1. Percentages
Objectives:
D Grade Express one quantity as a percentage of another
Prior knowledge:
Understand how to:
Convert fractions to equivalent fractions
Convert fractions to decimals
Convert decimals to percentages

2. Percentages
What is a percentage?
per
percent
cent
out of
hundred
So we can think of percentages also as fractions with a denominator
of 100:
This helps us to understand that
finding a percentage of a quantity
is the same as finding a fraction of a
quantity
e.g.
65 percent 65 65
per
cent 00

3. Percentages
Expressing one quantity as a percentage of another
Compare one quantity with the other.
e.g. compare 20 with 25
Write: 20
compare with 25
Write as an equivalent fraction with the denomination 100 20 25 80
100 ≡
This is now 80%
because is the same as 80%
100

4. Percentages
Sometimes you might need to have an intermediate equivalent fraction
e.g. compare 4 with 40
Write: 4
compare with 40
Simplify as an equivalent fraction 4 40 1 10 ≡
Now write as an equivalent fraction with the denominator of 100 1 10 10
100 ≡
This is now 10%
because is the same as 10%
100

5. Percentages
Now do these:
1. Write 4 as a percentage of 20
2. Write 50 as a percentage of 200
3. Write 14 as a percentage of 28
4. Write 4 as a percentage of 25
5. Write 18 as a percentage of 45 4 20 ≡
100 50
200 ≡ 25
100 21 28 ≡ 3 4 10
100 4 25 ≡ 16
100 18 45 ≡ 2 5 40
100

6. Percentages
Harder percentages of quantities can be found using a calculator. 24
compare with
can be read as ÷ 34
Convert from a fraction to a decimal:
Using a calculator:
24 ÷ 34 =
Convert from a decimal to a percentage:
× 100 = 70.59
70.59 %

7. Percentages
Now do these:
1. Write 3 as a percentage of 72
2. Write 42 as a percentage of 76
3. Write 45 as a percentage of 135
4. Write 37 as a percentage of 52
5. Write 92 as a percentage of 56
3 ÷ 72 =
× 100 = %
42 ÷ 76 =
× 100 = %
45 ÷ 135 =
× 100 = %
37 ÷ 52 =
× 100 = %
92 ÷ 56 =
× 100 = %