Understanding Percentages

Percentages are fractions with a denominator of 100.

For example,	50 percent (50 %) = =
	20 percent (20 %) = =

Changing a fraction or decimal to a percentage - simply multiply by 100.

Examples:	x 100 = 50		so	= 50 %
	x 100 = 25		so	= 25 %
	x 100 = 33		so		= 33		%
	0,35 x 100 = 35		so	0,35 = 35 %
	0,625 x 100 = 62,5		so	0,625 = 62 %

Changing a percentage to a decimal or fraction - simply divide by 100.

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Finding a Percentage

Example 1: Work out 25 % of 40.

Method: Write 25 % as a fraction and then multiply by 40.

	25 % of 40	=		x 40
		=	x 40
		=	10

Example 2: Calculate 50 % of 60.

		=		x 60
		=	x 60
		=	30

10 % = = so 10 % of a quantity is simply one tenth, which can be worked out by dividing by 10.

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Increasing or Decreasing by a Percentage

Example 1: Increase R40 by 8 %.

Method: Work out the 8 % and add it on.

	8 % of 40	= of 40
		= 40 ÷ 100 x 8
		= 3,2 (calculator method)

So, 8 % of R40 = R3,20 (note: calculator will give 3,2, but this must be written as R3,20 for money)

Now add this on to R40 to give R43,20.

OR

Work out (100 + 8) % of 40	= 108 % of 40
	= of 40
	= 40 ÷ 100 x 108 (on calculator)
	= R43,20

Example 2: Decrease R40 by 8 %.

In this case, we subtract the 8 %.

R40 – 3,20 = R36,80

OR

100 – 8 = 92 so 92 % of 40 = R36,80 (giving the answer directly)

Reduction = 30 % of 80 = R24

Sale price = 80 – 24 = R56

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Writing an Amount as a Percentage

This is the same thing as writing as a fraction, then changing it to a percentage.

Example 1: I score 18 out of 20 in a test. What is this as a percentage?

	Fraction	=
	x 100	=	100 ÷ 20 x 18
		=	90
	So,	=	90 %

Example 2: I have 40 sweets and I eat 8. What fraction have I eaten?

=

20 %

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