9
MASTER
Fractions, decimals and
percentages
Check
P15
Strengthen
P17
Extend
P21
5 Which is larger, _2 or _3 ?
1
Test
P25
9.1 Comparing fractions
1
_
6 a Copy this bar. Shade ___
10 .
1
b Copy this bar. Shade _8 .
1
_
_
c Which is smaller, __
10 or 8 ?
1
1
You will learn to:
• Order fractions
• Use fractions to describe parts of shapes.
Key point
7 a Draw and shade bars to show these fractions.
i
_1
5
ii
_1
3
iii
_1
7
The number above the line in a
fraction is the numerator.
The number below the line is the
denominator.
b Write the fractions _3 , _5 and _7 in ascending order.
Fluency
• How many parts would you cut a shape
into to make: halves, thirds, quarters,
fifths?
• What fraction of each shape is shaded?
Why learn this?
You can compare fractions to find the
best deals in the sales.
Discussion Two fractions have different denominators and a
numerator of 1. Can you decide which is larger without drawing bars?
_3
C
Warm up
5
b
D
c
d
Key point
Q2b Literacy hint
3
7 1
Numbers in ascending order go
from smallest to largest.
3 Write each set of fractions in ascending order.
d
7
4
b _9
7
5
__
11
10
__
11
3
__
11
e
_7
9
_7
__
15
3
__
15
4 Angie eats _5 of a pizza. Ian eats _5 .
Who eats more?
2
1
Topic links: Division
1
1
4 _2 … _3
a
Discussion How could you order _8 , _8 and _8 without drawing bars?
_4
__
11
1
1
3 _8 … _2
C
A fraction is a part of a whole.
_6
1
_1
2 _6 … __
12
9 What fraction of each bar is shaded?
3
_1
Reasoning / Modelling
A
b Now write the fractions _25 , _45 and _5 in ascending order.
3
a _7
1
1
_2
1
c _6
9
6
__
15
2
__
15
_4
6
_3
6
10 What fraction of each shape is shaded?
a
b
c
d
e
11 Explore A piece of A5 paper is a fraction of a piece of A4 paper.
What fraction is it?
Is it easier to explore this question now you have completed the lesson?
What further information do you need to be able to answer this?
Explore
B
5
Shop B – _5 off all prices
Which shop offers the better discount? Explain how you know.
1
1
1 _3 … _4
2 a Match each fraction to the correct shaded bar.
_4
numerator
denominator
Work with a partner to complete these statements using < or >.
Shade in squares on a copy of this grid to help explain your answers.
B
A
Shop A – _3 off all prices
1
Explore
A piece of A5 paper is a fraction of a
piece of A4 paper. What fraction is it?
Investigation
1 Which bar shows
1
a _2
b _14 ?
5
1
2
8 Real Two shops are offering different discounts.
Exercise 9.1
_2
1
12 Reflect Choose A, B or C to complete each statement.
Q3 Strategy hint
Draw and shade a diagram to help.
In this lesson, I did...
A well
So far, I think fractions are...
A easy
When I think about the next lesson, I feel... A confident
B OK
B OK
B OK
C not very well
C hard
C unsure
If you answered mostly As and Bs, did this surprise you? Why?
If you answered mostly Cs, write down one question in this lesson that you
found hard. Ask a friend or your teacher to explain this question to you again.
Pi 1, Section 9.1
Unit 9 Fractions, decimals and percentages
Reflect
CONFIDENCE
1 1
2
Check
P15
MASTER
Strengthen
P17
Extend
P21
Test
P25
9.2 Equivalent fractions
5 Write these improper fractions as mixed numbers.
You will learn to:
6 Rectangular chocolate bars are divided into 10 pieces.
a
e
_5_
b
4
7
3
f
_6_
c
5
9
4
g
_9_
__
d
7
11
5
h
12
10
17
6
CONFIDENCE
• Identify equivalent fractions
• Simplify fractions by cancelling
• Change an improper fraction to a mixed number.
Fluency
3
In the fraction 7, what is
• the denominator
• the numerator?
Ossian eats 17 pieces of chocolate.
Write the number of bars of chocolate he has eaten, as a mixed number.
7 For each bar write down the fraction that is shaded.
Explore
How many ways can you describe the
shaded part of this shape?
Why learn this?
Writing fractions in different ways can help
when you are comparing amounts.
Warm up
Q7 hint
a
4
b
u
8
c
u
12
d
u
16
8 Janet and Harrinda order a pancake each.
Janet cuts hers into two equal pieces and eats one piece.
1 Work out the missing number.
a 3×7=u
b 2 × u = 14
c u × 5 = 35
2 Work out
a 24 ÷ 8
d 24 ÷ 6
c 18 ÷ 3
f 77 ÷ 7
b 99 ÷ 11
e 35 ÷ 5
d 6 × u = 18
Harrinda cuts his into four equal pieces and eats two of them.
Q3a hint
3 a How many thirds are there in one whole?
b How many quarters are there in one whole?
c How many fifths are there in one whole?
a Have they eaten the same amount of pancake?
b Copy and complete this statement.
_1_ u
__
=
2 4
4 What fraction of each bar is shaded?
a
b
c
Worked example
d
Which of these fractions are equivalent?
e
3
4
f
Worked example
Write the improper fraction
4 = 11
3 3
u
Discussion What can you say about the size of these fractions?
