Page 120 - MAT KS3 Y8 Cambridge CheckPoint

11.4 Using percentages

5 In a music examination candidates can get a distinction, a pass or a fail.
Here are the results.
a Compare the proportion of boys and girls who gained
a distinction. Distinction Pass Fail
b Compare the proportion of boys and girls who failed. Boys 28 214 35
c Did boys or girls do better in the examination? Girls 23 91 37
Give a reason for your answer.

6 Users gave feedback on three music tracks they had been listening too. They rated them
as poor, average, good or excellent. Here are the results.
a What percentage of the feedback Poor Average Good Excellent Total
for each track was average?
Track A 30 24 64 31 149
b Which track had the highest
Track B 9 24 27 23 83
proportion of average ratings?
Track C 6 18 22 20 66
c Which track had the highest
proportion of ratings that were either good or excellent?
d Which track got the best feedback? Give a reason for your answer.

7 The table shows the masses, to the nearest
kilogram, of two groups of adults who were Underweight Normal Overweight Total
recorded as underweight, normal or
Women 245 562 314 1121
overweight.
Use percentages to compare the weight Men 85 266 285 636
distributions of men and women. Comment
on the proportions that are underweight and the proportions that are overweight.

Summary

You should now know that: You should be able to:
★ A percentage is a fraction out of a hundred. ★ Calculate percentages and solve problems
★ You can find a percentage of a quantity by writing involving them.
the percentage as a fraction or a decimal and ★ Calculate percentage increases and decreases and
converting. solve problems involving them.
★ You can find simple percentages mentally. For ★ Express one given number as a fraction or
more complicated questions, you can use written percentage of another.
working or a calculator. ★ Use equivalent fractions, decimals and
★ You can find a new amount after a percentage percentages to compare different quantities.
increase (or decrease) by first calculating the ★ Calculate accurately, choosing operations and
increase (or decrease) and then adding it to (or mental or written methods appropriate to the
subtracting it from) the original amount. numbers and context.
★ Percentages are a good way to compare parts of, or ★ Solve word problems involving percentages.
changes to, two different quantities.
★ When solving a word problem using percentages,
it is important to choose the calculations carefully
to avoid errors.

118 11 Percentages