fractions - rose park primary...

$: Fractions - ROSE PARK PRIMARY SCHOOLrpps67.weebly.com/.../haese_mathematics_year_6_-_fractions.pdf · Chapter 5 Fractions Contents: A Fractions B Fractions as division C Proper and$
5Chapter 5Fractions

Contents:

A FractionsB Fractions as divisionC Proper and improper fractions

D Fractions of quantities

E Fractions on a number lineF Equal fractions

G Comparing fractions

H Adding and subtracting fractions

AUS_11magentacyan yellow black

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Y:\HAESE\AUS_06\AUS06_05\093AUS06_05.cdr Wednesday, 30 January 2013 9:15:22 AM BRIAN

Opening problem

94 FRACTIONS (Chapter 5)

The students in Amelia’s class have all been given

a week to do a project. So far, Amelia has done3

8,

Charlie has done5

8, and Matilda has done

1

2.

Things to think about:

a Has Amelia completed more of the project than

Charlie?

b Has Amelia completed more of the project than

Matilda?

c Which of the problems a or b was easier to solve? What made the other one harder?

d The next night, Amelia completed another1

2of her project. What total fraction has she

completed now?

Every day we see quantities which can be expressed as fractions. It is therefore important that we

can understand, compare, add, and subtract fractions.

16_ Qw hands

Qt_ open

Qe full

Qr remaining

size 8_ Qw

\\Qw_ apple


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Y:\HAESE\AUS_06\AUS06_05\094AUS06_05.cdr Thursday, 7 February 2013 12:30:29 PM GR8GREG

FRACTIONS (Chapter 5) 95

A fraction is a part of any quantity.

For example, a chocolate bar is divided into 5 equal parts.

If George takes 2 of the parts, we say that George has taken

2

5of the chocolate bar.

2

5is a fraction which shows that we had a whole, we divided it into

5 equal parts, and we are looking at 2 of them.

numerator

bar

denominator

2

5

The numerator shows how many parts we are looking at.

The denominator shows how many equal parts there are altogether.

The fraction wall below shows some of the different ways of dividing a whole into equal parts.

FRACTIONSA

Activity 1 Fraction walls

In words,2

5is

“two fifths”.

| {z }taken byGeorge

Aq_p

1

Qw Qw

Qe

Qt

Qo

Qi

Qu

Qy

Qr

QeQe

QrQrQr

QtQtQtQt

QyQyQyQyQy

QuQuQuQuQuQu

QiQiQiQiQiQiQi

QoQoQoQoQoQoQoQo

Aq_pAq_pAq_pAq_pAq_pAq_pAq_pAq_pAq_p

whole

halves

thirds

quarters

fifths

sixths

sevenths

eighths

ninths

tenths


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Y:\HAESE\AUS_06\AUS06_05\095AUS06_05.cdr Wednesday, 13 February 2013 4:06:37 PM BRIAN


What to do:

Use the fraction wall to complete this table:

Number of

equal parts

One part as

a fractionFraction

in words

All parts form

the fraction

11

1one whole

1

1

a 2 one half

b1

3

c one quarter

d one fifth

e1

6

6

6

f 7

g one eighth

h1

9

9

9

i 10

EXERCISE 5A

1 Write a fraction to show:

a three quarters b two thirds c two fifths

d four fifths e three eighths f five eighths

g two sevenths h three tenths i one hundredth

2 Write these fractions in words:

a1

3b

3

4c

3

5d

7

8

e4

9f

5

7g

5

12h

17

20

i11

30j

4

25k

3

100l

97

100

3 For each of the following fractions, state the numerator:

a2

3b

4

5c

3

7d

1

8

4 For each of the following fractions, state the denominator:

a2

3b

4

5c

3

7d

1

8

PRINTABLETABLE


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Y:\HAESE\AUS_06\AUS06_05\096AUS06_05.cdr Wednesday, 6 February 2013 9:31:44 AM GR8GREG


5 What fraction of the square is shaded?

a b c d

e f g h

i j k l

6 Copy the circles and shade the fractions given:

a1

6b

1

3c

2

3d

5

6

7 Draw a diagram to represent the following fractions:

a2

4b

5

8c

1

9d

4

12

8 Is3

8of this triangle shaded? Explain your answer.

