : In a week a car dealer sells 10 red cars, 8 blue cars, 20 white cars and

2 black cars. What proportion of cars sold were red? What proportion were not

black? Well, 10 + 8 + 20 + 2 = 40 cars were sold in a week. But 10 cars were red

so the proportion of red cars sold is

which can also be denoted 1:4. The proportion of cars sold that were not black is

or 19 : 20.

Percentages Worksheet