Exercise 9.2
_4_
3
as a mixed number.
Three thirds make one whole.
There is one third left over.
4
3
3
3
3
a
b
c
d
= 1 whole
Topic links: Multiples and factors, Sequences
1
3
Key point
An improper fraction is a fraction in
which the numerator is greater than
the denominator.
A mixed number has a whole
number part and a fraction part.
An improper fraction can be written
as a mixed number.
2
3
6
8
Draw the fractions
as bars, all the
same length.
3
4
2
3
6
8
Equivalent fractions are fractions
that represent the same amount
but use different numerators and
denominators.
Q9 hint
3 6
=
4 8
Equivalent fractions are the same size.
4
5
2
3
4
5
9 Which of these fractions are equivalent?
2
3
Key point
3
6
8
10
3
6
8
10
Unit 9 Fractions, decimals and percentages
4
Check
P15
MASTER
10 Match the equivalent fractions in the diagram.
8
Write 16
= u = u.
1
3
2
6
3
6
4
12
1
2
a
1
2
×
=
×3
6
=
×
18
b
×3
1
3
=
×
6
×2
=
12
×2
Key point
5
Simplify 10
Multiplying or dividing the numerator
and denominator by the same
number gives an equivalent fraction.
When the numerator and
denominator are as small as
possible, the fraction is simplified.
For example
÷5
Both 5 and 10 can be divided by 5, so divide
the numerator and denominator by 5.
5 = 1
10
2
÷5
a
÷10
10
20
=
b
50
=
60
c
2
6
90
=
110
=
1
3
÷2
÷5
a
5
15
=
b
25
=
35
c
15
=
55
2
4
How many counters would each player get if there were
a 2 players
b 3 players
c 4 players?
1
=
b
6
=
10
c
18
14
=
20
1
3
Explore
÷
15 Explore How many ways can you describe
the shaded part of this shape?
Is it easier to explore this question now you have completed the lesson?
What further information do you need to be able to answer this?
6
Q16a hint
i Look back at Q4.
ii Look back at the first worked
example.
iii Look back at Q7.
16 Reflect
a This lesson used lots of pictures. Copy and complete these sentences.
i ‘Pictures help with understanding fractions because __________________’
ii ‘Pictures help with understanding improper fractions because _________’
iii ‘Pictures help with understanding equivalent fractions because ________’
b Close your eyes and think of one third.
What did you see, a fraction or a picture? Write or draw what you saw.
Pi 1, Section 9.2
Draw a bar for 18.
Divide it into thirds.
1
Find 3 of 18
÷2
a
1 A game for 2 to 4 players has 12 counters.
Worked example
÷
14 Copy and complete
Exercise 9.3
2 Sally loses 4 of the counters for the game in Q1.
a How many are lost?
b How many are left?
÷
13 Copy and complete
Why learn this?
Doctors calculate fractions of a dose of
medicine depending on the weight and age
of the patient.
Explore
How would a doctor work out how
much of a dose would be required for
different weight patients?
÷2
12 Simplify these fractions.
Copy and complete
Fluency
Work out
• 20 ÷ 5
• 30 ÷ 10
• 66 ÷ 6
• 49 ÷ 7
• 32 ÷ 10
Warm up
×
CONFIDENCE
• Calculate simple fractions of quantities.
Worked example
Reflect
Test
P25
You will learn to:
11 Use your answer
to Q10 to copy
and complete.
5
Extend
P21
9.3 Calculating with fractions
Q10 hint
8
16
Strengthen
P17
1
How many in each 3?
18 ÷ 3 = 6
3 Work out
a
e
1
3
1
9
of 30
b
of 27
f
1
2
1
4
c
of 10
g
of 24
Discussion How could you find
1
100
1
5
1
6
of 25
d
of 18
h
1
7 of 14
1
10 of 50
Q3 hint
1
7
1
5
of 21
Q4 hint
of 50
Use division to help you.
Draw bars to help you.
of a number?
4 Work out
a
e
1
3
1
9
of 12
b
of 81
f
1
4 of 24
1
10 of 40
c
g
1
8
1
6
of 32
d
of 42
h
Unit 9 Fractions, decimals and percentages
6
Check
P15
MASTER
1
c 80
h 150
d 55
i 274
e 99
j 352
Some of your answers will be
decimal numbers.
6 Real / Finance The price of this bag is
1
reduced by 4 in a sale.
a Work out of £20.
b How much is the bag in the sale?
• Add and subtract simple fractions.
£20 − £u = £u
£20
7 Real / Finance Two shops sell MP3 players at
the same original price. Both shops have a sale.
Which MP3 player is cheaper?
Explain how you know.
1 OFF
3
1 OFF
4
8 Real / Finance All the prices in a clothes
1
shop are reduced by 3 in a sale.
For each item work out
1
a 3 of the price
b the sale price.
ALL PRICES REDUCED BY
£33
9 A shop sells jeans for £45.
1
It reduces the price by 10 in a sale.
1
a Work out 10 of £45
b Copy and complete:
Sale price of jeans = £45 − £u = £u
c Work out the sale price of
i a jacket, original price £36
ii a pair of trainers, original price £98
iii a shirt, original price £29.50.