9 What fraction of the dots are red?

a b c

10

What fraction of the cats are: a black b white?


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Y:\HAESE\AUS_06\AUS06_05\097AUS06_05.cdr Wednesday, 30 January 2013 11:02:42 AM GR8GREG

TASTYCHEESE 1 kg

BUTTER


11 a What fraction of the flowers are:

i in the vase ii lying on the table?

b What fraction of the flowers are:

i tulips ii daisies?

12

a What fraction of the children are:

i wearing hats ii not wearing hats?

b What fraction of the children are:

i boys ii girls?

13 Give the fraction shown in each diagram:

a b c

14 Copy and complete the following sketches to show:

a

a glass which is half

full of water

b

a petrol gauge

showing the tank is

three quarters full

c

a pizza with one third

missing

d

the container is3

5full

e

five ninths of the balls

are blue.

PRINTABLEDIAGRAMS

?

BUTTER 1 kgBUTTER

BUTTER 1 kg

?

MILK

1 L

MIL

K

1L

?

E

F

FUEL


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Y:\HAESE\AUS_06\AUS06_05\098AUS06_05.cdr Tuesday, 12 February 2013 9:03:50 AM GR8GREG


When we write a fraction such as1

4bar, the bar indicates division.

So,1

4can be written as 1 ¥ 4, and 1 ¥ 4 can be written as

1

4.

We can see this by dividing a pizza into four equal portions.

Each person will get one quarter of the pizza.

1

pizza

¥ 4

people

=1

4of a pizza each

Self Tutor

Write the following divisions as fractions:

a 2 ¥ 7 b 3 ¥ 8

a 2 ¥ 7 =2

7b 3 ¥ 8 =

3

8

EXERCISE 5B

1 Write the following divisions as fractions:

a 4 ¥ 5 b 1 ¥ 7 c 3 ¥ 10

d 8 ¥ 9 e 2 ¥ 11 f 12 ¥ 13

2 Suppose 2 pizzas are shared equally

between 3 people.

a Look at what Kim gets. What

fraction of a pizza is this?

b Check that the other two people each

get the same amount as Kim.

c Copy and complete:

...... pizzas ¥ ...... people = ...... of a pizza each.

Self Tutor

Write the following fractions as divisions:

a1

6b

4

9

a1

6= 1 ¥ 6 b

4

9= 4 ¥ 9

FRACTIONS AS DIVISIONB

Example 2

Example 1

Bill Jane

Emma Tony

Janice

TeeganKim


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3 Write the following fractions as divisions:

a1

3b

2

5c

7

8

d3

4e

8

13f

11

20

Self Tutor

Write the following fractions as divisions, and hence as whole numbers:

a12

4b

42

6

a12

4= 12 ¥ 4

= 3

b42

6= 42 ¥ 6

= 7

4 Write the following fractions as divisions, and hence as whole numbers:

a20

5b

27

3c

55

11d

7

7

e24

12f

19

19g

0

8h

108

9

A fraction which has numerator less than its denominator is called a proper fraction.

A fraction which has numerator greater than its denominator is called an improper fraction.

For example:2

3is a proper fraction.

4

3is an improper fraction.

4

3=

3

3+

1

3= 1 +

1

3

To see how improper fractions occur, suppose you

and a friend share three cookies. Each person

receives three halves of a cookie, which is3

2cookies.

We can also see that3

2=

2

2+

1

2= 1 +

1

2.

So each person receives one and a half cookies. We

can write this as 11

2cookies.

PROPER AND IMPROPER FRACTIONSC

Example 3

you friend


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Y:\HAESE\AUS_06\AUS06_05\100AUS06_05.cdr Thursday, 31 January 2013 10:33:15 AM GR8GREG


When an improper fraction is written as a whole number and a proper fraction, it is called a

mixed number.

For example, 21

2is a mixed number. It means two

wholes and one half.

We can write mixed numbers as improper fractions, and vice versa.

