USING MENTAL METHOD: 11.1
Some
percentages are easy to find because they are simple fraction.
*if
you know 10%, you can find any multiple of 10%
EXAMPLE:
1. a)
35% of 84 b) 49% of 230
35% = 25% + 10% 50% -
1%
25% = 21 50% = 115
10% = 8,4 1% = 2,3
35% = 21 + 8,4 49 % = 155 – 2,3
=
29,4 =112,7
C)
77% of 4400 d) 99% of 7900 e) 45% of 56 000
77% = 100% - 25% + 2% 99%= 100% - 1% 45% = 50% - 5%
100%
= 4400 100% = 7900 50% = 28 000
25% = 1100 1% = 79 5% = 280
2% = 44 99% = 7900 - 79 45% = 28000 - 280
77% = 4400 – 1100 + 44 = 7821 =27720
=3344
2. A. look at alicia's method for finding 85%.
Answer = 50% + 25% + 10%
B. work out 85 % of:
i) 7200g ii) $64 iii) 3.6m/ 360cm iv) 1800ml
50% = 3600 50% = 32 50% = 180 50% = 900
25% = 1800 25 % = 16 25% = 90 25% = 450
10% = 720 10% = 6,4 10% = 36 10 % = 180
85 % = 3600 + 1800 + 720 85% = 32+16+6,4 85% = 180+90+36 85% = 900+450+ 180
= 6120g = $272/$5 = 306cm/3,06m = 1530ml
v) 85 second
50% = 42.5
25% = 21.25
10% = 85
85% = 42.5+21.25.85
= 72,25
3. Use this fact ( 26% OF $78 = 20.28 ) to find:
a) 52% of $78 b) 13% of 78kg C) 65% of 78 d) 104% of 78 milion
20.28 x 2 = 41 20.28 / 2 = 11 20.28 x 4 = 82
COMPARING DIFFERENT QUANTITIES: 11.2
You will need to compare groups that are different size.
EXAMPLE:
1. 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 value
cinema: 168/270 x 100 = 62%
theatre: 78/152 x 100 = 52%
b) work out the percentage of men in each value
cinema: 102/270 x 100 =38%
theatre: 74/152 x 100 = 48%
2. There are 425 girls & 381 boys in a school. 31 girls & 48 boys are overweight.
a) work out the percentage of the girls are overweight
31/425 x 100 = 7%
b) work out the percentage of the boys are overweight
48/381 x 100 = 12%
c) work out the percentage of all the students that are over weight
79/860 x 100 = 9%
3. This table shows the result of survey in factory
smoker non-smoker total
men 12 64 76
women 9 32 41
a) What percentage of men are smoker
12/76 x 100 = 15%
b) Compare the percentage of men and women who are non-smoker
men: 64/76 x 100 = 84%
women: 32/41 x 100 = 78%
PERCENTAGE CHANGES: 11.3
You can use percentages to describe a changes in a quantity. it could be increase or decrease.
A percentage change is always calculated as a percentage of the initial value.
The initial value is 100%. it is important to choose the correct value to be 100%.
EXAMPLE:
1. Here are the prices of three items in Alain,s shop.
Game 40% Phone $120 Computer $500
Alain increase all the prices by $10. Find the percentage increase for each items.
Game: 10/40 x 100 = 25% Phone: 10/120 x100 = 8.3% Computer: 10/500 x 100 = 2%
2. These are the masses of three children one April.
Luke 6 kg Bridget 14 kg Tomas 25 kg
Over year, the mass of each of them increased by 10%. Work out the new mass of each child.
Luke: 10/100 x 6 =0.6kg Bridget: 10/100 x 14 = 1,4kg Tomas: 10/100 x 25 = 2,5kg
3. The price of a car was $20 000. In ta sale, the price decreased by 4%.
After the sale it increased 4%.
a) What mistakes has Ahmad made?
estimating the sales price
b)What is the correct price after the sales?
4% => 4/100 x $20 000 = 800
= 20 000 - 800 = 19.200
price after sale = 4/100 x 19 200 = 768
= 19 200 + 768
PRACTICAL EXAMPLES: 11.4
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:
1. A woman bought an old chair for $240. She sold it for $300.
Work out the percentage profit.
$300 - $240 = 60
60/240 x 100% = 25%
2. A man bought a car for $15 900. He sold it for $9500
Work out the percentage loss.
15 900 - 9500 = 6400
6400/15900 x 100% = 40,25%
3.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.
6 x 6.5 = 39
Discount = 10/100 x 39 =3,9
after discount = 39 - 3,9 = 35,1
39-35,1 = 3.9