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11.1 Using mental methods

11.1 Using mental methods

Some percentages are easy to #nd because they are simple fractions.

!ere are examples of these on the #rst page of this unit. If you know 10%, you can
fi nd any multiple of 10%.
You can use the easy ones to work out more complicated percentages.

You can o"en do this quite easily. You do not always need a calculator.
Worked example 11.1
There are 4600 people in a stadium. 58% are males. How many is that?

100% = 4600
58% = 50% + 10% – 2% These are all easy percentages to fi nd.
50% = 2300 50% = 1 2 You could have found
1
10% = 460 10 is easy. Just divide by 10. 50% + 5% + 3%.
1% = 46 Divide 10% by 10 to fi nd 1%. Is that easier?
58% = 2300 + 460 – (2 × 46) = 2668 Do this sum in your head or on paper.

) Exercise 11.1 Do not use a calculator in this exercise

1 Work out:
a 35% of 84 b 49% of 230 c 77% of 4400 d 99% of 7900 e 45% of 56 000.

2 Look at Alicia’s method for finding 85%. 85% = 50% + (3 × 10%) + (5 × 1%)
a Find a better way to work out 85%.
b Work out 85% of:
i 7200 g ii $64 iii 3.6 m iv 1800 ml v 85 seconds.
3 Work out:
a 12.5% of 80 b 0.5% of 7000 c 150% of 62 d 125% of 260 e 110% of 36.

4 26% of 78 = 20.28 You can have
more than 100%.

Use this fact to find:
a 52% of $78 b 13% of 78 kg c 65% of 78 km d 104% of 78 million.

5 19% of 256 = 48.64

Use this fact to find:

a 19% of 128 b 9.5% of 256 c 19% of 512 d 9.5% of 512.
6 a Show that 30% of 65 is the same as 65% of 30.
b Show that 20% of 45 is the same as 45% of 20.
c Now try to generalise this result.

7 Copy and complete this table.
Percentage 5% 20% 40% 60% 80% 120%

Amount ($) 72

104 11 Percentages