For example, at a class picnic there were

3 apple pies, each cut into quarters.

Sam ate one quarter of a pie.

We see there are now 23

4pies remaining.

Each whole pie has 4 quarters, and we have 3 quarters of the third pie, so we have 2 lots of 4 plus

3 quarters = 11 quarters.

So, 23

4=

11

4.

Self Tutor

Write 21

3as an improper fraction.

21

3is 2 wholes and one third.

Each whole has 3 thirds, so there are

2 £ 3 + 1 = 7 thirds in total.

) 21

3=

7

3

EXERCISE 5C

1 Determine whether each of the following is a proper fraction, an improper fraction, or a mixed

number:

a3

5b

7

6c

1

9d 3

1

3

e11

8f

8

11g 4

2

5h

40

7

2 What mixed number do these diagrams show?

a b c

Example 4

1 2

3 4

5 6

7 8

9 10

11

1 2

3

4 5

6

7

TASTY CHEESE 1 kg

TAST

TASTY CHEESE 1 kg

TASTY CHEESE 1 kg

TASTY CHEESE 1 kg

50 cm 1 m

2L

1L


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Y:\HAESE\AUS_06\AUS06_05\101AUS06_05.cdr Monday, 11 February 2013 3:38:51 PM GR8GREG


3 This diagram shows 31

2pizzas.

a How many halves are there in

31

2pizzas?

b Copy and complete: 31

2=

::::

2

4 a What mixed number is represented

by this diagram?

b How many quarters are shaded?

c Copy and complete: ...... =::::

4

5 Write as an improper fraction:

a 11

4b 2

1

2c 3

2

3d 2

5

6e 1

3

5

f 51

3g 6

1

2h 2

3

8i 4

1

6j 3

7

10

Self Tutor

Write5

3as a mixed number.

5

3is 5 thirds.

This is 1 whole, and 2 thirds left over.

So,5

3= 1

2

3

6 After the school picnic there were

17 quarter sandwiches left over.

a How many whole sandwiches can

be formed from the quarters?

b Once the whole sandwiches have

been formed, how many quarters

are left over?

c Copy and complete:17

4= ::::::

7 Write as a mixed number:

a4

3b

9

4c

11

6d

16

5e

19

4

f15

2g

14

3h

17

7i

33

10j

35

8

Example 5

1 2

3

4 5


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Y:\HAESE\AUS_06\AUS06_05\102AUS06_05.cdr Thursday, 31 January 2013 10:13:54 AM GR8GREG


8 19 carrots are shared equally between 5 horses.

How many carrots does each horse receive?

Give your answer as a mixed number.

Chris has 18 golf balls. He gives one third of them to his

brother Josh. How many golf balls does Josh receive?

To find out, we can divide the golf balls into 3 equal groups.

We see that1

3of 18 balls is 6 balls.

We also notice that 18 ¥ 3 = 6.

Each group contains1

3of the golf balls.

So, to find1

3of a number, we divide the number by 3.

Self Tutor

Find1

4of 24.

1

4of 24 = 24 ¥ 4

= 6

EXERCISE 5D

1 Find:

a1

2of 10 b

1

2of 36 c

1

3of 12 d

1

3of 45

e1

4of 20 f

1

4of 44 g

1

5of 30 h

1

5of 120

i1

6of 30 j

1

10of 70 k

1

8of 48 l

1

12of 600

FRACTIONS OF QUANTITIESD

Example 6


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Y:\HAESE\AUS_06\AUS06_05\103AUS06_05.cdr Thursday, 7 February 2013 12:32:30 PM GR8GREG


2 Find:

a1

3of 30 people b

1

4of 20 lollies c

1

5of 35 drinks

d1

10of 650 g e

1

2of $38 f

1

4of 60 minutes

Self Tutor

On the first day of school this year, there were 27 Year 6

students in a class.1

3of the students were aged 12 years or

older. How many students were 12 years or older?

The full class is 27 students.

So,1

3of 27 is 27 ¥ 3 = 9 students.

There were 9 students aged 12 years or older.

3 Viktor played 15 games of tennis for his school team. He

won one third of them. How many games did Viktor win?