1
3
£12
USUALLY £160
1
NOW
OFF
10
of
£40
1
11 of
£99
1
7
of
£21
1
5
of
£30
1
4
of
£16
1
9
of
£81
Hint
1
3
b
c
d
b
‘To write a fraction in its simplest
form’ means to ‘simplify’ it.
c
Warm up
3 Write these improper fractions as mixed numbers.
d
9
5
9
7
b
e
8
3
7
4
c
f
3
2
11
6
Worked example
1
5
Explore
Reflect
Work out +
11 Explore How would a doctor work out how much of a dose would be
required for different weight patients?
Is it easier to explore this question now you have completed the lesson?
What further information do you need to be able to answer this?
12 Reflect The final task in the investigation asked you to write a tile to
match the odd one out.
Write another tile to match the odd one out.
Discuss with a classmate how you worked out what to write on your tile.
Topic links: Factors, Division, Dividing by 10
Q2 Literacy hint
Work out the answer for each tile.
of
£9
2 Write a new tile to match the odd one out.
7
a
£180 REDUCED
1
by
5
Garage B
1 Each of these tiles has a matching pair except one. Find the odd one out.
Explore
How do builders decide how much
mortar to use for different sized bricks?
1 What fraction of each of these bars is shaded?
a
1
8
• sevenths
are there in one whole?
Why learn this?
Distances and measurements are often
given as fractions. To work out a total
distance you need to add them.
a
Investigation
of
£20
• fiths
2 What fraction of each of these shapes is shaded?
Write each fraction in its simplest form.
Garage A
1
5
Fluency
How many
• quarters
Exercise 9.4
£18
£45
10 Real Two garages offer different deals on tyres.
Which garage has the cheaper tyres?
of
£30
Test
P25
You will learn to:
Q6b hint
1
4
1
6
Extend
P21
9.4 Adding and subtracting fractions
Q5 hint
b 700
g 88
CONFIDENCE
5 Find 10 of
a 40
f 123
Strengthen
P17
1
5
2
5
1 + 2= 3
5 5 5
+
2
5
=
3
5
The denominators are the same,
so add the numerators.
Q12 hint
What did you do first? Then what did
you do?
Pi 1, Section 9.3
4 Work out
a 13 + 13
b
2
10
f
e
1
+ 10
2
1
7+7
4
3
11 + 11
c
g
2
2
5+5
5
2
12 + 12
d
h
1
3
9+9
1
7
+ 15
15
Discussion What is a quick way of adding fractions with a
common denominator?
Key point
Fractions with a common
denominator have the same
denominator. (They have that
denominator ‘in common’.)
Unit 9 Fractions, decimals and percentages
8
Check
P15
MASTER
Worked example
3
5
Work out −
3–1 2
=
5 5 5
• Understand percentage as ‘the number of parts per 100’
• Write a percentage as a fraction or decimal.
9
6
10 − 10
f
4
7
6
7
− 27
c
− 27
g
5
4
6−6
11
3
15 − 15
d
h
4
2
5−5
10
9
11 − 11
Discussion What is a quick way of subtracting fractions with a
common denominator?
1
Q6a hint
6 Amy walks 7 of a mile each day.
a How far does she walk in two days?
b How far does she walk in a week?
You could draw a bar model to
help you.
7 A recipe for a batch of biscuits uses 14 of a cup of sugar. Hayden
makes two batches of biscuits. How much sugar does he use?
7
9
+ 39 =
d
3
5
+ 25
u 1u
=
9 9
e
4
9
+ 79
b
6
9
+ 59
c
6
7
+ 37
f
7
7
11 + 11
g
2
3
+ 13
When the numerator and
denominator are the same, the
fraction equals one whole.
b Write five pairs of fractions which add to 1.
•
•
•
Why learn this?
Companies use percentages to record how much
profit they have made.
•
•
23
100
5
10
9
10
37
100
99
100
Explore
Which savings account gives you the
best interest rate?
1 Simplify these fractions. Divide by 2, 5 or 10.
Key point
9 a Work out the missing numbers in these calculations.
3 u 5
4 u 7
5 u
+
= =u
+
= =u
+
=1
5 5
5
7 7
7
11 11
Fluency
Write these fractions as decimals.
Exercise 9.5
8 Work out these additions. Write your answers as mixed numbers.
a
CONFIDENCE
e
b
Test
P25
You will learn to:
The denominators are the same,
so subtract the numerators.
5 Work out
2
1
a 3−3
Extend
P21
9.5 Introducing percentages
3
5
1
– 5
2
= 5
1
5
Strengthen
P17
a
15
40
b
30
70
c
18
22
d
70
90
e
8
10
f
25
55
2 What fraction of each of these grids is shaded?
a
b
c
d
Q1a hint
÷5
15
45
=
÷5
a 1 – 11
12 =
c 1–
12 – 11 = u
12 12 12
2
5
d 1–
b 1 – 73 =
4
9
e 1–
2
3
u–3 u
=
7 7 u
f 1–
7
8
11 Angharad cuts a pizza into 12 slices.
She eats 4 slices and her friend Barney eats 3 slices.
a What fraction of the pizza have they eaten altogether?
b What fraction of the pizza is left?
Reflect
Explore
12
Warm up
10 Copy and complete these subtractions.
Q11a hint
u
1 pizza = 12
4
1
9
of the guests at a party drink cola and 9 drink lemonade.
