Chapter 11
(percentages)
In this chapter you will learn more about percentages.
11.1 Using mental method
Some percentages are easy to find because they are
simple fractions. But some of them are hard to find because they are not always
a simple fraction.
Example
Question
26% of 78 =
20.28
Use this
fact to find:
A)52% of $78 B) 13% of 78 kg C) 65% of 78 km
D) 104% of 78 million
Answer
A) 20.28 × 2 = 40.56 B) 20.28 ÷ 2 = 10.14 C)
D) 20.28 × 4 = 81.14
Question
à Work out:
A) 12.5% of 80 B)
0.5% of 7000 C) 150% of 62
D) 125% of 260 E) 110% of 36
à Work out:
A) 35% of 84 B) 49% of 230 C) 77% of 4400
D) 99% of 7900 E) 45% of 56000
11.2 comparing different quantities
You will often need to compare groups that are
different sizes.
Example
Question
This table shows the results of a survey in a factory.
|
SMOKER
|
NON-SMOKER
|
TOTAL
|
MEN
|
12
|
64
|
76
|
WOMEN
|
9
|
32
|
41
|
A) What percentage of men are smokers?
B) Compare the
percentages of men and women who are non-smokers
Answer
A) 12/76 × 100% = 15,78 %
B) Men : 64/76 ×
100 % = 84,21 %
Women: 32/41 × 100% = 78,04 %
Question
Ø
There were 270 people in cinema. There were 168 women and 102 men.
There were
152 people in a theatre. There were 78 women and 74 men.
A) Work out the percentage of women in each venue.
B) Work out the
percentage of men in each venue.
Answer
A) 113,3
B) 86,3
11.3 percentages changes
You can use
percentages to describe a change in a quantity. It could be an INCREASE or a
DECREASE.
Question
Ø The price of a car was $ 20.000. In a sale, the price decreased by 4%.
After the sale it increased by 4%
A) What mistake has Ahmad made?
B) What is the
correct price after the sale?
Ahmad said”
the price after the sale is % 20.000 again”
Answer
A) Estimating the
sale price
B) 4%4= 4/100 ×
$20 000 = 800
= 20 000 – 800 = 19 200
Price after sale = 4/100 x 19 200
= 768
= 19 200 + 768
11.4 Practical
examples100 x $20 0
Profit: sell for more
than you buy
Loss: sell for less
than you buy
Discount: reduction
in the price, it is usually given as a percentage
Interest: bank
charges
Tax: if you buy
something the price may include a additional price.
Examples
Question
Ø A women bought an old chair for $240. She sold
it for $ 300
Work out the
percentages profit.
Ø A man
bought a car for $ 15 900. He sold it for
$9500
Work out the
percentages loss.
Ø A bottle
of juice costs $ 6.50
If you buy six bottle
you can get 10% discount.
Work out how much he
sells them for.
Answer
Ø $ 300 - $
240 = 60
60/240 x 100 % = 25 %
Ø 15 900 –
9500 = 6400
6400/15900 x 100% =
40, 25 %
Ø 6 x 6.5 =
39
Discount = 10/100 x
39 = 3, 9
After discount = 39 –
3, 9 = 35, 1
39-35, 1 = 3.9
00 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
= 19 200 + 7684% =>
4/100 x $20 000 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
= 19 200 + 7684% =>
4/100 x $20 000 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
= 19 200 + 7684% =>
4/100 x $20 000 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
= 19 200 + 7684% => 4/100
x $20 000 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
4% => 4/100 x $20 000 = 800
= 20 000 - 800 =
19.200
price after sale = 4/100 x 19 200 =
768
= 19 200 + 768