Math 3

4.2 Angles

See, feel and learn.

A

BC

• If two straight lines AB and BC meet at a point A
B, the angle is formed at B between the line AB arm
and BC. It is called angle ABC (∠ABC)
B angle C
• Here, the point B where the lines AB and BC Vertex arm
meet is called the vertex and the straight lines
AB and BC are called arms of ∠ABC.

• We write angle ABC or angle CBA or ∠ABC or ∠CBA with vertex in the
middle. (Angle = ∠ = )

Observe the following as angles

Mathematics 3 Approved by CDC 101

A

When two straight lines meet at a Angles C
point, the space formed between them
B
at the corner is called an angle.

In the above triangle.
• Triangle ABC is written as DABC.
• Angles A, B and C are written as

∠A, ∠B and ∠C.
• There are three angles in a triangle.

Comparison of angles:

Narrow space Wide space
(Small angle) Tall (Big angle)

Dwarf

11 12 1 Narrow space 11 12 1 Wide space
10 2 (Small angle) 10 2 (Big angle)

93 93

84 84
765 765

Activity - 1:

Taking two pencils:

102 Approved by CDC Mathematics 3

Join the tip of pencils and shift one as shown in diagram.
A

BC

Space is formed between them which is
called an angle.
• It is written as ∠ABC.
• Symbol ∠ represents the angle.
• Line segments AB and BC are taken

as arms.
• B is called the vertex.

Activity - 2:

Taking two bamboo logs and described angles with Pema (lesser height) and
Munna (greater height).

Pema
Munna

Mathematics 3 Approved by CDC 103

P
A

Dwarf Tall
(Pema) (Munna)

BC QR

It is lesser angle. It is written as It is greater angle. It is written as
∠ABC. B is the vertex line segments ∠PQR. Q is the vertex line segments
AB and BC are the arms. PQ and QR are the arms.

Here,
• ∠PQR is greater than ABC. Written as, ∠PQR > ∠ABC

• ∠ABC is lesser than ∠PQR. Written as ∠PQC < ∠PQR
• Symbol of greater than is >
• Symbol of lesser than is <

Activity - 3:

Position of arms in right angle. A right angle is of 90° angle.

A
K

BC

Finger LM Set Square

Bamboo sticks

Here,
ABC = 90° (A right angle)
KLM = 90° (A right angle)
PQR = 90° (A right angle)

104 Approved by CDC Mathematics 3

Activity - 4:

Angles can be shown in different positions of arms as follows for compression.

P K
A

B C Q RL

MX Y Z

Here,
• The angles formed between two pencils are ∠ABC, ∠PQR,

∠KLM and ∠XYZ respectively.

• ∠PQR is greater than ∠ABC. i.e. ∠PQR > ∠ABC

• ∠KLM is greater than ∠PQR. i.e. ∠KLM > ∠PQR

• ∠XYZ is greater than ∠KLM. i.e. ∠XYZ > ∠KLM

• ∠PQR is lesser than ∠KLM. i.e. ∠PQR < ∠KLM

• ∠ABC is lesser than ∠XYZ. i.e. ∠ABC < ∠XYZ

See, feel and do.

1. Write the names of the following angles. Also name the vertex and
the arms as given in the example.

AP N

Q

BC R and M O
and
Angle : ∠ABC Angle : Angle :
or ∠CBA or or

Vertex : B Vertex : Vertex :
Arms : AB and BC Arms : Arms :

Mathematics 3 Approved by CDC 105

X EG
Z
Y OL
and
Angle : F K
or
Angle : Angle :
Vertex : or or
Arms :
Vertex : and Vertex : and
Arms : Arms :

2. Name the angles indicated in the following figures as given in
example.

A AD K

BC B L M
C N
∠ABC

D C C H Z Y
E B G  W X
D
A F
E

106 Approved by CDC Mathematics 3

3. Put the correct letters in the following figures from the given names
and vertices of angles.

∠ XYZ ∠ AOB ∠ NOM
Vertex Y Vertex O Vertex O

∠ PQR ∠ WXY ∠ LMN
Vertex Q Vertex X Vertex M

4. Compare the following pair of angles and write smaller or bigger
accordingly.

A XZ L

P

B CQ R YM N

X RM

D

E F Y Z ST ON

Mathematics 3 Approved by CDC 107

5. Compare the following pairs of angles: (Use = or > or <).

AP L P

C BQ R M NQ R

∠ABC ∠PQR ∠LMN ∠PQR

WA X
U

X YB C V WY Z

∠WXY ∠ABC ∠UVW ∠XYZ

6 Colour the smaller angles as follows.

108 Approved by CDC Mathematics 3

4.3 Identifying geometrical shapes

See, feel and learn.