4 Of the 250 students at a school, one fifth were absent with

chicken pox. How many students were absent?

5 One sixth of the cars from an assembly line were painted

white. If 480 cars came from the assembly line, how many

were painted white?

6 Ling had $900 in her bank account. She spent one fifth of

her money on a new badminton racquet. How much did the

racquet cost?

7 While Evan was on holidays, one eighth of the tomato plants

in his greenhouse died. If he had 96 plants alive when he

went away, how many plants:

a died b were still alive?

Self Tutor

Find2

5of 30.

1

5of 30 is 30 ¥ 5 = 6

)2

5of 30 is 6 £ 2 = 12

Example 8

Example 7To find

13

of 27,

we need to divide 27into 3 equal parts.


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8 Find:

a2

3of 9 b

3

4of 24 c

2

5of 45

d3

5of 35 e

4

7of 21 f

5

6of 54

g7

10of 120 h

8

9of 72 i

13

20of 400

9 55 passengers were on the bus one morning. Two fifths of the passengers were school children.

How many school children were on the bus?

10 Richard spent three quarters of his working day

installing computers, and the remainder of the time

travelling between jobs. If his working day was

8 hours, how much time did Richard spend installing

computers?

11 Sasha shot for goal 16 times during a netball match.

She scored a goal with seven eighths of her shots.

How many goals did Sasha score?

12 A business hired a truck to transport boxes of

equipment. The total weight of the equipment was

3000 kg, but the truck could only carry5

8of the

boxes in one load.

a What weight did the truck carry in the first

load?

b If there were 80 boxes of equal weight, how

many did the truck carry in the first load?

In Chapter 1, we placed natural numbers on a number

line.

We can do the same thing with fractions.

For example, to place the fraction3

4on a number line,

we divide the interval between 0 and 1 into 4 equal parts.

Each of the small intervals has length1

4.

We count 3 intervals from 0, and mark3

4with a dot.

FRACTIONS ON A NUMBER LINEE

0 5 10

3 7

0 1

Er


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0 1 2

1EuTu

0 1 0 1

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0 1 2 0 1 32


Self Tutor

Place the fractions5

7and 1

3

7on a number line.

Since these fractions both involve sevenths, we divide the number line into

intervals of length1

7.

EXERCISE 5E

1 Place the following fractions on a number line:

a2

5and

4

5b

3

6and

5

6c

1

4and

7

4

d2

3and 2

1

3e

6

5and

13

5f

5

8and 1

7

8

g2

10,

5

10, and

9

10h

1

6,

11

6, and 1

1

6i

6

7,

12

7, and 2

2

7

2 Identify the value indicated by the red dot:

a b

c d

e f

g h

3 a Place the fraction1

4on a number line.

b On the same number line, place the fraction3

8.

c Which value is larger,1

4or

3

8? Explain your answer.

4 a Place the fractions2

3and

4

6on the same number line.

b What do you notice about these fractions?

Example 9

2 4 3 4 5


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Investigation Equal fractions


Two fractions are equal if they describe the same amount.

They lie at the same place on the number line.

For example, we can represent the

fractions2

3and

4

6by shading

diagrams.

We see the same amount is shaded

in each case, so2

3=

4

6.

2

3is shaded

4

6is shaded

What to do:

1 a Use grid paper to construct three identical squares with sides 6 cm

long, or click on the icon to obtain a template.

b Divide the first square into two equal halves.

Shade one of the halves, so that1

2of the square is shaded.

c Divide the second square into four equal quarters.

Shade two of the quarters, so that2

4of the square is shaded.

d Do you think that the fractions1

2and

2

4are equal? Check your answer by placing

them on a number line.

e Divide the third square into six equal sixths. How many sixths do you need to shade,

to make a fraction equal to1

2and

2

4?

