Primary 4 Chapter 5 Fractions Notes (I) - · PDF file4) Express the mixed number in its...

P4 | Chapter 5 Fractions | Notes (I)

© JustEdu Holdings Pte Ltd -1-

Mixed Numbers

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

A mixed number is obtained when a whole number is added to a fraction.

Worked Example 1 Noel ate 1 apple pie. Ken ate 1

4 of an apple pie.

How much apple pie did they eat altogether? Solution:

1 + 14

= 1 14

They ate 1 14

apple pies altogether.

Primary 4 Chapter 5 Fractions Notes (I)

1 14

is a mixed number where

1 is the whole number and

14

is the fraction.

141

Fraction Whole Number

Topics with more concepts or lengthy notes are broken up into 2-3 weeks so it would not be too overwhelming for the students to learn all the concepts at once.

Speech bubbles are placed at the side from time to time to serve as a reminder.

Key words are in bold to emphasise their importance.



Write down the mixed number represented for Questions 1 and 2. 1)

1 + 34

= __________

2) 2 + 1

6 = __________

3) Express the mixed number in its simplest form. ________ wholes ________ parts = 4

6 = 4

4) Express the mixed number in its simplest form. The first one has been done for you. (a) 1 3

6 = 1 1

2 (b) 2 6

8 = 2

(c) 6 3

9 = 6 (d) 3 8

12 = 3

1 whole 3 quarters

To express in its simplest form, divide both the numerator and denominator by the same number until they cannot be divided further. E.g. 3 4

8 = 3 1

2

1 whole

1 whole

1 sixth

÷4 ÷4

Practice questions to further enhance student’s understanding of new topic.



When a numerator of a fraction is equal to or greater than its denominator, we get an improper fraction. Hence 6

6 and 7

6 are improper fractions.

Can you find other improper fractions on the number line below? 1 1

6 1 2

6 1 3

6 1 4

6 1 5

6

1

6 2

6 3

6 4

6 5

6 6

6 7

6 8

6 9

6 10

6 11

6 12

6

The value of an improper fraction is equal or greater than 1. It can be expressed as a whole number or a mixed number.

Improper Fractions

At a cake shop, cakes are cut into 6 equal pieces.

16

= 1 sixth

56

= 5 sixths

66

= 6 sixths = 1 whole

76

= 7 sixths = 16

1

0

2

Visuals help our students to grasp the concept quickly.



5) How many thirds are there in 2 2

3?

2 2

3 =

3 = __________ thirds

There are __________ thirds in 2 2

3.

As much as we would love to show you everything,

we cannot be showing you the best.

Do drop by any JustEdu centre to view the full set!



Worked Example 2 Express 11

9 as a mixed number.

Solution: Method 1: 119

= 11 ninths

= 9 ninths + 2 ninths

= 99

+ 29

= 1 + 29

= 1 29

We separate 11 ninths into 9 ninths + 2 ninths because we know

99

= 1!

Sub-titles are used to identify the different learning objectives of the topic.

Convert Improper Fractions to Mixed Numbers



Method 2:

Hence, 11

9 = 1 2

9

11) Express 32

7 as a mixed number using both Method 1 and Method 2.

Method 1: 32

7 = sevenths

= sevenths + sevenths = + = + =

Method 2: 32 ÷ 7 = R

327

=

Quotient

11 9

We can think of this line as a division symbol, ÷

11 ÷ 9 = 1 R 2

= 1 2 9 Denominator

Remainder

1 9 1 1

– 9 2

Note:

77

= 1

147

= 2

217

= 3

287

= 4

7 3 2

–

Alternative method is presented to cater to different learning styles and abilities of students.



12) Express 1610

as a mixed number in its simplest form using both Method 1 and

Method 2. Method 1: 16

10 = tenths

= tenths + tenths = + = + = Method 2: 16 ÷ 10 = R

1610

=

=

Note: 1010

= 1

10 1 6 –



Convert Mixed Numbers to Improper Fractions Worked Example 3 Express 2 5

6 as an improper fraction.

Solution: Method 1: 2 5

6 = 2 + 5

6

= 126

+ 56

= 176

Method 2:

multiply these

1 2 Then add this to

the product

6 × 2 5 +

6 × = 17 2 5 +

This is your new numerator.

2 5 6 2 5

6

2 5 6 =

17 6

3

Note: 1 = 6

6

2 = 126

Alternative method is presented to cater to different learning styles and abilities of students.

P4 | Chapter 5 Fractions | Practice 1


1) Shade all the boxes with mixed numbers to help Mew Mew find the way to

its dinner.

3 18

9 25

4312

10 311

4 2 3

7 2 1

9 5 4

7 1 1

4

15

8 4

9 37

9 1

7 10

10

2) Write the mixed number for each of the following. (a) 1 whole and 1 quarter is __________. (b) 2 wholes and 5 eighths is __________ .

Primary 4 Chapter 5 Fractions Practice 1

Our notes are complemented with 2-3 sets of comprehensive

practice papers each week. This is to ensure our students

are able to apply the concepts into different types of Mathematical sums.



3) Shade the following to show the given number of parts.

(a) 2 23

(b) 3 38

4) Fill in the boxes on the number line with the following mixed numbers.

5) Fill in the boxes on the number line with mixed numbers in its simplest form. (a) (b) 4 2

5

2 2 2 2 2 2 3 3 3 3 3 3 18

4

28

48

58

78

18

28

38

58

68

(a) (b) (c) (d)

0 1 2 3 12

4 5

2 38

3 12

2 34

3 78



6) Write mixed numbers for the following. Express your answers in its simplest form. (a) Find the volume of water in each container. __________ l __________l (b) Find the total mass of the papayas. The papayas have a total mass of __________kg.