The rest drink tea.
a What fraction drink cola or lemonade?
b What fraction drink tea?
13 Explore How do builders decide how much mortar to use for
different sized bricks?
Is it easier to explore this question now you have completed the lesson?
What further information do you need to be able to answer this?
14 Reflect
a Write down two fractions that add to more than 1.
b Copy and complete this sentence about your fractions.
u
u
Q14 hint
Worked example
Write why you chose the numerator
and denominator of each fraction.
Show that your fractions add to more
than 1.
Write an addition calculation for your
fractions and find the answer.
What percentage of this grid is shaded?
Key point
Per cent means ‘out of 100’.
‘%’ stands for ‘per cent’.
There are 100 squares.
35 out of 100 squares are shaded.
So 35% is shaded.
‘I chose u and u because __________________________’
9
Pi 1, Section 9.4
Unit 9 Fractions, decimals and percentages
10
3 What percentage of each of these grids is shaded?
b
50
1
a 50% = 100 = 2
b 10% =
u
100
10% = u = u
u
c 1% = 100
d
1% = u
u
u
u
d 25% = 100 = 20 = 4
e 75% =
75
25% = u
75% = u
u
10 Write these percentages as fractions in their simplest form.
u
u
fraction as a percentage?
100
How do you write a percentage as a fraction?
5 Finance For every £100 Tim earns, he pays £20 in tax.
What percentage does Tim pay in tax?
£20 out of £100 = u%
Key point
Worked example
You can write percentages as
fractions or decimals.
Write 20% as a fraction.
First write 20% as a fraction of 100.
÷2
20% = 20 = 2 = 1
100 10
5
÷10
Then simplify the fraction by dividing the numerator
and denominator by the same number. Keep doing
this until the fraction is in its simplest form.
÷2
7 Write these percentages as fractions.
a 91% =
u
100
d 30%
b 19% =
e 70%
u
100
Write 35% as a decimal.
Write 35% as a fraction out of 100. Then
divide 35 by 100 to write it as a decimal.
8 Write these percentages as decimals.
a 45%
b 67%
c 81%
d 42%
e 99%
f 94%
g 73%
h 87%
i 90%
j 37%
k 5%
l 7%
m 9%
n 3%
o 1%
Discussion What is a quick way of writing percentages as decimals?
11
÷10
100
=
÷10
Worked example
35
35% = 100 = 0.35
c 60% =
100 = 10 = 5
u
u
40% =
u
100
=
÷10
10
=
5
÷2
11 Write down each percentage and its equivalent fraction from the table.
70%
21
100
51%
1
10
80%
39
100
21%
4
5
10%
7
10
39%
51
100
Warehouse B
1
5
off all prices.
a Write 40% as a fraction.
b Which warehouse offers the better discount?
100
30% =
u
Warehouse A 40% off all prices.
u
f 90%
u
100 = 10 = 5
÷2
÷10
12 Finance Two furniture warehouses offer different discounts.
Q7d hint
c 37% =
u
b 80% =
Q5 hint
6 Finance A bank account pays £2 interest on savings of £100.
What percentage is this?
÷10
Q10a hint
u
a 40% = 100 = 10 = 5
4 Write the fractions shown in Q2 as percentages.
Discussion How do you write a
u
10
13 a Write 60% as a fraction.
b Complete the statements below using < or >.
i
ii
1
5
4
5
u 60%
u 60%
Explore
c
You need to know these fraction,
decimal and percentage conversions.
50% = 0.50 = 0.5
1
10
=
Q9 hint
14 Explore Which savings account gives you the best interest rate?
Is it easier to explore this question now you have completed the lesson?
What further information do you need to be able to answer this?
15 Reflect Which is easier
• writing a percentage as a fraction
• writing a percentage as a decimal?
Explain why.
Pi 1, Section 9.5
Q15 hint
Write ‘________________ is easier,
because _____________________.’
Unit 9 Fractions, decimals and percentages
Reflect
a
9 Write these percentages as fractions and decimals.
The first one has been done for you.
12
Check
P15
MASTER
Strengthen
P17
Extend
P21
7 Finance Last year farmers were paid 30p per litre of milk. They are
paid 10% less this year.
How much are they paid per litre this year?
9.6 FINANCE: Finding percentages
8 Finance A freelance hairdresser charges £30 an hour. She has to
pay 10% to the salon she works at.
a How much does she pay to the salon?
b How much does she earn per hour?
Discussion When you know 10% of £30, how can you use this to
easily work out 20% of £30?
You will learn to:
Find 1% of 300
Explore
Can you ever be 110% confident?
Can the price of something be 110% of
the original?
Why learn this?
Price increases and decreases are often
given in percentages. You can use them to
work out whether you are getting a good deal.
b 350 ÷ 10
e 720 ÷ 10
c 840 ÷ 100
f 55 ÷ 10
2 Find 50% of
a 30
d 54
b 90
e 18
c 160
f 19
3 Finance All prices are reduced
by 50% in a sale.
How much is the reduction
on each item?
b 30
e 94
1
50% is the same as 2.
To find 50% of an amount you divide
by 2.