2 a Draw two circles with radius 3 cm, or print them using the template.

b From the centre of the first circle, measure and rule 3 lines, 120±

apart. Since 3 £ 120± = 360±, you have divided the circle into

thirds. Shade two of the sectors, which is2

3of the circle.

c From the centre of the second circle, measure and rule 9 lines,

40± apart. Since 9 £ 40± = 360±, you have divided the circle

into ninths. Shade six of the sectors, which is6

9of the circle.

d Do you think that the fractions2

3and

6

9are equal? Check your answer by placing

them on a number line.

EQUAL FRACTIONSF

DEMO

TEMPLATE

We

Yo


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Y:\HAESE\AUS_06\AUS06_05\107AUS06_05.cdr Friday, 1 February 2013 12:38:02 PM BRIAN


In the Investigation, you should have found that1

2=

2

4, and

2

3=

6

9.

Notice how these numbers are related:

1

2=

2

4or

1

2=

2

4

2

3=

6

9or

2

3=

6

9

This suggests that:

Multiplying or dividing both the numerator and the denominator by the same non-zero number

produces an equal fraction.

This rule allows us to write a given fraction with a different numerator or with a different

denominator, without changing the fraction’s value.

Self Tutor

Express with denominator 18:

a7

9b

5

6c

22

36

a7

9

=7£ 2

9£ 2f9 £ 2 = 18g

=14

18

b5

6

=5£ 3

6£ 3f6 £ 3 = 18g

=15

18

c22

36

=22¥ 2

36¥ 2f36 ¥ 2 = 18g

=11

18

EXERCISE 5F.1

1 Write3

4with denominator:

a 8 b 12 c 16 d 20

2 Write4

10with denominator:

a 20 b 30 c 50 d 5

3 Express with denominator 8:

a1

4b

1

2c

3

4d 1 e

10

16


a1

2b

4

5c

5

6d

3

10e

1

5

f2

3g 1 h

3

5i

14

60j

18

90

Example 10

*2

*2

/2

/2

*3

*3

/3

/3


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5 Express in hundredths:

a1

2b

1

4c

4

5d

9

10e

7

25

f13

50g 1 h

17

20i

34

200j

44

400

6 Which two of the following fractions are equal?

A8

20B

4

12C

3

8D

1

5

E6

9F

9

24G

3

5H

10

20

SIMPLEST FORM

We say that a fraction is written in simplest form if it is written with the

smallest possible whole number numerator and denominator.

For example, the fraction9

12is not written in simplest form,

because we can write9

12as

3

4.

To write a fraction in simplest form, we must find the largest number that is a factor of both the

numerator and the denominator. We then divide the numerator and denominator by this value.

Self Tutor

Write in simplest form:

a5

20b

8

12

a5

20

=5¥ 5

20¥ 5

f5 is a factor of

both 5 and 20g=

1

4

b8

12

=8¥ 4

12¥ 4

f4 is the largest

factor of both

8 and 12g=

2

3

Example 11

Game Equal fractions

Click on the icon to play a game where you must find equal fractions. GAME

9

12=

3

4

/3

/3

A fraction is in simplest form

when the numerator and

denominator do not have any

factors in common, except 1.


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Y:\HAESE\AUS_06\AUS06_05\109AUS06_05.cdr Friday, 15 March 2013 11:29:49 AM BRIAN


EXERCISE 5F.2

1 Write in simplest form:

a2

4b

4

8c

3

9d

2

10e

5

15

f4

24g

6

10h

20

30i

18

21j

24

32

2 Which of these fractions is written in simplest form?

A6

8B

3

12C

10

21D

14

20E

7

28

We often wish to compare the size of two fractions.

For example, if you were offered3

5or

7

10of a block of chocolate, which would you choose?

If two fractions are written with the same denominator, we can simply compare the sizes of the

numerators.

Self Tutor

Which is larger: a4

7or

6

7b

13

5or 2

1

5?

a 6 is larger than 4, so6

7is larger than

4

7.

b 21

5as an improper fraction is

11

5.

13 is larger than 11, so13

5is larger than 2

1

5.

If two fractions do not have the same denominator, we write one of them as an equal fraction

which has the same denominator as the fraction we are comparing with. We can then compare the

numerators.

Self Tutor

Which is larger:3

5or

7

10?

We multiply the numerator and denominator of3

5by 2, so that both

fractions have denominator 10.

