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.
Primary 4
Chapter 5 Fractions
Notes (I)
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.
Key words are in bold
to emphasise their
importance.
Worked Example 1
Noel ate 1 apple pie. Ken ate
1
4
of an apple pie.
How much apple pie did they eat altogether?
Speech bubbles are placed
at the side from time to
time to serve as a reminder.
Solution:
1 1 is a mixed number where
4
1 is the whole number and
1
4
is the fraction.
Whole Number
1+
1
1
4
Fraction
1
1
=1
4
4
They ate 1
1
apple pies altogether.
4
-1-
P4 | Chapter 5 Fractions | Notes (I)
© JustEdu Holdings Pte Ltd
Practice questions to
further enhance student’s
understanding of new
topic.
Write down the mixed number represented for Questions 1 and 2.
1)
1 whole
1+
3
4
= __________
2+
1
6
= __________
3 quarters
2)
1 whole
1 whole
1 sixth
3)
Express the mixed number in its simplest form.
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 ÷4 = 3 1
8 ÷4
2
________ wholes ________ parts = 4
4)
6
=4
Express the mixed number in its simplest form.
The first one has been done for you.
(a)
1
3
6
=1
(c)
6
3
9
=6
1
2
-2-
(b)
2
6
8
(d)
3
8
12
=2
=3
P4 | Chapter 5 Fractions | Notes (I)
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Improper Fractions
At a cake shop, cakes are cut into 6 equal pieces.
1
6
= 1 sixth
5
6
= 5 sixths
6
6
= 6 sixths = 1 whole
7
6
= 7 sixths =
Visuals help our students
to grasp the concept
quickly.
1
6
When a numerator of a fraction is equal to or greater than its denominator,
we get an improper fraction.
Hence 6 and 7 are improper fractions.
6
6
Can you find other improper fractions on the number line below?
1
0
1
6
2
6
3
6
4
6
5
6
6
6
11
12
13
14
7
6
8
6
9
6
10
6
6
6
6
6
15
6
11
6
2
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.
-3-
P4 | Chapter 5 Fractions | Notes (I)
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5)
2
3
How many thirds are there in 2 ?
2
2
3
=
3
= __________ thirds
2
3
There are __________ thirds in 2 .
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!
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P4 | Chapter 5 Fractions | Notes (I)
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Sub-titles are used to
identify the different
learning objectives of
the topic.
Convert Improper Fractions to Mixed Numbers
Worked Example 2
Express
11
9
as a mixed number.
Solution:
Method 1:
11
9
= 11 ninths
We separate 11 ninths into 9
ninths + 2 ninths because
we know
9
= 1!
9
= 9 ninths + 2 ninths
=
9
9
+
=1+
=1
2
9
2
9
2
9
-5-
P4 | Chapter 5 Fractions | Notes (I)
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Alternative method is
presented to cater to
different learning styles
and abilities of students.
Method 2:
11
9
We can think of this line as a division symbol,
11
÷
1
9 11
– 9
2
9= 1R2
=
1
2
9
÷
Remainder
Denominator
Quotient
Hence,
11)
11
9
=1
Express
2
9
32
7
as a mixed number using both Method 1 and Method 2.
Method 1:
32
7
=
sevenths
=
sevenths +
=
+
=
+
Note:
7
=1
7
14
=2
7
21
=3
7
28
=4
7
sevenths
=
Method 2:
32 ÷ 7 =
R
7 32
–
32
7
=
-6-
P4 | Chapter 5 Fractions | Notes (I)
© JustEdu Holdings Pte Ltd
12)
Express
16
10
as a mixed number in its simplest form using both Method 1 and
Method 2.
Method 1:
16
10
Note:
=
tenths
=
tenths +
=
+
=
+
10
10
=1
tenths
=
Method 2:
16 ÷ 10 =
16
10
R
=
10 1 6
–
=
-7-
P4 | Chapter 5 Fractions | Notes (I)
© JustEdu Holdings Pte Ltd
Convert Mixed Numbers to Improper Fractions
Worked Example 3
Express 2
5
6
as an improper fraction.
Solution:
Alternative method is
presented to cater to
different learning styles
and abilities of students.
Method 1:
2
5
6
=2+
=
12
6
=
17
6
5
6
5
6
+
Note:
1= 6
2=
6
12
6
Method 2:
1
2
5
6
2
2
multiply these
3
5
6
Then add this to
the product
2×6 + 5
2×6+ 5
=
17
This is your new numerator.
2 65
17
= 6
-8-
P4 | Chapter 5 Fractions | Notes (I)
© JustEdu Holdings Pte Ltd
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.
Primary 4
Chapter 5 Fractions
Practice 1
1)
Shade all the boxes with mixed numbers to help Mew Mew find the way to
its dinner.
3
1
8
4
15
8
2)
9
2
5
43
12
2
3
7
2
4
9
10
1
9
5
37
9
1
7
4
7
3
11
1
1
4
10
10
Write the mixed number for each of the following.
(a)
1 whole and 1 quarter is __________.
(b)
2 wholes and 5 eighths is __________ .
-1-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
3)
4)
Shade the following to show the given number of parts.
(a)
2
2
3
(b)
3
3
8
Fill in the boxes on the number line with the following mixed numbers.
23
5)
2
1
8
2
2
37
4
8
(c)
(b)
(a)
2
23
31
8
2
8
2
4
8
2
5
8
2
7
8
3
1
38
3
2
38
38
(d)
3
5
8
6
4
38
Fill in the boxes on the number line with mixed numbers in its simplest form.