100%
50%
Topic links: Number system
c 740
h 75
d 3000
i 99
e 9000
j 199
10 Finance A car showroom increases all its prices by 1%.
Work out the increase in price for each of these vehicles.
a Peugeot £10 000
b VW £12 000
c Toyota £13 000
d Vauxhall £15 000
e Audi £18 000
f Alfa Romeo £25 000
g BMW £35 000
h Porsche £51 000
11 Finance Jon receives a pay rise of 1%. Before this he earned
£45 000 a year.
a How much is his pay rise?
b How much does he earn now?
Investigation
SALE
50%
£460
£26
£184
DVD
c 250
f 123
Finance
A savings account pays 1% interest each month.
At the beginning of January Shane put £10 000 into the account.
1 a How much interest will he receive at the end of January?
b How much will he now have in his account?
2 a How much interest will he receive at the end of February?
b How much will he now have in his account?
3 Work out how much he will have in his account at the end of March.
00:00
Key point
1
10% (‘ten per cent’) is the same as 10.
To find 10% of an amount you divide by 10.
100%
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
6 Finance A bank pays 10% interest on all its accounts each year.
How much interest would each of these amounts earn in a year?
a £3000
b £1200
c £180
d £445
e £183
f £963
13
50%
2 parts
4 Finance The price of petrol increases by 50%.
Before this it was £0.90 per litre.
a How much does it increase by?
b What is the price now?
5 Find 10% of
a 400
d 85
Key point
b 920
g 56
To find 1% of an amount you divide
by 100.
10 parts
12 Explore Can you ever be 110% confident?
Can the price of something be 110% of the original?
Look back at the maths you have learned in this lesson.
How can you use it to answer this question?
13 Reflect Write down what you think is the most important thing to
remember when working with percentages.
Compare what you have written with others in your class.
Have you written the same?
If no, then try to convince others that what you wrote is more
important.
Pi 1, Section 9.6
Explore
Warm up
Exercise 9.6: Real-life percentages
1
1% = 100
So to find 1%, divide 300 by 100.
300 ÷ 100 = 3
9 Find 1% of
a 600
f 50
1 Work out
a 20 ÷ 10
d 240 ÷ 100
Key point
Worked example
Q13 hint
Look back at everything you have
learned in this lesson and lesson 9.5.
Reflect
CONFIDENCE
• Calculate percentages.
Fluency
1
Work out 2 of
• 30
• 50
• 25
FINANCE
Test
P25
Unit 9 Fractions, decimals and percentages
14
Master
P1
Strengthen
P17
CHECK
Extend
P21
9 Check up
Test
P25
Log how you did on your
Student Progression Chart.
Equivalent fractions, decimals and percentages
11 Match each percentage to its equivalent fraction.
60%
81%
1
10
1
2
10%
50%
1
4
1
100
1%
25%
6
10
81
100
Fractions
12 Write whether each statement is true or false.
1 a Match each fraction to a diagram.
1
2
3
6
1
6
a 10% = 0.01
5
6
d
B
A
3
10
b 0.23 = 23%
e
= 0.03
19
100
= 1.9
c
1
2
= 50%
f 60% = 0.6
13 Write 30% as
C
D
a a decimal
Finding percentages
b Which pair of fractions are equivalent?
2 Which two of these fractions are equivalent?
14 Carys eats 17 sweets out of a packet of 100.
What percentage is this?
2
4
3 Write these fractions in order from smallest to largest.
3
14
1
14
15 Find 50% of £36
7
14
16 Find 1% of 230
4 Copy and complete this statement using > or <.
1
3
17 In a sale 10% is taken off all the prices.
a Work out 10% of £75
b What is the sale price of an item costing £75?
… 15
5 Work out
1
a 3 of 36
b
1
5
of 30
18 How sure are you of your answers? Were you mostly
1
4
6 A sale advertises off all prices. A pair of trousers costs £28 before the sale.
Just guessing
1
4
a Work out of £28
7 What fraction of each bar is shaded? Simplify your answers where possible.
Challenge
19
a
b
1
4
of £24 = £6
Write down three different questions with fractions of amounts that have the answer £6
20 Describe a system for finding 90% of any number.
c
8 Write these improper fractions as mixed numbers.
4
3
b
9
5
9 Work out
4
3
a 13 + 13
b
19
23
c
12
11
d
11
6
5
+ 23
10 Work out these calculations. Simplify your answers where possible.
4
3
3
1
a 10 – 10
b 8+8
15
Confident
What next? Use your results to decide whether to strengthen or extend your learning.
b What is the sale price of the trousers?
a
Feeling doubtful
Reflect
2
3
c
19
20
4
− 20
e
4
9
5
9
+
d 1−
f
5
6
2
5
+ 62
21 One hundred people were surveyed and
asked which TV channel they were
watching at 8 pm the previous evening.
a How many people were watching
Channel 4?
b What percentage of the 100 people
surveyed is this?
c What percentage were watching BBC1.
d What percentage were watching either
Satellite TV or Channel 5?
e True or false?:
1
4
Television channel watched
T
30
25
Frequency
1
2
b a fraction
20
15
10
5
0
BBC 1
BBC 2
ITV
Channel Channel Satelite
4
5
TV
Other
Channel
of viewers were watching ITV.
Unit 9 Fractions, decimals and percentages
16
Master
P1
STRENGTHEN
Check
P15
Extend
P21
Test
P25
9 Strengthen
9 What should you divide by to find these fractions of an amount?
a
1
4
b
1
5
1
7
c
d
Q9a hint
1
9
10 Four people have a bill for £48. They decide to split it into quarters.
How much do they each pay?