3

5=

3£ 2

5£ 2=

6

10

7

10is greater than

6

10, so

7

10is greater than

3

5.

COMPARING FRACTIONSG

Example 13

Example 12 Convert mixed numbers

to improper fractions

before comparing them.


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FRACTIONS

Discussion

(Chapter 5) 111

EXERCISE 5G

1 Which is larger:

a5

12or

7

12b

4

5or

3

5c

8

9or

13

9

d11

7or 1

3

7e

19

4or 5

1

4f

28

6or 4

5

6?

2 Keith and Caroline ate sushi for dinner. Keith had

31

3pieces of sushi. Caroline cut her sushi pieces into

thirds, and ate 8 of the thirds.

Who had more sushi for dinner?

3 Which is larger:

a1

2or

3

4b

1

3or

3

6c

3

4or

7

8

d5

8or

1

2e

2

3or

5

9f

1

4or

5

20

g4

3or

5

6h

13

15or

6

5i

15

4or 3

1

2?

4 Arnold spends1

3of his income on rent, and

2

9of his income on groceries. Does he spend

more on rent or on groceries?

5 Trent and Meredith each own a cage of birds.

a What fraction of Trent’s birds are yellow?

b What fraction of Meredith’s birds are yellow?

c In which cage is there a greater fraction of yellow birds?

Are improper fractions always larger in size than proper fractions?

Trent’s cage Meredith’s cage


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A pizza is divided into 8 equal pieces. Sam takes 3 pieces,

and Pam takes 2 pieces. This means that together they have

taken a total of 5 pieces.

Notice that Sam has taken3

8of the pizza, Pam has taken

2

8,

and together they have taken5

8.

So,

3

8+

2

8=

5

8

Sam eats 1 of his pieces of pizza, so he has 2 pieces remaining. We can also say that Sam took3

8

of the pizza, he ate1

8of the pizza, and he has

2

8of the pizza remaining.

So,

3

8¡ 1

8=

2

8

To add or subtract fractions with the same denominator, we add or subtract the numerators.

The denominator stays the same.

Self Tutor

Find: a2

5¡ 1

5b

4

9+

7

9

a2

5¡ 1

5

=2¡ 1

5

=1

5

b4

9+

7

9

=4 + 7

9

=11

9

= 12

9

ADDING AND SUBTRACTING FRACTIONSH

Example 14

+ =

¡ =

Sam

Pam


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Y:\HAESE\AUS_06\AUS06_05\112AUS06_05.cdr Friday, 1 February 2013 12:39:12 PM BRIAN


EXERCISE 5H.1

1 Find:

a1

4+

2

4b

2

3¡ 1

3c

5

4¡ 2

4

d3

8+

4

8e

1

5+

3

5f

5

7¡ 3

7

g6

11¡ 2

11h

9

20+

8

20i

21

25¡ 13

25+

1

25

2 Find:

a4

5+

2

5b

7

10+

6

10c

6

7+

5

7

d11

15+

8

15e

10

13+

8

13+

11

13f

11

14+

13

14¡ 1

14

Self Tutor

Find: 2 +4

7+

6

72 +

4

7+

6

7

= 2 +4 + 6

7

= 2 +10

7

= 2 + 13

7

= 33

7

3 Find:

a 3 +1

9+

4

9b 2 +

3

10+

4

10c 5 +

6

7¡ 4

7

d 1 +5

6+

2

6e 4 +

13

15+

4

15f 7 +

12

17+

10

17

Self Tutor

Find3

8¡ 2

8+

5

8, giving your

answer in simplest form.

3

8¡ 2

8+

5

8

=3¡ 2 + 5

8

=6

8

=6¥ 2

8¥ 2f2 is a factor of both 6 and 8g

=3

4

Example 16

Example 15


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Y:\HAESE\AUS_06\AUS06_05\113AUS06_05.cdr Wednesday, 30 January 2013 4:14:11 PM GR8GREG


4 Find, giving your answer in simplest form:

a3

4¡ 1

4b

2

9+

1

9c

7

6¡ 3

6

d1

8+

2

8+

3

8e

8

4¡ 3

4¡ 3

4f

3

10+

7

10¡ 2

10

Self Tutor

Find 23

5+ 8

4

5.