(a)
0
1
2
2
1
3
(b)
4
5
42
5
-2-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
6)
Write mixed numbers for the following.
Express your answers in its simplest form.
(a)
Find the volume of water in each container.
2l
2l
1l
1l
__________
(b)
l
__________l
Find the total mass of the papayas.
The papayas have a total mass of __________kg.
-3-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
Do drop by our centre
to view the full set of
materials.
-4-
P4 | Chapter 5 Fractions | Practice 1
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Visuals help our students
to grasp the concept
quickly.
7)
Study the diagrams and write an improper fraction for each of the
following.
(a)
11 quarters = __________
(b)
17 fifths = __________
-5-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
8)
9)
Write an improper fraction for each of following.
(a)
8 sevenths =
(b)
7 fifths =
(c)
11 eighths =
(d)
13 thirds =
Write each of the following as a mixed number and an improper fraction.
(a)
Mixed number →
Improper fraction →
Mixed number →
Improper fraction →
(b)
Do drop by our centre
to view the full set of
materials.
-6-
P4 | Chapter 5 Fractions | Practice 1
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10)
Fill in the missing fractions in each box.
Express your answers in its simplest form.
(a)
2
1
0
(b)
2
1
11)
Write each mixed number as an improper fraction.
(a)
1 = __________ quarters
3
4
= __________ quarters
3
4
1
1 = __________ quarters
1
3
4
=
Do drop by our centre
to view the full set of
materials.
-7-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
12)
Write down the improper fractions for the shaded parts.
(a)
1 whole
1
5
6
=
5
6
There are __________ sixths in 1 .
(b)
1 whole
3
4
9
=
4
9
There are __________ ninths in 3 .
-8-
P4 | Chapter 5 Fractions | Practice 1
© JustEdu Holdings Pte Ltd
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.
Primary 4
Chapter 5 Fractions
Practice 8
Worked Example 1
Electrician Adam had 14 m of wire.
2
7
of it was damaged and cut off.
1
He used another 6 4 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?
Speech bubble is placed by
the side from time to time
to serve as a reminder.
Look out for the units.
Worked examples are
used to guide students
Solution:
on the answering of the
question. It is also useful
for students
to refer to
2
× 14 m = 4 m
(a)
when revising.
7
Notice that 2 has no unit.
7
2
7
of the wire ≠ 2 m of the wire
7
Therefore, you have to find its length.
The length of the wire that was damaged was 4 m.
(b)
14 m – 4 m – 6
1
4
m=4m–
=3
4
4
m–
=3
3
4
m
1
4
1
4
m
m
The length of the remaining wire was 3
-1-
3
4
m.
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
Students are drilled and
different
Solve the following problem sums. All essential workings must be shownexposed
clearly.toAnswers
aretypes
to
of problem sums to prepare
be given in the correct units and in their simplest form.
them for examination.
1)
Amelia bought 16 kg of apples.
She used
5
8
of it to bake apple pies and gave 1
4
9
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
Gloria prepared another 4
1
2
3
5
of the fruit punch.
l of fruit punch.
How much fruit punch was there now?
Ans:__________
-2-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
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
5
12
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?
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.
Worked Example 2
Tina had 60 eggs.
She broke 6 eggs.
1
2
She then gave
(a)
(b)
Ans:__________
of the remaining eggs to her neighbour.
What fraction of the eggs did Tina break?
How many eggs did she give to her neighbour?
Solution:
(a)
6
60
=
1
10
1
10
Tina broke
(b)
Alternatively,
1
of the remaining =
of the eggs.
2
1
2
× 54
60 – 6 = 54 (Remaining eggs)
54
6
?
54 ÷ 2 = 27
Tina gave 27 eggs to her neighbour.
-3-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
4)
Fiona has 60 notepads. She lost 10 of them.
She gave away
2
5
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:__________
-4-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
Do drop by our centre
to view the full set of
materials.
-5-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
Worked Example 3
The total cost of a shirt and a pair of pants is $75.
The cost of the shirt is
2
3
that of the pair of pants.
How much does the shirt cost?
Solution:
Pants
$75
Shirt
3 units + 2 units = 5 units
5 units → $75
1 unit → $75 ÷ 5 = $15
2 units → $15 × 2 = $30
The shirt costs $30.
Look out !!!
2 units
The cost of the shirt is
that of the pair of pants.
3 units
This would help you to draw the model.
-6-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
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:__________
Do drop by our centre
to view the full set of
materials.
-7-
P4 | Chapter 5 Fractions | Practice 8
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-8-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
8)
Ans:__________
Taylor has a bouquet of roses.
The number of blue roses is
1
3
the number of pink roses.
The number of pink roses is
1
2
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.
3
Container A has 7 as much water as Container B.
1
Container C has 3 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?
Tip: Draw a model.
Ans:__________
-9-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
*10)
2
5
4
of Christina’s salary is 7 of Brittany’s salary.
Christina earns $900 more than Brittany.
What is their total salary?
Students are further exposed
to more challenging
questions in their Practice.
These questions are often
differentiated by the asterisk*
next to question’s number.
Ans:__________
-10-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd
* 11)
The volume of water in Tank X was
1
5
the volume of water in Tank Y.
After 23 ml of water was removed from Tank X and 1845 ml of water
Do drop by our centre
to view the full set of
materials.
-11-
P4 | Chapter 5 Fractions | Practice 8
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* 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.
Do drop by our centre
to view the full set of
materials.
-12-
P4 | Chapter 5 Fractions | Practice 8
© JustEdu Holdings Pte Ltd