Fractions, decimals and percentages
2
Fractions, decimals and percentages
This chapter is about working with fractions, decimals and percentages.
Objectives
This chapter will show you how to
If you cook a batch of 40 pancakes, you need these skills to help share them equally with 5 friends.
? find a fraction of an amount using a calculator D ? write one quantity as a fraction of another D ? calculate a percentage increase or decrease D ? write one quantity as a percentage of another D C
? understand and use the retail prices index (RPI) D C
? calculate with fractions using a calculator D C
Before you start this chapter
1 Write down the common factors of 18 and 27.
2 Write down the highest common factor of 48 and 36.
3 Simplify a_48
b_28_0
c_238_2
4 Find the missing number in each of these conversions.
a 7.5 litres 5 ml
b 32mm 5 cm
c 0.6km 5 m 5 cm d_12hour 5 minutes
5 Work out 15% of ?50.
6 Anna needs ?250 to buy a new bicycle. She saves ?18 each week. For how many weeks must she save so that she has enough money?
7 Use your calculator to work out _18_2050_as a decimal.
8 a Convert 24% to a decimal. b Convert 124% to a decimal.
9 Calculate 40 3 _16_000_.
2.1 Fraction of an amount
Why learn this?
Understanding fractions helps you to understand musical note lengths.
Objectives D Find a fraction of an amount with a calculator in complex situations
Skills check
1 Use the and keys on your calculator to calculate these.
a_25 3 720ml
b _79 3 8109
c_13_75 3 655kg
2 Use the and keys on your calculator to calculate each of
the missing numbers. Give your answers as mixed numbers.
a_21_5 3 1 hour 5 minutes
b_15_2 3 1 litre 5 ml
Finding a fraction of an amount using a calculator
There are many makes and models of calculators available.
Most scientific calculators have a fractions key.
The fractions key may look like this
a
b c
or this
.
Make sure you know which is the fractions key on your calculator, and how to use it!
D Example 1 Use a calculator to work out a _15 of 4 cookies b _17_5of 314 cars
a_15_3 4 5 _45_cookies b_17_5_3 314 5 146_18_5_cars
Using the
a
b c
key:
1
a
b c
5 3 4 5
Using the
a
b c
key:
7
a
b c
15 3 314 5
Not all calculators will give the answer as a mixed number ? you'll have to press another button to change it to this form.
D
AO2
Exercise 2A
1 Ryan runs a dog rehoming centre. On average he feeds each dog _34 of a tin of food per day. This week there are 23 dogs at the centre. How many tins of dog food does Ryan need for this week?
D
AO3
2 Heather buys 80 duvets for ?595. She sells _25 of them for ?12 each and _17_6of them for ?10 each. a How much profit does Heather make?
b How many duvets does she have left over?
20
Fractions, decimals and percentages
3 In a school election Jack got _29 of the votes and Rebecca got _49 of the votes. Rebecca had 42 more votes than Jack. How many students didn't vote for Jack or Rebecca?
4 There are 48 members in a scout group. Of these members, _58 are boys. Of the boys, _13 are 12 years old or over. Half of all the scouts are 12 years old or over. How many of the scouts are girls under the age of 12?
D
AO2
2.2 One quantity as a fraction of another
L
Why learn this? This topic often comes up in an exam.
Objectives D Write one quantity as a fraction of another
Skills check
1 Find the missing number in each of these conversions.
a 1kg 5 g
b 1km 5 m
c 1m 5 cm
2 Simplify each fraction to its lowest terms.
a _26
b _18_2
c_12_50
Writing one quantity as a fraction of another
To write one quantity as a fraction of another ? first write both quantities in the same units ? then write the first quantity over the second quantity ? finally, simplify the fraction.
Example 2
a Write 40p as a fraction of ?6.