You will:
• Strengthen your understanding with practice.
parts
11 A team of football players share their winnings of £66 between them.
1
They take 11 each.
How much does each player get?
12 Copy and complete these simplified fractions.
Fractions
4 5
10
1 Which is the largest fraction in each set of three bars?
a 3
b 5
12
Q1 hint
6
7
7
12
Which bar has the most parts
shaded?
2
7
1
12
7
2 Which is larger
a three quarters or two quarters
7
9
2
9
3 Look at the bars. Which is larger, 51 or
1
12 ?
d
11
12
6
12
or
or
11
15 ?
Read out loud, ‘seven ninths or ….?’
1
5
b
1
9
or
1
3
c
1
7
or 18?
You could draw bars to help you.
Make the two bars the same length.
5 Work out the number shown by the shaded part.
10
a
b
20
c
1
6 Find 3 of 15
12 4 3 5
15
20 4
5
d
15 4
5
1
Draw a bar to show 3.
1
15
a 12
b 27
Work out how many in one part.
c 18
1
8 a Find 4 of 20
1
b Find 5 of 10
Q8a hint
Draw a bar to show
20
1
4.
1
1
17
4
f
4
2 5 1
7
14
10 5 2
11
55
4
4
How many parts are shaded?
How many parts are in the whole bar?
What fraction of the bar is shaded?
What fraction of the bar is unshaded?
Q14 hint
a
b
c
d
Use the steps in Q13.
Q16a hint
Red
b
c
2
7
5
9
When you add amounts of the same
thing (whatever it is), just add the
actual amounts. For example,
3 bananas + 1 banana = u bananas.
Blue
Q16b hint
+
+
3
7
2
9
Read out loud, ‘two sevenths add …’.
Q17a hint
17 Work out
1
4
a 12 + 12
b
4
7
+ 27
c
4
9
1
9
d
3
11
+
Draw a bar showing twelfths.
Colour in one twelfth and four twelfths.
How much is coloured altogether?
5
+ 11
Q18a hint
18 Complete these calculations.
c Find 6 of 12
d Find 10 of 30
410
45
e
4
16 a Three fifths add one fifth is u.
Q6 hint
7 Find 3 of
30 5
40
4
15 A spinner is shaded red and blue.
Gwennan says, ‘The spinner has two colours
and one of them is red. So half the spinner is red.’
a Explain why she is wrong.
b Draw a spinner with one half red.
12
10 4 2 5
5 5
20
410
c
14 What fraction of each bar is shaded?
Q4 hint
4 Which is larger
or
4
45
13
a
b
c
d
1
12
1
2
d
4
1
5
a
2
42
Q2c hint
b three fifths or two fifths
7
15
or
b
4 5 2
9
18
e
c
42
a
Work out how many in one part.
7 2 u
a 9–9=9
6 3 u
b 11 – 11 = 11
4 1 u
c 5–5=5
Read out loud, ‘seven ninths take
away two ninths is u.’
Unit 9 Fractions, decimals and percentages
18
19 Work out
1
1
a 1−5
1
c 1−3
d 1−4
5
6
2
3
7
9
15
20 Work out
a 1−
3
5
b 1−
c 1−
d 1−
1
5
5
4
21
of these bars are shaded.
a How many whole bars are shaded?
b Copy and complete this statement.
5
4
Finding percentages
Q19a hint
1
b 1−7
1
5
5
5
1
5
1
5
1
5
Read out loud, ‘five fifths minus
three fifths.’
= 14
22 a Draw bars to show
b Copy and complete this statement.
u
=13
a
e
9
8
u
= 15
=
uu
8
u
b
9
7
f
11
9 =
= 17
uu
u
b 500
c
7
6
g
13
8
=
u1
6
u
= uu
d
8
5
h
11
6 =
=
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
c 420
b £320
Q3a hint
100%
c £450
d £17
b 1400
e 450 m
c £1500
f 900 kg
5
50%
50%
Q5 hint
To find 1% divide by 100.
Enrichment
uu
parts
d 88
parts
5 Find 1% of
a 300
d 300 km
23 Copy and complete
6
5
2 Find 10% of
a 30
4 Find 50% of
a £60
5
3
5
3
100%
1 a What do you divide by to find 10%?
b Work out 10% of £60
3 a What do you divide by to find 50%?
b Work out 50% of 34
Q20a hint
u
Q1a hint
1 The graph converts fractions to percentages.
uu
u
100%
90%
Equivalent fractions, decimals and percentages
Q1b hint
1 a What fraction of this grid is not shaded?
b What percentage of the grid is shaded?
Remember that u% is another way
of saying ‘u out of 100’.
Percentage
80%
70%
60%
50%
40%
30%
20%
10%
2 Copy and complete these equivalent fractions and percentages.
a
b
c
0
1
5
2
5
3
5
Fraction
4
5
5
5
Use the graph to copy and complete these conversions.
