Page 117 - MAT KS3 Y8 Cambridge CheckPoint

11.3 Finding percentages

11.3 Finding percentages

There are times when you need to write one number as a
To write a fraction as a decimal,
percentage of another.
divide the numerator by the
Here are some examples:
denominator.
r writing a price increase as a percentage 7 = 7 ÷ 8 = 0.875
r finding the percentage of people who are unemployed 8
r estimating the percentage change in a population.
To write a decimal as a percentage,
To write one number as a percentage of another, write the multiply by 100.
numbers in the form of a fraction and then change the 0.875 = 87.5%
fraction to a percentage.

If the numbers are simple, you can do this mentally. For more complicated numbers, use a calculator.

Worked example 11.3

a There are 40 people on a bus and 28 are women. What percentage are women?
b One Monday, the bus carried 364 passengers and 157 were women. What percentage were women?
c On Tuesday there were 427 passengers. What is the percentage increase in the number of passengers?

a The fraction who are women is 28 = 7 . It is easy to cancel the numbers to give a simple fraction.
7 40 10 1 7
= 70% are women. = 10% so = 7 × 10 = 70%.
10 10 10
157
b The fraction who were women is . This fraction does not cancel to a simple fraction.
364
157
= 0.431… Divide to find the equivalent decimal, 157 ÷ 364 = 0.431…
364
0.431… = 43.1% Multiply the decimal by 100 to get the percentage. Round
the answer if necessary.
c The increase is 427 − 364 = 63.
63
The percentage increase is × 100 Divide by the initial number of passengers, 364, not by 427.
= 17.3% 364

✦ Exercise 11.3

1 a Anders’ test marks are
Science: 7 out of 10 History: 17 out of 20 Geography: 27 out of 40
shown in the box.
Change each of them to English: 37 out of 50 Maths: 67 out of 80 Art: 17 out of 30
a percentage.
b Which subject gave him the best mark?

2 There are 753 students in a college. 419 are female.
a What percentage of the students are female? b What percentage of the students are male?

3 Sasha is reading a novel with 427 pages. She has read 276 pages.
a What percentage has she read? b What percentage has she still got to read?
4 There are 24 men and 36 women in a choir.
a What percentage of the choir are men? b What percentage are women?
c 10 more men and 10 more women join the choir. What are the percentages of men and women now?

11 Percentages 115