Fractions and Percentages MEP Pupil Text 11 - CIMT
[Pages:28]11 Fractions and Percentages MEPPupilText11
11.1 Fractions, Decimals and Percentages
Percentages can be converted to fractions because 'percentage' simply means 'per hundred'. They can also be converted very easily to decimals, which can be useful when using a calculator. Fractions and decimals can also be converted back to percentages.
Worked Example 1
Convert each of the following percentages to fractions.
(a) 50%
(b) 40%
(c) 8%
Solution
(a) 50% = 50 100
=1 2
(b) 40% = 40 100
=2 5
(c) 8% = 8 100
=2 25
Worked Example 2
Convert each of the following percentages to decimals.
(a) 60%
(b) 72%
(c) 6%
Solution
(a) 60% = 60 100
= 0.6
(b) 72% = 72 100
= 0.72
(c) 6% = 6 100
= 0.06
Worked Example 3
Convert each of the following decimals to percentages.
(a) 0.04
(b) 0.65
(c) 0.9
Solution
(a) 0.04 = 4 100
= 4%
(b) 0.65 = 65 100
= 65%
(c) 0.9 = 9 10
= 90 100
Information
= 90%
'Per cent' comes from the Latin , 'per centum', which means 'for each hundred'.
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MEP Pupil Text 11
Worked Example 4
Convert each of the following fractions to percentages.
(a) 3 10
(b) 1 4
(c) 1 3
Solution
To convert fractions to percentages, multiply the fraction by 100%. This gives its value as a percentage.
(a) 3 = 3 ? 100% 10 10
(b) 1 = 1 ? 100% 44
(c) 1 = 1 ? 100% 33
= 30%
= 25%
=
33
1 3
%
Exercises
1. Convert each of the following percentages to fractions, giving your answers in their simplest form.
(a) 10%
(b) 80%
(c) 90%
(d) 5%
(e) 25%
(f) 75%
(g) 35%
(h) 38%
(i) 4%
(j) 12%
(k) 82%
(l) 74%
2. Convert each of the following percentages to decimals.
(a) 32%
(b) 50%
(c) 34%
(d) 20%
(e) 15%
(f) 81%
(g) 4%
(h) 3%
(i) 7%
(j) 18%
(k) 75%
(l) 73%
3. Convert the following decimals to percentages.
(a) 0.5
(b) 0.74
(c) 0.35
(e) 0.1
(f) 0.52
(g) 0.8
(i) 0.04
(j) 0.18
(k) 0.4
(d) 0.08 (h) 0.07 (l) 0.3
4. Convert the following fractions to percentages.
(a) 1 2
(e) 1 10
(i) 8 25
(b) 7 10
(f) 9 10
(j) 7 20
(c) 1 5
(g) 4 5
(k) 7 25
(d) 3 4
(h) 4 50
(l) 2 3
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11.1
MEP Pupil Text 11
5. (a) Complete the equation
2 = ? = 16
3 15
?
(b) Change 7 to a percentage. 20
(MEG)
6. (a) Water is poured into this jug. Copy the diagram and show accurately the water level when the jug is three-quarters full.
(b) What percentage of the jug is filled with water?
(SEG)
7.
Plan of a garden
Orchard
Vegetable Patch
Lawn
Pond
Not to scale
(a) In the garden the vegetable patch has an area of 46.2 m2 . The orchard has an area of 133.6 m2 . What is the total area of the vegetable patch and the orchard? Give your answer to the nearest square metre.
(b) The garden has an area of 400 m2 .
(i) The lawn is 30% of the garden. Calculate the area of the lawn. (ii) A pond in the garden has an area of 80 m2 . What percentage of the
garden is taken up by the pond? (SEG)
11.2 Fractions and Percentages of Quantities
Percentages are often used to describe changes in quantities or prices. For example,
'30% extra free'
'10% discount'
'add
17
1 2
%
VAT'
This section deals with finding fractions or percentages of quantities.
Worked Example 1
Find 20% of ?84.
Solution
This can be done by converting 20% to either a fraction or a decimal.
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MEP Pupil Text 11
Converting to a fraction Note that
20% = 20 = 1 100 5
Therefore
20% of ?84 = 1 ? ?84 5
= ?16.80 .
Converting to a decimal
Note that
20% = 0.2
Therefore
20% of ?84 = 0.2 ? ?84 = ?16.80.
Worked Example 2
A shopkeeper decides to increase some prices by 10%. By how much would she increase the price of:
(a) a loaf of bread costing 90p
(b) a packet of cereal costing ?2.00?
Solution
First note that 10% = 1 . 10
(a) 10% of 90p = 1 ? 90 p 10
= 9p.
So the cost of a loaf will be increased by 9p.
(b) 10% of ?2 = 1 ? ?2 10
= ?0.20 or 20p. So the cost of a packet of cereal is increased by 20p.
Worked Example 3
A farmer decides to sell 25% of his 500 cows. How many cows does he sell?
Solution
First note that 25% = 1 . 4
So he sells 125 cows.
25% of 500 = 1 ? 500 4
= 125.
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11.2
MEP Pupil Text 11
Worked Example 4
Natasha invests ?200 in a building society account. At the end of the year she receives 5% interest. How much interest does she receive?
Solution
First convert 5% to a fraction. 5% = 5 = 1 100 20
5% of ?200 = 1 ? ?200 20
= ?10 . So she receives ?10 interest.
Exercises
1. Find
(a) 10% of 200
(d) 25% of ?100
(g)
33
1 3
%
of
?12
(j) 80% of 20 kg
(m) 5% of 100 m
(b) 50% of ?5 (e) 40% of ?500 (h) 75% of 800 (k) 70% of 5 kg (n) 20% of 50 m
(c) 20% of ?8 (f) 90% of 200 (i) 75% of 1000 (l) 30% of 50 kg (o) 25% of ?30
2. Find (a) 2 of 80 5 (d) 1 of 360 4
(b) 3 of 120 4
(e) 4 of 150 5
(c) 1 of 90 5
(f) 3 of 500 10
3. A firm decides to give 20% extra free in their packets of soap powder. How much extra soap powder would be given away free with packets which normally contain
(a) 2 kg of powder
(b) 1.2 kg of powder?
4. A house costs ?30 000. A buyer is given a 10% discount. How much money does the buyer save?
5. John has invested ?500 in a building society. He gets 5% interest each year. How much interest does he get in a year?
6. Karen bought an antique vase for ?120. Two years later its value had increased by 25%. What was the new value of the vase?
7. Ahmed wants to buy a new carpet for his house. The cost of the carpet is ?240. One day the carpet shop has a special offer of a 25% discount. How much money does he save by using this offer?
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