=
%
100
=
3 Write these percentages as fractions.
u
u
u
a 59% = 100
b 23% = 100
c 51% = 100
d 19%
e 17%
f 93%
4 Write these percentages as fractions and then simplify the fraction.
÷10
÷10
a
b
30% =
100
=
70% =
10
100
÷10
c
100
=
÷10
19
10
÷10
÷10
d
÷10
10% =
=
10
90% =
100
=
=
%
100
=
%
Q3 hint
How many squares out of 100 would
you colour in?
a
3
5
= u%
b
u
5
= 80%
c
1
5
= u%
2 a What fraction of each shape is shaded?
b Look at the fractions and use any patterns you notice to help
you write three more equivalent fractions.
3 Write down the next three terms in each of these sequences.
a 51, 52, 53, 54, …
b
11 9 7
,
11, 11 11,
…
11 9
, 13, …
c 1, 13
4 Reflect Tammy said, ‘In this lesson, I am doing lots of dividing.’
Look back at your work in these Strengthen lessons.
Write down the numbers of three questions where you were dividing.
For each one, write whether you were working with fractions or
percentages, or both.
Do you agree with Tammy?
Reflect
22
=
=
100
10
÷10
Unit 9 Fractions, decimals and percentages
20
Master
P1
Check
P15
Strengthen
P17
Test
P25
EXTEND
9 Extend
You will:
Children’s wards
6 Work out 20% of
To work out 20%, find 10% and
multiply by u.
b 189 cm
c 194 ml
a 30% of 560
b 90% of 430
c 70% of 670
d 40% of 720
e 80% of 820
f 60% of 380
d 265 km
7 Work out
1
5 Accident and Emergency
1
15 Elderly Services
30%
10% 10% 10% 10% 10% 10% 10% 10% 10% 10%
9 Finance Computer prices are reduced by 30% in a sale. A tablet costs £520.
What does it spend the most on from this list?
a Work out 30% of £520
2 The pictogram shows the favourite sports in a school.
a Which is the most popular sport?
b How many people chose swimming?
c How many people chose hockey?
d How many people were surveyed altogether?
Q7a hint
8 Scott works out 50% by working out 10% and then
multiplying by 5. Caroline finds 50% by halving.
Use both methods to find 50% of 70.
Which method did you find easier?
1 Finance A hospital records what fraction of its budget it spends on
different departments.
Maternity
Q5b hint
a £321
• Extend your understanding with problem-solving.
1
8
1
9
5 a What is 10% of 721?
b What is 20% of 721?
Favourite sport
Rugby
Football
b Work out the sale price of the tablet.
10 What fraction of each shape is shaded?
Write each answer in its simplest form.
Key:
5 20 students
a
b
c
d
e
f
T
Tennis
Hockey
Swimming
3 Finance
a A shop sells shoes for £100. The price is reduced in a sale to £75.
What percentage were the shoes reduced by?
b Amit puts £100 into a savings account. He receives interest and after
a year has £102.
What percentage interest does he get per year?
4 100 people were asked which type of restaurant is their favourite.
Favourite restaurant
50
a
Frequency
40
35
c 1% of 4 kg
d 50% of 3 km
3
5
+ 35 + 25
b
11
6
15 + 15
4
+ 15
19
20
c
11
+ 13
20 + 20
13 Prices are reduced by 10% in a sale. A TV costs £650.
a Work out 10% of £650
b What is the sale price?
30
25
14 Two cycle shops are having a sale. Each shop sells similar bikes.
20
15
10
5
Italian
British
Indian Mexican
Thai
Chinese
Type of restaurant
T
a What percentage of people preferred Thai restaurants?
b What fraction of people preferred
i Indian restaurants
ii Italian restaurants
Topic links: Types of number, Bar charts, Proportion
Shop A:
Original price £99
1
9
Shop B:
Original price £100
10% off all prices
off all prices
a Work out the sale price of the bike in each shop.
b You want to buy the cheapest bike.
Which shop would you buy it from?
15 A competition offers these prizes.
• 50% of £120
•
iii Mexican or Thai restaurants?
Give your answer as fractions in their simplest form.
21
b 10% of £66
12 Work out these. Write your answers as mixed numbers.
45
0
11 Work out
a 50% of 50 cm
1
5
1
9
of £300
• of £900
Which prize is worth the most?
Subject links: Science (Q23)
Unit 9 Fractions, decimals and percentages
22
16 Write down the next two terms in each of these sequences.
a 21, 1, 121, 2, …
b 41, 42, 43, 1, 141, …
23 STEM A baby is expected to gain 50% of its birth weight after
3 months. A newly born baby weighs 8 lbs.
How much should she weigh after 3 months?
17 a Sort these cards into sets of three equivalent values.
0.5
0.1
1%
10%
0.12
0.91
0.25
1
2
0.01
25%
1
10
91%
1
100
24 The marks in an exam are
50%, 65%, 70%, 70%, 95%, 60%, 63%, 72%, 70%, 75%
a What is the modal mark?
b What is the mean mark?
c What is the range of marks?
Write 0.5 = u = u
1
4
19
100
19%
91
100
Q17a hint
0.83
0.19
83%
25 Finance For Christmas Chanelle is given £200. She spends 51 on
clothing and 52 on an MP3 player. She saves the rest.
a How much does she spend on clothing?
b How much does she spend on an MP3 player?
c What fraction does she spend?
d What fraction does she save?
e How much does she save?
50%
b Which card does not belong with a group?
c Write two other cards to complete the set for the odd one out.
