Primary 4 Mathematics...© 2016 Marshall Cavendish Education Pte Ltd Primary 4 Mathematics My Pals Are Here, Book B, Chapter 8: Fractions Shaping Maths, Book A, Unit 3: Fractions ©

© 2016 Marshall Cavendish Education Pte Ltd

Primary 4 Mathematics

My Pals Are Here, Book B, Chapter 8: FractionsShaping Maths, Book A, Unit 3: Fractions

Fractions


Chapter Learning Outcomes

• Understand mixed numbers• Understand improper fractions• Convert improper fractions to mixed numbers• Convert mixed numbers to improper fractions• Compare and order fractions • Find a fraction of a set


Understand Mixed Numbers

A mixed number is made up of a whole number and a fraction.

Mixed numbers have values greater than 1.

+ =34

34

1 1 34



68

= 34

Express the fraction part in its simplest form.

3 68 is another example of a mixed number.

+ =68

1 1 1 68

The common factor of 6 and 8 is 2.

6 8

34

=÷ 2

÷ 2



Number lines can be used to show mixed numbers.

0 1 2

mixed numbers

16

26

36

46

56

13

12

23

123

11

6 12

6 13

6 14

6 15

6

11

3 11

2

Identify and on

the number line. 11

3 11

2


Let’s Try!What mixed number does each of the following represent? Express each mixed number in its simplest form.a)

b)

c)

2 5

6

2 12

2 48

2 1

4

=


Let’s Try!Find the missing fractions on the number line.

0 1 2 15

25

35

45

115

125

135

145


Understand Improper Fractions

44

54

64

, and are improper fractions. An improper fraction has a value equal to or greater than 1.

1 quarter = 14 2 quarters = 2

4 3 quarters = 34 4 quarters =

44

5 quarters = 54 6 quarters =

64


Understand Improper FractionsNumber lines can be used to show improper fractions.

An improper fraction can be expressed as a whole number or a mixed number.

improper fractions

0

1 2

17

27

37

47

57

67

77

87

97

107

117

127

137

147

11

7 12

7 13

7 14

7 15

7 16

70


Let’s Try!

What improper fraction does each of the following represent?

a)

b)

c)

318

85

134

8

13 quarters =

31

fifths =

eighths =


Let’s Try!Fill in the missing improper fractions in their simplest forms.

1 2 3

44

54

64

74

94

84

52

114

124


Let’s Try!

Express each improper fraction in its simplest form.

83

92

166

226

a)

c)

b)

d) 308

3510

72

154


Convert Improper Fractions to Mixed Numbers

= 4 thirds= 3 thirds + 1 third= 1 whole + 1 third

43

43= 3

3+ 1

3=1+ 1

3=11

3

43Convert to a mixed number.


Let’s Try!Convert each improper fraction to a mixed number or a whole number. Express each answer in its simplest form.

213

125

a)

c)

b)

d) 326

184

7 2 2

5

5 1

3 4 1

2


Convert Mixed Numbers to Improper Fractions

2 13=

63+

13

=73

2 13

Convert to an improper fraction.

63

13


a)

c)

b)

d)

Let’s Try!

Convert each mixed number to an improper fraction. Express each answer in its simplest form.

2 46

168

167

3 45

83

137

195

74


Compare and Order Fractions

52

74Which is smaller, or ?

74

52is smaller than .

52

74 =

× 2

× 2

52

104


Since and are both greater than 1, compare

and .is greater than . So, is greater than .


85

43Which is greater, or ?

85

85

43

35

13

35

13

85

43

43



12 is a common multiple of 3 and 4.

134


134

123

12

3= 1 8

12

Convert the mixed numbers to fractions with a common denominator.

13

4= 1 9

12


Compare and Order Fractions13

412


213

314

So, is smaller than .

134

123



20 is a common multiple of 4 and 5.

185

2 14

Which is greater, or ?

185

=7220

Convert the mixed number to an improper fraction with a common denominator.

185

2 14

2 1

4= 2 5

20=

4520



185

2 14

Which is greater, or ?

So, is greater than .

185

2 14

185 2 1

4



35

114

Arrange , and in increasing order. 11

3

11

3

35

11

4

The first common multiple of 3 and 4 is 12.

114= 1 3

12

113= 1 4

12

is smaller than 1.

So, is the smallest.

35

35

11

3 is the greatest.



35

114


3

11

3

35

11

4

3 1 1, 1 , 15 4 3

smallest



53

87

Arrange , and in decreasing order. 15

8

15

8

53

87

87= 11

753= 12

3

Since the whole numbers are the same, compare the fraction parts.



53

87

Arrange , and in decreasing order. 15

8

Compare , and to .