D
b In Diane's class there are 13 boys and 14 girls. What fraction of the class are boys?
a_64_0_0_0_ 5 _11_5_
Write ?6 as 600p and then write 40 over 600. Remember to simplify the fraction to its lowest terms.
b_12_37_
13 1 14 5 27 students altogether. 13 out of the 27 are boys.
Exercise 2B
1 In Polly's dog training class, three of the dogs pass their elementary certificate. The other four do not pass.
D
What fraction of the dogs pass?
2.2 One quantity as a fraction of another
21
D
2 During April it was sunny for 14 days. What fraction of the days in April were not sunny?
AO2
3 Donna said, 'I've got 5 red sweets and 9 blue sweets so the fraction of my sweets that are red is _59 .' Is Donna correct? Explain your answer.
D
4 In each case, write the first quantity as a fraction of the second.
a ?2, ?7
b 1 hour, 24 hours
c 6 weeks, 8 weeks
D
5 In each case, write the first quantity as a fraction of the second.
a 20p, ?1
b 5 minutes, 1 hour
c 5 days, 2 weeks
d 30cm, 1m
e 750g, 1kg
f 12m, 1km
AO2
6 Lauren gets ?5 pocket money per week. Each week she buys a magazine for ?1.75 and she saves ?1.50. The rest is left over for her to spend on other things. What fraction of her pocket money does Lauren a spend on a magazine b save c have left over?
2.3 Calculating with fractions
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Why learn this?
By learning how to enter fractions into a calculator you can save a lot of time.
Objectives D C Use the fractions key on a calculator with mixed numbers
Skills check
1 Use the fractions key on a calculator to simplify these fractions.
a _23 _46
b _57 55_
c_56_25
2 Use the fractions key on a calculator to convert these mixed
numbers to improper fractions.
a 3_89
b 4_11 27_
c 16_12 _85
3 Use the fractions key on a calculator to convert these improper
fractions to mixed numbers.
a_1_730_
b_11_956_
c_23_223_
Calculating with fractions using a calculator
To carry out any calculations involving fractions, enter the fractions on your calculator using the fractions key. Make sure you practise using your calculator so you become skilled.
22
Fractions, decimals and percentages
Example 3
Calculate
a 3_12 2 1_25
b 4_34 4 _25
c 15 3 2_38
D
a 3_12_ 2 1_25_ 5 2_11_0_
Using the
a
b c
key:
3
a
b c
1
abc
2 2 1
a
b c
2
a
b c
5 5
b 4_34_ 4 _25_ 5 11_78_
Using the
a
b c
key:
4
a
b c
3
abc
4 4 2
a
b c
5 5
c 15 3 2_38_ 5 35_58_
Using the
a
b c
key:
15 3 2 abc
3
a
b c
8 5
Exercise 2C
1 Work out these. Give all your answers as mixed numbers.
a 3_14 1 6_29
b 5_14 2 2_38
c 8_12_5 1 9_11 1_2
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2 A football stadium has 72000 seats. Each seat is _45 m wide. If all 72000 seats were placed next to each other in a line, how long would the line be?
D
Give your answer in
a metres b kilometres c miles. 1km _58 mile
3 Fred added four identical mixed numbers. He got an answer of 8_34 . What were the mixed numbers that Fred added?
4 When Joe was born he weighed 3.5kg. Three months later he weighed 4.75kg. What is his increase in weight as a fraction of his birth weight?
5 AThwe atatepr-ibsuotptecnoendtasionsth1a2t34_34 _12liltirtersesoof fwwaatetre.r pour out every minute. At this rate, how long will the water-butt take to empty? Give your answer in minutes and seconds.
AO2
D
AO3
6 Which calculation gives the largest answer?
a 24 3 _78
b 15 3 1_25
c 8_14 3 2_161_
D
7 A basketball bounces to _45 of the height from which it was dropped.
How high is the second bounce if it is dropped initially from 2_12 m?
2 12 m
? m
2.3 Calculating with fractions
D
AO2
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