Page 119 - MAT KS3 Y8 Cambridge CheckPoint

11.4 Using percentages

11.4 Using percentages

The price of a scarf increases from $20 to $25.
Both prices increase by $5.
The price of a coat increases from $100 to $105.
The price of the scarf increases by 25%.
Both prices have increased by the same amount but they have
The price of the coat increases by 5%.
not increased by the same percentage.
Percentages are a better way than amounts to compare changes of this sort.

Worked example 11.4

There are 247 people at a concert. 103 of them are children.
There are 305 children and 527 adults at a football match.
Which had a larger proportion of children?

103
The fraction of children at the concert is . This is the number of children over the total audience.
247
The percentage of children is 41.7%. This is 103 ÷ 247 × 100.
305
The fraction of children at the match is . The denominator is 305 + 527, the total number of
832
people.
The percentage of children is 36.7%. This is 305 ÷ 832 × 100.
There is a larger proportion of children Compare the proportions with percentages.
at the concert.

✦ Exercise 11.4

1 a Change these fractions to percentages.
13 27 69
b Write the fractions in order from smallest to largest. 17 38 93
2 This table shows the ages of students in three colleges.

School New College City College State College
Under 13 141 183 254
Age
13 or more 291 208 372

a Find the percentage of students who are under 13 in each college.
b Which college has the greatest proportion of students aged 13 or more?

3 The table shows some price changes in
Item Computer Printer Game console Software
a sale. All prices are in dollars.
a Find the percentage reduction Normal price 549 189 135 109
for each item.
b Which item has the best reduction? Sale price 449 119 65 85
4 A survey records how many trains arrive at a
station on time or late on three separate days. Day Friday Saturday Sunday
a Find the percentage of trains that are late
On time 67 53 35
on each day.
b Which day had the best record? Late 10 12 9

11 Percentages 117