Triangles

• Which type of shapes are given in diagrams? Triangle
• How many line segments are included in them? 3
• How many angles are there in each shapes? 3

The enclosed geometrical shape
bounded by three line segments is

called triangle.

A BA B

A 109
B C CC

Mathematics 3 Approved by CDC

In the above figures :
• ABC are the triangles.
• It is written as DABC.
• Line segments AB, BC and AC are

called the sides of triangle.
• A, B and C are called the corners

or vertices (singular: vertex) of
triangle.

The name of triangle, sides and angles.

A It is DABC.
Sides AB BC AC
B Angles A B C
C
I am like a triangle.
I am triangle.

P It is DPQR
Sides PQ QR PR
R Angles P Q R
Q
Triangle using pencils. I am like a triangle.

K I am like a triangle.
Mathematics 3
It is DKLM.
Sides KL LM KM
L M Angles K L M

Triangle using bamboo sticks.

110 Approved by CDC

D It is DDEF.
Sides DE EF DF
EF Angles D E F
Triangle using nails.
I am like a triangle.
Quadrilaterals

• Which type of shapes are given in diagrams? Quadrilaterals
• How many line segments are included in them? 4
• How many angles are there in each shapes? 4

The enclosed geometrical shape
bounded by four line segments is

called quadrilateral.

DB B C
AA
D
B C D CA
Mathematics 3 Approved by CDC 111

In the above figures :
• ABCD area the quadrilateral.
• It is written as ABCD.
• Line segments AB, BC, CD and DA

are called the sides of triangle.
• A, B, C and D are called the

corners or vertices or angles of the
quadrilateral.

The name of quadrilaterals, sides and angles.

D • It is DABCD.
A • Sides are

BC AB BC CD DA
I am quadrilateral • Angles are

ABCD

I am quadrilateral

PS • It is DPQRS.
• Sides are
QR
I am quadrilateral PQ QR RS SP
• Angles are

PQRS

I am quadrilateral

M • It is DKLMN. I am quadrilateral
N • Sides are Mathematics 3

KL KL LM MN NK
I am quadrilateral • Angles are

112 K L MN

Approved by CDC

• It is DABCD.
• Sides are

AB BC CD DA
• Angles are

ABCD

I am quadrilateral I am quadrilateral

Square P Q

The quadrilateral having all
sides equal is called square.
All the angles of the square

are also equal.

SR

I am like a square.
EH

FG My face is like a square.

Square using 4 equal nails.
EF = FG = GH = EH and

∠E = ∠F = ∠G = ∠H

Mathematics 3 Approved by CDC 113

AD

BC I am like a square.
Square using 4 equal bamboo sticks.

AB = BC = CD = AD and
∠A = ∠B = ∠C = ∠D

Rectangle

The quadrilateral having opposite
sides equal is called rectangle.

All the angles of rectangle are also
equal.

AD

BC I am like a rectangle.

Rectangle using pieces of wire.
AB = CD, AD = BC and
∠A = ∠B = ∠C = ∠D

114 Approved by CDC Mathematics 3

PQ

SR I am like a rectangle.
Rectangle using pieces of wooden stick.

PQ = SR, PS = QR and
∠P = ∠Q = ∠R = ∠S

KN

LM I am like a rectangle.
Rectangle using piece of pencil.
The quadrilateral having
KL = NM, KN = LM and two adjecent sides equal is
∠K = ∠L = ∠M = ∠N
called kite.
Kite

B

A

C

D I am like a kite. 115
Kite using pencils. Approved by CDC

AB = BC, AD = DC and
∠A = ∠C

Mathematics 3

DD

D I am like a kite.