18 Work out
a 51 of 20 cm
b
1
3
of £33
c
1
4
d
of 48 kg
1
9
of 27 inches
19 During a 10-hour flight a pilot spends
•
1
10
of the flight in a holding pattern
•
1
20
of the flight climbing
•
1
20
of the flight descending
•
8
10
of the flight cruising.
27 Finance Annie Matts leaves £48 000 in her will. She leaves
• 51 to her son
• 10% to her granddaughter
1
• 12
to her sister
• the rest to charity.
a Work out how much she leaves to each person.
b How much is left to charity?
1
5
20 A rectangle has a perimeter of 20 cm. One of the sides measures of
the total perimeter.
a What is the length of this side?
b What are the lengths of the other sides?
c Calculate the area of the rectangle.
28 Problem-solving Write a list of 10 numbers so that 50% of them
1
are odd, 10
are multiples of 5 and 15 are larger than 60.
B
Q21 hint
5
6
1 65
Q28 hint
Work out how many of each type of
number you need.
50% of 10 = u
Write 6 = u
11
6
7
10
17
100
2 65
17
6
1
4
70%
10
12
25%
1
10
10%
17%
A baby spends
1
• 2 of the day sleeping
1
• 4 of the day playing
1
• 6 of the day crying
1 How many hours are left for eating?
2 Write a problem-solving question like this about your day.
5
Key
Car
i train
Bus
ii bus
T
Train
i train
1
Investigation
A
22 Real The pie chart shows how students travel to school.
a What fraction travel by
iii car?
b What percentage travel by
2
To work out 5 , work out 5 and multiply
by u.
26 Which is greater, 31 of £60 or 51 of £200?
Work out how long she spends doing each.
21 Match each value in column A
with a value in column B.
Q25 hint
29 Reflect Sarah and Jim are discussing Q17.
Here is what they said they did.
• Sarah says, ‘First, I looked at each percentage and tried to find a
matching decimal. Then, I looked at each decimal and tried to find a
matching fraction. That’s how I found the odd one out.’
• Jim says, ‘First, I listed all the decimals in my book. Then, beside
each decimal, I wrote its matching percentage and fraction.
Then I compared my lists with the cards. That’s how I found the
Q29 hint
odd one out.’
Write ‘____ method is best, because
Write down what you did to answer Q17.
_____________________________.’
Which method is best, Sarah’s, Jim’s or yours? Explain why.
Reflect
83
100
ii bus
iii car?
23
Unit 9 Fractions, decimals and percentages
24
Check
P15
Master
P1
Strengthen
P17
Extend
P21
TEST
11 Convert these percentages to fractions.
9 Unit test
Log how you did on your
Student Progression Chart.
a 33% =
u
b 10% =
100
u
=
100
u
10
c 50% =
u
100
=
u
10
=
u
2
12 What fraction of these shapes has been shaded?
a
b
1 Write these fractions in order from smallest to largest.
7
9
2
5 12
13 , 13 , 13 , 13 , 13
c
2 a What fraction of each shape is shaded?
i
ii
13 Work out
a
iii
b
1
3
b
1
3
10 + 10
3
+ 10
c
4
5
− 53
d 1 − 47
15 Which is the odd one out in each of these lists? Explain why.
1
3
a 50% 0.05
of 18
5 70 dog owners completed a survey. 17 of the dog owners said they visited
the vet regularly.
How many is this?
1
2
16 Copy and complete
u
5
a 4 = 1u
b 10% 0.1
b
7
=
5
1
100
c 7% 0.7
7
10
uu
u
17 Work out
a 76 + 72
b 51 + 54 + 53
Give your answers as mixed numbers.
6 Write down the number that makes these sentences correct.
a If you cut a pizza into twelfths you cut it into ____ pieces.
b To find 18 you divide by ____.
c Calculating 15 is the same as dividing by ____.
18 A savings account rewards savers with 1% interest on their savings
each year. Ellie invests £450.
How much interest does she receive after a year?
7 In a test of 100 questions Chaitra correctly answered 53 questions.
What percentage did she get?
Challenge
8 Work out
a 15 of £65
b
1
7
of 35 metres
c
1
9
of 99 kg
9 Match each question with the correct answer.
A 10% of 4000
i 40
B 1% of 400
ii 4
C 50% of 80
iii 400
D 10% of 80
iv 80
E 50% of 160
v 8
d
1
5
of 345 litres.
19 Write these in order of size from smallest to largest by converting them
to fractions.
0.25
29
100
24%
30%
0.03
20 Work out
a
1
2
1
4
of 600
b
1
3
1
5
of the answer to part a
c of the answer to part b
d of the answer to part c
All your answers should be whole numbers.
e Find a number smaller than 600 for which this would also work.
f How many other numbers can you find for which this would work?
21 Reflect Which question in the unit test made you think the hardest?
Explain why.
Q21 hint
Write, ‘Question ___ made me think
hardest, because ______________.’
Reflect
4 Work out
a 12 of 14
c
+ 39
14 Write these percentages as decimals.
a 45%
b 63%
b Which two fractions in part a are equivalent?
3 Which is the smallest fraction?
a 17
b 19
4
9
10 Everything is reduced by 10% in a sale.
The original price of a pair of sneakers was £40.
a Work out 10% of £40.
b What is the sale price of the sneakers?
25
Unit 9 Fractions, decimals and percentages
26