23

5+ 8

4

5

=13

5+

44

5

=13 + 44

5

=57

5

= 112

5

5 Find:

a 22

3+ 1

2

3b 4

3

5¡ 2

1

5c 3

2

7+ 5

3

7

d 62

8¡ 3

5

8e 1

5

9+ 3

2

9+ 4

7

9f 8

1

10¡ 5

7

10+ 6

3

10

6 Simon and Shane went hiking. On the first day

they walked5

9of the total distance. They had a

steep climb on the second day and only walked

2

9of the total distance.

What fraction of the total distance was

completed after 2 days?

7 Leah wrote 11

4pages of a story before tea, and another 2

1

4pages after tea. How many pages

had she completed?

8 Spiros had9

10of a bag of fertiliser. He used

6

10of a bag for his tomatoes.

a What fraction of a bag of fertiliser was left?

b Suppose a full bag contains 20 kg of fertiliser. How many kilograms of fertiliser does

Spiros have left?

Example 17

them to improper fractions.

To add or subtract mixed

numbers, we first convert


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9 Sarah and Jane went apple picking.

Sarah picked 13

5bags and Jane picked 2

4

5bags.

a How many bags of apples did they pick

altogether?

b How many more bags did Jane pick than

Sarah?

ADDING AND SUBTRACTING FRACTIONS WITH UNEQUAL

DENOMINATORS

Sometimes the fractions we want to add or subtract do not have the same denominator.

For example, suppose Anita drinks1

2of a can of soft drink, and

Melissa drinks3

8of the can. What fraction of the can did they

drink?

In the same way that it is easier to compare two fractions if they have the same denominator, it is

also easier to add or subtract fractions if they have the same denominator.

In the situation above, we need to find1

2+

3

8.

We can write1

2with denominator 8 by multiplying the numerator and denominator by 4.

So, we have1

2+

3

8

=1£ 4

2£ 4+

3

8

=4

8+

3

8

=7

8

So, Anita and Melissa drank7

8of the can of soft drink.

Qw

Ei

Multiplying the numerator

an equal fraction.

and denominator by the

same number produces


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Self Tutor

Find:

a5

9¡ 1

3b

3

5+

7

10

a5

9¡ 1

3

=5

9¡ 1£ 3

3£ 3fconverting to 9thsg

=5

9¡ 3

9

=2

9

b3

5+

7

10

=3£ 2

5£ 2+

7

10fconverting to 10thsg

=6

10+

7

10

=13

10

= 13

10

EXERCISE 5H.2

1 Find:

a1

2¡ 1

4b

1

6+

2

3c

5

8¡ 1

4

d1

3+

1

12e

19

30¡ 2

5f

2

7+

30

49

2 Find:

a4

5+

3

10b

10

12+

3

4c

7

9+

21

45d

23

25+

51

100

Self Tutor

Find:

a 11

4+ 2

1

2b 4 ¡ 1

2

3

a 11

4+ 2

1

2

=5

4+

5

2

fconverting to

improper fractionsg=

5

4+

5£ 2

2£ 2fconverting to quartersg

=5

4+

10

4

=15

4

= 33

4

b 4 ¡ 12

3

=4

1¡ 5

3

fconverting to

improper fractionsg=

4£ 3

1£ 3¡ 5

3fconverting to thirdsg

=12

3¡ 5

3

=7

3

= 21

3

Example 19

Example 18


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3 Find:

a 11

2+ 2

3

8b 3

1

3¡ 2

1

6c 1

2

5+ 1

9

10

d 71

2¡ 5

3

4e 2

2

7+ 1

10

21f 6

2

3¡ 3

2

15

4 Find:

a 1 ¡ 4

9b 3 ¡ 1

5

8c 7 ¡ 4

2

7d 9 ¡ 6

5

12

5 Joshua baked a cake to share with friends. Lisa ate2

9, and Rebecca ate

1

3of the cake. What

fraction of the cake did the girls eat between them?