D
Kite using match sticks.
PQ = PS, QR = SR and

∠Q = ∠S

N

MO

P I am like a kite.
Kite using tooth brushes.

MN = MP, NO = PO and

∠N = ∠P

Circle The plane region bounded by a curve
where each point of curve are equidistance
EA from a fixed point is called circle.
O
• Curve ABCDE is called circumference of circle.
DB • OA = OB = OC = OD = OE which are called radios
C
of circle.
• Fixed point 'O' is called centre of circle.

116 Approved by CDC Mathematics 3

I am circle. I am like a circle.

Circle made of rope. I am like a circle.

Circle made of piece of bamboo. I am like a circle.

Mathematics 3 Approved by CDC 117

Tracing the outline of objects.

Bangle Circle

Dice Square

Bread Quadrilateral

Sandwich Triangle

Solar panal Rectangle
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See, feel and do.

1. Join the dots. Name the shape and colour the pictures.

I am quadrilateral. I am

I am I am

I am I am

I am I am 119
Mathematics 3 Approved by CDC

2. Match the followings as their shapes.

120 Approved by CDC Mathematics 3

3. Name the following shapes.

It is It is

It is It is

It is It is

It is It is
Mathematics 3
Approved by CDC 121

4. Write the name, sides, vertices and angles of the following triangles.
AP

R

BC Q

Name : ∆ABC Name :
Sides : AB, BC, CA Sides :
Vertices : A, B and C Vertices :
Angles : ∠ABC, ∠BCA, ∠BAC Angles :

L W

M NX Y

Name : Name :
Sides : Sides :
Vertices : Vertices :
Angles : Angles :

5. Fill in the blanks.

a) The side of the triangle is the longest.

b) Vertices of the triangle are , P
Q
and .

c) The angle is the biggest.

d) Name of this triangle is . R

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6. Complete the following table with the names of the quadrilaterals, their
sides and angles.

K NAB W ZP S

L M D CX YQ R

Fig. Name of Sides Angles
quadrilateral LM MN KN ∠KLM ∠LMN ∠MNK ∠NKL

(a) KLMN KL

(b)

(c)

(d)

7. a) In the given quadrilateral ABCD, sides AB = BC = A B
CD = DA and ∠ABC = ∠BCD =∠CDA = ∠DAB.
D C
So, ABCD is a P S

b) In the given quadrilateral PQRS, PQ = SR and QR Q R
= PS and ∠PQR = ∠QRS = ∠RSP = ∠SPQ.

So, PQRS is a

8. Name the shape of following objects.

A blackboard A carom board A Set square A book

Mathematics 3 Approved by CDC 123

9. Trace the following objects.
Trace a rectangle using a match box.

Trace a quadrilateral using a block of broken tile.

Trace a kite using a kite.

Trace a circle using a base of bottle.

124 Approved by CDC Mathematics 3

Trace a rectangle using a block of tile.
Trace a quadrilateral using a piece of set square.
Trace a kite using a bangle.

Trace a circle using a piece of wood.

Mathematics 3 Approved by CDC 125

Unit Revision Test

1. Write down the name of following shapes.
It is in shape.

It is in shape.

It is in shape.

It is in shape.

It is in shape.

126 Approved by CDC Mathematics 3

2. Answer the following questions from the given shapes.

A Number of shape
BC Number of angles
Name of vertices
Name of angles

P Q Number of sides
Name of vertices
Name of angles

SR

3. Which of the following is square and rectangle? Write down by
measuring the sides with ruler.

A B AB = cm

D BC = cm
It is a
CD = cm

C AD = cm

PS PQ = cm
QR = cm
Q R RS = cm
It is a PS = cm

Mathematics 3 Approved by CDC 127

4. Trace the shape of following objects using pencil. Also write down
the name of shapes.

It's shape is

It's shape is

It's shape is

It's shape is Approved by CDC Mathematics 3

128

5Unit

BASIC OPERATIONS ON
MATHEMATICS

Estimated periods - 36

Objectives

At the end of this unit, students will be able to:
do addition and subtraction upto 5 digits number.
develop the concept of addition for multiplication.
find multiplication with one two and three digits.
develop the concept of division using subtraction.
find division with one and two digits.

