# compare quantities as percentages by LHqv7zW

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```									                               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
Percentages

What is a percentage?
percent
percent
out of
hundred

So we can think of percentages also as fractions with a denominator
of 100:
e.g. 65 percent           This helps us to understand that
finding a percentage of a quantity
per    65               is the same as finding a fraction of a
cent    00
00               quantity
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      80
≡
25     100
This is now 80%        because 80 is the same as 80%
100
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      1
≡
40     10
Now write as an equivalent fraction with the denominator of 100
1    10
≡
10   100

This is now 10%       because 10 is the same as 10%
100
Percentages

Now do these:
4        20
1.        Write 4 as a percentage of 20         ≡
20       100
50       25
2.        Write 50 as a percentage of 200       ≡
200      100
21       3     10
3.        Write 14 as a percentage of 28        ≡        ≡
28       4 100
4.        Write 4 as a percentage of 25      4        16
≡
25       100
5.        Write 18 as a percentage of 45    18       2     40
≡       ≡
45       5     100
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 = 0.7059

Convert from a decimal to a percentage:

0.7059 × 100 = 70.59

70.59 %
Percentages

Now do these:

1.        Write 3 as a percentage of 72        3 ÷ 72 = 0.04167
0.04167 × 100 = 4.167 %
42 ÷ 76 = 0.5526
2.        Write 42 as a percentage of 76
0.5526 × 100 = 55.26 %
45 ÷ 135 = 0.3333
3.        Write 45 as a percentage of 135
0.3333 × 100 = 33.33 %
37 ÷ 52 = 0.7115
4.        Write 37 as a percentage of 52 0.7115 × 100 = 71.15 %
92 ÷ 56 = 1.6429
5.        Write 92 as a percentage of 56 1.6429 × 100 = 164.29 %

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