1 l

2 l

1 l

2 l



Do drop by our centre to view the full set of materials.



7) Study the diagrams and write an improper fraction for each of the

following. (a)

11 quarters = __________

(b)

17 fifths = __________

Visuals help our students to grasp the concept quickly.



8) Write an improper fraction for each of following. (a) 8 sevenths = (b) 7 fifths = (c) 11 eighths = (d) 13 thirds = 9) Write each of the following as a mixed number and an improper fraction. (a)

Mixed number → Improper fraction → (b) Mixed number → Improper fraction →




10) Fill in the missing fractions in each box.

Express your answers in its simplest form. (a) (b)

11) Write each mixed number as an improper fraction. (a) 1 = __________ quarters

34

= __________ quarters

1 3

4= __________ quarters

1 3

4 =

1

0 1 2

1 2




12) Write down the improper fractions for the shaded parts. (a)

1 5

6 =

There are __________ sixths in 1 56

.

(b)

3 4

9 =

There are __________ ninths in 3 49

.

1 whole

1 whole



Worked Example 1 Electrician Adam had 14 m of wire.

27 of it was damaged and cut off.

He used another 614 m of wire for the living room.

(a) What was the length of wire that was damaged? (b) What was the length of remaining wire?

Solution:

(a) 27

× 14 m = 4 m

The length of the wire that was damaged was 4 m.

(b) 14 m – 4 m – 6 14

m = 4 m – 14

m

= 3 4

4 m – 1

4 m

= 3 3

4 m

The length of the remaining wire was 3 3

4 m.

Primary 4 Chapter 5 Fractions Practice 8

Look out for the units.

Notice that 27

has no unit.

27

of the wire ≠ 27

m of the wire

Therefore, you have to find its length.

Speech bubble is placed by the side from time to time to serve as a reminder.

Topics with more concepts or lengthy notes are broken up into 2-3 weeks so it would not be too overwhelming for the students to learn all the concepts at once.

Worked examples are used to guide students on the answering of the question. It is also useful for students to refer to when revising.



Solve the following problem sums. All essential workings must be shown clearly. Answers are to be given in the correct units and in their simplest form. 1) Amelia bought 16 kg of apples.

She used 58

of it to bake apple pies and gave 1 49

kg of it to her neighbours.

What was the mass of the apples she had left?

Ans:__________

2) Gloria prepared 20 l of fruit punch for a party.

After a few hours, the guests finished 35

of the fruit punch.

Gloria prepared another 4 12

l of fruit punch.

How much fruit punch was there now?

Ans:__________

Students are drilled and exposed to different types of problem sums to prepare them for examination.



3) The distance between Town G and Town H is 240 km. Mr Koh drove from Town G towards Town H in the morning and he

completed 512

of the distance.

Mrs Koh took over the driving from Mr Koh and drove 85 km in the afternoon. What was the distance left for them to reach Town H?

Ans:__________

Worked Example 2 Tina had 60 eggs. She broke 6 eggs.

She then gave 12

of the remaining eggs to her neighbour.

(a) What fraction of the eggs did Tina break?

(b) How many eggs did she give to her neighbour? Solution:

(a) 660

= 110

Tina broke 1

10 of the eggs.

(b) 60 – 6 = 54 (Remaining eggs)

54 ÷ 2 = 27

Tina gave 27 eggs to her neighbour.

54

?

6

Alternatively, 12

of the remaining = 12

× 54

Different worked examples are introduced in the practice papers to guide students on how to answer the different type of questions. It is also useful for students to refer to when in doubt.



4) Fiona has 60 notepads. She lost 10 of them.

She gave away 25

of her remaining notepads.

How many notepads did she give away?

Ans:__________

5) There were 100 people in a cinema.

Halfway through the movie, 16 people left. 5

12 of the remaining people were women.

How many women remained in the cinema?

Ans:__________



Worked Example 3 The total cost of a shirt and a pair of pants is $75.

The cost of the shirt is 23

that of the pair of pants.

How much does the shirt cost? Solution: 3 units + 2 units = 5 units 5 units → $75 1 unit → $75 ÷ 5 = $15 2 units → $15 × 2 = $30 The shirt costs $30.

$75 Pants

Shirt

Look out !!!

The cost of the shirt is that of the pair of pants.

This would help you to draw the model.

2 units

3 units



7) The total mass of 2 girls is 88 kg.

If the mass of one girl is 3

5 of the other, what is the mass of the heavier girl?

Ans:__________




Ans:__________ 8) Taylor has a bouquet of roses.

The number of blue roses is 13

the number of pink roses.

The number of pink roses is 12

the number of red roses.

What fraction of the bouquet are red roses?

Ans:__________

9) Lindsay has 3 containers of water, A, B and C.

Container A has 37

as much water as Container B.

Container C has 13

as much water as Container A.

If the total volume of water is 22 l, how many litres of water are there in Container A?

Ans:__________

Tip: Draw a model.



10) 25

of Christina’s salary is 47

of Brittany’s salary.

Christina earns $900 more than Brittany. What is their total salary?

Ans:__________

*

Students are further exposed to more challenging questions in their Practice. These questions are often differentiated by the asterisk* next to question’s number.



11) The volume of water in Tank X was 15

the volume of water in Tank Y.

After 23 ml of water was removed from Tank X and 1845 ml of water

*




12) Gordon has two number cards. The first card contains a whole number that is smaller than 15. The second card contains a proper fraction.

*


Primary 4 Chapter 5 Fractions Notes (I) - · PDF file4) Express the mixed number in its...

Documents

Transcript of Primary 4 Chapter 5 Fractions Notes (I) - · PDF file4) Express the mixed number in its...