Teaching Materials

Abacus, place value chart, multiplication chart, geo-board, magic board
etc,

Activities

It is better to:
let the students do the addition and subtraction without and with carrying
from the discussion by using the abacus and place value chart.
ask the students write the word problems on addition and subtraction in
mathematical form and solve them.
ask the students make their own simple word problems on addition with
carrying and solve them.
able to activated the students about the relation of addition to know
multiplication also relate the students about the relation of subtraction
over division.
involve the students to demonstrate the activities related to this lesson
suggested in the curriculum prescribed by CDC.

Mathematics 3 Approved by CDC 129

One and one two
Two and two four
This is the game
We need to show

One two's are two
Two two's are four
This is the game
We need to show

Two device are in two
Eight divide two is four

This is the game
We need, to show.

130 Approved by CDC Mathematics 3

5.1 Addition

See, feel, learn and do.

Shyam and Krishna Maya have following marbles. They take together and find
how many marbles will be there.

Hundred Tens Ones Hundred Tens Ones
3 46

+6 3 2
9 78

They have 978 marbles
at all.

9 78

Shyam and Krishna Maya have following marbles. They take together and find
how many marbles will be there.

Hundred Tens Ones Hundred Tens Ones
3 46

+5 5 3
8 99

They have 899 marbles
at all.

8 99 131
Mathematics 3 Approved by CDC

Mina, how many hundreds, Sir, let me think
tens and ones are there in 325 = 300 + 20 + 5
Oh! Sir, there are 3
325? hundreds, 2 tens and 5

Very good, ones.
Mina!

Remember Let’s add tens and make
1 ten = 10 ones the groups of hundreds
1 hundred = 10 tens
and tens!

See, feel and do.

1. Perform the following as shown below:

6 tens + 7 tens = 13 tens = 1 hundred + 3 tens
8 tens + 9 tens = tens = hundred + tens
13 tens + 15 tens = tens = hundred + tens

2. Do the following as shown below:

3 6 7 5 6 8 6 2 2 2 4 3
+ 4 5 4 + 3 5 4 + 1 9 7 + 3 8 9

8 2 1

2 6 5 2 6 7 2 4 6 6 3 2
3 4 3 3 4 8 1 3 2 1 4 5
+ 1 5 7 + 1 5 4 2 5 4 2 5 6
+ 1 3 5 + 3 4 7

Request to the teacher:

Please ask the students to make such types
of addition problems and add them.

132 Approved by CDC Mathematics 3

Addition by using abacus without and with carrying

See, feel and learn.

Th H T O Th H T O Th H T O

+= Th H T O
2443 + 3353 = 5796 2 4 4 3
+ 3 3 5 3

5 7 9 6

See, feel and do.

1. Do the following as shown above.

Th H T O Th H T O Th H T O

+= Th H T O

+
+=

Th H T O Th H T O Th H T O

+ = Th H T O

+
+=

Th H T O Th H T O Th H T O

+ = Th H T O

+ = +
Approved by CDC
Mathematics 3 133

Th H T O Th H T O Th H T O

+= Th H T O
+

+=

T Th Th H T O T Th Th H T O T Th Th H T O Th H T O
+
+=

+=

Addition of 4 digit numbers without carrying

Suniva, can you add 4 Mam, let me Let me try.
digit numbers? think.

Yes, Suniva, can you
add 3562 and 3214?

Oh! I got the idea. Sir, it is the
same method as addition of 3

digit numbers, isn’t it?

Good! Th H T O
3 5 6 2
+ 3 2 1 4

6 7 7 6

134 Approved by CDC Mathematics 3

See, feel and do.

1. Perform the following task:

Th H T O Th H T O Th H T O
5 2 6 3 4 3 5 2 2 7 4 3
+ 2 4 3 4 + 1 5 4 3 + 3 0 4 6

Th H T O Th H T O Th H T O
3 6 2 8 2 3 4 1 6 2 1 2
+ 4 2 6 1 3 2 1 5 1 0 3 4
+ 1 3 2 3 + 2 3 0 1

Th H T O Th H T O
2 2 2 2 1 2 3 2
3 3 3 3 2 5 2 1
3 2 2 2 3 1 4 2
+ 1 0 1 1 + 1 0 0 1

Addition up to 3 digit numbers with carrying

Zinnia, how many tens
and ones are in 24?