6 Every day, Angus feeds his chickens1

5of a large

tub of feed. If Angus’ tub is9

10full at the start

of the day, how much is left after he has fed his

chickens?

7 Samantha is an artist. She spends 31

2hours on

Saturday painting a portrait, and a further 21

4hours

finishing it off on Sunday.

How long did it take her to paint the portrait?

8 31

8tonnes of earth needs to be removed to level

a housing block. A truck moves 11

2tonnes in the

first load.

How much earth still needs to be moved?

KEY WORDS USED IN THIS CHAPTER

² denominator ² equal fractions ² fraction

² improper fraction ² mixed number ² number line

² numerator ² proper fraction ² simplest form

1 What fraction is represented by the following?

a b c

Review set 5


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Practice test 5A Multiple Choice


2 What fraction of the cars in this car park are blue?

3 Write the following divisions as fractions:

a 6 ¥ 11 b 15 ¥ 19

4 Write as a mixed number:

a9

5b

13

3c

35

6


a5

6b

2

3c

10

24

6 Find:

a1

4of $200 b

2

5of 100 g c

3

8of 56 cm

7 Place the following fractions on a number line:

a1

6and

4

6b

4

8and

11

8c

6

7and 1

4

7

8 An athlete runs2

5of a race in the first hour and

3

10in

the second hour.

What fraction of the race has he completed?

9 Which is larger:

a6

10or

3

10b

19

7or 2

3

7c

4

5or

22

25d 5

2

3or

31

6?

10 Find:

a12

7¡ 8

7b

8

11+

9

11c

3

8+

1

4d 5

1

3¡ 1

1

9

Click on the icon to obtain this printable test.PRINTABLE

TEST


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Practice test 5B Short response

1 Copy this circle and shade5

8of it.

2 a What mixed number is represented by

this diagram?

b Write the mixed number as an improper

fraction.

3 Write these fractions as divisions, and hence as whole numbers:

a40

8b

72

9c

99

11

4 Write as an improper fraction:

a 35

6b 4

3

7c 5

2

5

5 Write in simplest form:

a2

16b

25

45

6 Write5

6with denominator:

a 12 b 30 c 48

7 Sarah went on a holiday for 20 days. It rained

on one quarter of the days. On how many days

did it rain?

8 Which is greater,3

7or

10

21?

9 Find:

a 3 +3

5+

4

5b 4

1

10¡ 2

4

10c

5

6+

14

18

10 A cyclist completes5

14of her training ride in the first hour and

3

7in the second hour.

What fraction of her ride has she completed?


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Y:\HAESE\AUS_06\AUS06_05\119AUS06_05.cdr Tuesday, 5 February 2013 4:15:38 PM GR8GREG

Practice test 5C Extended response


1 Answer the Opening Problem on page 94.

2 At a barbecue, Adam ate 51

3sausages, and Jill ate

32

3sausages.

a Write each of these values as an improper

fraction.

b How many sausages did they eat in total?

c How many more sausages did Adam eat than

Jill?

3 a Place the fraction5

9on a number line.

b On the same number line, place the fraction2

3.

c Which of these fractions do you think is larger?

d Check your answer to c by writing the fractions with the same denominator.

4 Judy has to write 60 Christmas cards to send to her friends and family. She writes1

3of

them on Monday.

a How many cards did Judy write on Monday?

b How many cards does she still need to write?

c Judy writes remaining cards on Tuesday.

i How many cards did she write on Tuesday?

ii How many cards does she still need to write?

5 Caleb had a mathematics test and a spelling test on the same day. The results of each test

are shown below.

Mathematics test

1 6 X 11 16

2 X 7 X 12 X 17 X

3 X 8 13 X 18

4 9 X 14 19 X

5 X 10 X 15 X 20 X

Spelling test

1 X 6 X

2 7 X

3 X 8 X

4 X 9

5 10 X

a What fraction of the mathematics questions did Caleb answer correctly?

b What fraction of the spelling questions did Caleb answer correctly?

c In which test did Caleb answer a greater fraction of questions correctly?

2

5of the


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