Decreasing order:

23=

1624

58=

1524

and are greater than .

is smaller than . 23

58

12

17

12

23

58

17

12

53

,158

, 87

23 is the greatest.

17 is the smallest.



52

113


7

13

7

52

11

3

52= 2 1

2is greater than 2.

So, is the greatest.

52

52



52

113


7

13

7

52

11

3

113= 1 7

21

137= 1 9

21

Compare and . 11

3 13

7

11

3Increasing order:

11

3,13

7, 5

2

is the smallest.



13

4 65

Arrange , , 2 and in decreasing order. 11

8

2 13

4

65

65

11

8

13

4 11

8, and are smaller than 2. So, 2 is the greatest.


is smaller than and .

So, is the smallest. is smaller than .


13

4Arrange , , 2 and in decreasing order.

65

118

2 13

4

65

11

8

65= 11

5

134= 115

20

115= 1 4

20

is smaller than . 11

8 11

5

11

8 13

4 65

65

134

2,13

4, 65

,118

Decreasing order: 11

8


Let’s Try!

Which is greater?

193

115

193

,2 23

2 59

, 2 23

a)

c)

b)

d)

76

, 115

3 23

, 3 57

2 23

3 57


Let’s Try!

Which is smaller?

3 23

2 12

13

8a)

c)

b)

d)

178

,138

2 12

185

, 3 23

, 3 56

174

, 196

196


Let’s Try!

Arrange the following in increasing order. a)

b)

74

, 2 35

,123

25

,156

,138

12

3, 74

, 2 35

25

,138

, 156


Let’s Try!

Arrange the following in decreasing order. a)

b) 2, 5

2,11

6,13

4

97

, 53

,119

52

, 2,134

,116

53

, 97

,119


Find a Fraction of a Set

Ben has 5 pens.

2 out of 5 pens are green.

of the pens are green.25



Priya has 15 pens.

of the pens are green.25

6 out of 15 pens are green.

5 equal groups 6

15=

25

2 out of 5 equal groups of pens are green.



25

5 units = 151 unit = 15 ÷ 5

= 32 units = 3 × 2

= 6So, of 15 is 6.

Divide 15 into 5 equal parts. One part is of 15.

15

25Find the value of of 15.

?

15



25

x 15

= 6

Divide 15 into 5 equal parts. One part is of 15.

15

25Find the value of of 15.

?

15


Fraction of a set

4 units = 241 unit = 24 ÷ 4

= 6David read 6 storybooks.

There were 24 storybooks on a shelf. David read of these storybooks. How many storybooks did he read?

14

read

24


Fraction of a set

x 24 = 6

David read 6 storybooks.

There were 24 storybooks on a shelf. David read of these storybooks. How many storybooks did he read?

14

read

24

14


Fraction of a set

4 units = 241 unit = 24 ÷ 4

= 6 (David)3 units = 6 x 3 = 18 (Janet)Janet read 18 storybooks.

There were 24 storybooks on a shelf. David read of these storybooks and Janet read the rest of the storybooks. How many storybooks did Janet read?

14

David

24

Janet ??


Fraction of a set

1 - ଵସ

= ଷସ

ଷସ

x 24 = 18

Janet read 18 storybooks.

There were 24 storybooks on a shelf. David read of these storybooks and Janet read the rest of the storybooks. How many storybooks did Janet read?

14

David

24

Janet ??



3 units = 211 unit = 21 ÷ 3

= 74 units = 7 × 4

= 2828 pupils went on the school trip altogether.

14A group of pupils went on a school trip. of the

pupils were boys. There were 21 girls. How many pupils went on the school trip altogether?

boys

?

21


Let’s Try!16Megan baked 60 cookies. were chocolate

cookies. The rest were strawberry cookies. How many strawberry cookies did Megan bake?

6 units = 601 unit = 60 ÷ 6

= 105 units = 10 × 5

= 50Megan baked 50 strawberry cookies.

chocolate

60

?


Reference — Textbooks

Learning OutcomesUnderstand mixed numbers 4B

pp. 7 – 94A pp. 72 – 74

Understand improper fractions

4B pp. 10 – 13

4A pp. 75 – 76

Convert improper fractions to mixed numbers

4B pp. 14 – 15

4A p. 77 – 78

Convert mixed numbers to improper fractions

4B pp. 16 – 17

4A p. 74


Reference — Textbooks

Learning OutcomesCompare and order fractions

4B pp. 18 – 28

4A pp. 79 – 84

Find a fraction of a set 4B pp. 29 – 36

4A pp. 95 – 101

Documents

Primary 4 Mathematics...© 2016 Marshall Cavendish Education Pte Ltd Primary 4 Mathematics My Pals Are Here, Book B, Chapter 8: Fractions Shaping Maths, Book A, Unit 3: Fractions ©