Yes, I know, there are 2 tens
and 4 ones in 24, Madam

Very good Remember
Zinnia. 1 ten = 10 ones

Let’s add ones and
make the groups of tens

and ones!

Mathematics 3 Approved by CDC 135

5 ones + 7 ones = 12 ones = 1 ten + 2 ones
8 ones + 9 ones = ones = ten + ones
12 ones + 17 ones = ones = tens + ones

Addition of 4 digit numbers with carrying

Can you add 2453 Let me try.
and 3218? I think it is also same
as in addition of 3 digit
1
Th H T O numbers, isn’t it?
2 4 5 3
+ 3 2 1 8

5 6 7 1

• First we add the digit of ones place.
3 ones + 8 ones = 11 ones = 1 ten + 1 one
We write 1 in ones place and carry 1 ten to tens column.

• Now, we add the digit of tens place.
1 ten (carry over) + 5 tens + 1 ten = 7 tens
7 tens are less than 10 tens. So, there is no carry over.

• Then we add the digit of hundred place.
4 hundreds + 2 hundreds = 6 hundreds
6 hundreds are also less than 10 hundreds. So, there is no carry over.

• Finally we add the digit of thousands place.
2 thousands + 3 thousands = 5 thousands.

Let’s try another sum.

Ok! mam

Add: 3 7 8 9 and 2 3
4 2.

136 Approved by CDC Mathematics 3

Th H T O • Addition of ones
111 9 + 2 = 11 = 1 ten + 1 one

3 7 8 9 • Addition of tens
+ 2 3 4 2 1 (carry over) + 8 + 4 = 13 tens = 1 hundred +

6 1 3 1 3 tens

• Addition of hundreds
1 (carry over) + 7 + 3 = 11 hundred = 1 thousand

+ 1 hundred

• Addition of thousands
1 (carry over) + 3 + 2 = 6 thousands.

See, feel and do.

1. Perform the following task as shown below:

Th H T O Th H T O Th H T O
1
2 3 5 6 3 2 4 8
5 3 4 7 + 4 2 3 8 + 2 4 1 7
+ 3 2 3 6

8 5 8 3

Th H T O Th H T O Th H T O

1 3 5 4 2 3 4 5 4 2 4 5
+ 2 1 3 9 + 3 4 8 6 + 3 6 6 7

Th H T O Th H T O Th H T O
2 5 7 8
+ 3 2 5 7 4 3 5 9 5 3 6 7
+ 3 2 6 4 + 2 8 5 4
Mathematics 3
Approved by CDC 137

Th H T O Th H T O Th H T O

4 8 4 5 2 5 7 8 4 3 5 9
+ 3 6 6 7 + 3 6 5 7 + 3 2 6 4

2. Perform the following task as shown below:

Th H T O Th H T O Th H T O

2 4 3 5 4 7 3 2 2 3 5 8
1 3 2 4 1 0 5 7 1 0 0 4
+ 3 1 0 6 + 2 1 0 6 + 2 1 3 5

6 8 6 5

Th H T O Th H T O Th H T O

5 2 4 3 1 2 3 4 3 2 3 6
1 1 5 6 4 5 6 7 1 3 5 4
+ 2 3 6 5 + 2 1 5 3 + 2 1 4 7

Th H T O Th H T O Th H T O

4 2 7 3 3 2 6 5 2 4 5 8
1 3 4 5 5 6 4 3 3 6 4 9
+ 2 1 8 4 + 5 2 6 + 2 5 6 3

Th H T O Th H T O Th H T O
4 2 3 7
1 7 6 5 2 1 3 2 6 7 8 9
+ 2 3 4 9 1 4 5 6 5 6 8
2 1 0 4 2 7
138 + 3 0 2 + 5

Approved by CDC Mathematics 3

Addition of more than 4 digit numbers without carrying

Remember the concept of T Th Th H T O
addition of 4 digit numbers by 2 5 3 4 2
+ 4 2 1 3 5
using the place value chart.
6 7 4 7 7
Add: 25342 and 42135.

