Percentages
1. Per cent means 'out of 100'
2. Percentage of a shape
3. Converting between percentages and decimals
4. Converting between percentages and fractions
5. Percentage of a number
Per cent means 'out of 100'
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The sign % stands for 'per cent' which means 'out of 100'.
So 40% means 40 out of 100 and 11% means 11 out of 100.
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Percentage of a shape
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40% of this shape is shaded because the shape is divided
into 100 equal parts and 40 of those 100 parts are shaded
(it wouldn't matter which 40 parts were shaded).
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To work out the percentage of this shape that is shaded,
you must first work out what each part represents.
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There are 20 equal parts, so each part represents 5%.
100% (the whole) ÷ 20 = 5%
6 of the parts are shaded, so 30% of the total shape is shaded.
6 x 5% = 30%
Converting between percentages and decimals
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To change a percentage to a decimal, divide by 100.
Change 48% to a decimal: 48 ÷ 100 = 0.48
To change a decimal to a percentage, multiply by 100.
Change 0.67 to a percentage: 0.67 x 100 = 67%
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Converting between percentages and fractions
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Write the percentage as a fraction over 100 and
then simplify:
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Learn these equivalent fractions and percentages:
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Percentage of a number
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To find 20% of 30, convert the 20% to a decimal and then
multiply by 30.
20% = 0.2
0.2 x 30 = 6
This is the best method as it always works.
Another way to find 20% of 30 is to first find 10% of 30
and then multiply by 2.
10% of 30 is 30 ÷ 10 = 3
2x3=6
Or a third way would be to recognise that 20% is
equivalent to one fifth, and so just divide 30 by 5.
30 ÷ 5 = 6
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Test Questions
1. In a block of 100 flats, 35 flats have a blue front door. What percentage of the
flats have a blue front door?
a) 3.5%
b) 35%
c) 70%
2. What is 40% as a fraction?
a) two fifths
b) one fifth
c) one half
3. What is one quarter as a percentage?
a) 25%
b) 20%
c) 4%
4. Joe got 15 out of 25 in a maths test. Emma got 65%. Who got the better result?
a) Joe
b) Emma
c) They both got the same result
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5. 75% of the children in a football team are boys. What percentage are girls?
a) 75%
b) 50%
c) 25%
6. What is 88% as a decimal?
a) 88
b) 8.8
c) 0.88
7. What is 1% of 500?
a)1
b) 5
c) 50
8. What is 50% of £80?
a) £40
b) £50
c) £80
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9. A 150 gram chocolate bar says it contains 20% cocoa. What is the weight of the
cocoa in grams?
a) 30 grams
b) 40 grams
c) 50 grams
10. In a survey, 15 out of 50 children had a pet cat. What percentage is this?
a) 7.5%
b) 15%
c) 30%
Answers:
1) Since there are a total of 100 flats and 35 of them have blue front door so the
percentages of flats with blue front door is (35/100)x 100 = 35%
2) 40/100 = 4/10=2/5 therefore the answer is two fifths
3) one quarter is ¼,
To calculate the percentage amount, multiply ¼ with 100
=> ¼ x 100 = 25%
4) Joe got 15/25, therefore he got (15/25) x 100 % i.e. 60 %
whereas Emma has 65 %
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so Emma’s result is better.
5) Since 75% of the team members are boys therefore percentage of girls is (100-75) =
25%
6) 88 % = 88/100 = 0.88
7) 1 % of 500 = (1/100) x 500 = 5
8) 50 % is 50/100 = ½
therefore 50 % of £80
= ½ x 80 = £40
9) Total weight of the bar = 150 g
Percentage of cocoa = 12 %
Therefore weight of cocoa is (12/100) x 150 =30 grams
10) To calculate the percentage multiply 15/50 with 100
therefore Percentage is (15/50) x 100 = 30%
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