Do the following task as shown below:

T Th Th H T O T Th Th H T O T Th Th H T O
4 3 2 6 5 3 4 2 5 6 5 6 2 5 7
+ 5 2 4 1 2 + 5 3 4 2 3 + 1 2 3 2 1

9 5 6 7 7

L T Th Th H T O L T Th Th H T O L T Th Th H T O
2 3 4 5 6 2 3 5 6 3 7 2 4 2 7 5 1 3
+ 4 5 2 3 1 6 + 5 2 3 5 1 7 + 2 4 0 2 6 4

Addition of more than 4 digit numbers with carry over

Lila, can you add Yes, I can because I
36986 and 24537? know the process of
addition of 4 digit
Good! Lila, you have
good idea. So, Let’s numbers.

do it.

Mathematics 3 Approved by CDC 139

T Th Th H T O • First add ones
11 1 1 6 + 7 = 13 ones = 1 ten + 3 ones
Write 3 in ones place and carry over 1 ten to
3 6 9 8 6
+ 2 4 5 3 7 tens place.

6 1 5 2 3 • Then add the tens.
1 ten (carry over) + 8 tens + 3 tens = 12

tens = 1 hundred + 2 tens
Write 2 in tens place and carry over 1

hundred to hundreds place.

• Similarly we add hundreds, thousands and
ten thousands.

See, feel and do.

Do the following task:

T Th Th H T O T Th Th H T O T Th Th H T O

4 5 3 8 7 2 4 5 6 8 5 3 6 5 7
+ 2 6 8 6 5 + 1 8 2 9 6 + 2 3 5 2 6

T Th Th H T O L T Th Th H T O L T Th Th H T O

2 7 3 8 5 3 6 7 5 4 2 4 7 2 6 8 5
+ 4 5 7 6 9 + 2 6 5 7 8 9 + 2 5 9 5 3 8

T Th Th H T O L T Th Th H T O T Th Th H T O

3 5 2 7 4 2 4 5 3 6 7 8 8 8 8 8
3 8 2 5 3 2 4 6 7 3 8 8 8 8
+ 6 4 3 + 2 3 5 2 5 4 8 8 8
+ 8 8

140 Approved by CDC Mathematics 3

Word problems on addition

A. Study and learn the following example.

There are 2432 students in school 'A' and 3254 students in school 'B'.

How many students are there altogether in both schools?

Students in school 'A' = 2 4 3 2

Students in school 'B' = + 3 2 5 4

5 6 8 6

∴ There are altogether 5686 students in both schools.

See, feel and do.

1. Do the following problems:

a) Ram had Rs. 2346. Shyam gives him Rs. 1433.

How much money does he have now?

∴ Ram has Rs. now.

b) A box contains 1265 marbles and another box

contains 2324 marbles. How many marbles are

there altogether?

∴ There are altogether marbles.

c) There are 4320 apples in one box and 2457

apples in another box. How many apples are there

altogether?

∴ There are altogether apples.

Mathematics 3 Approved by CDC 141

d) A Farmer sold 1324 kg of potatoes in Baishakh,

2142 kg in Jestha and 2231kg in Asar. How

many kgs of potatoes did he sell in three months?

∴ He sold kg potatoes in three months.

e) Mohan gave Rs. 50125 donation to orphan

house, Rs. 25600 to Bir Hospital and Rs. 32260

to a Bridha Ashram. How much money did he

donate altogether?

∴ He donated Rs. altogether.

Study and learn the following example:

The cost of a radio is Rs. 2975 and the cost of a television is Rs. 5675. What is
the total cost of both items?

The cost of a radio 111
The cost of a television
= 2975
= +5 6 7 5

8650

∴ The total cost of both items is Rs. 8650.

2. Solve the following problems:

a) The cost of a bicycle is Rs. 4276 and the cost

of a telephone set is Rs. 1645. What is the total 4 2 7 6
+ 1 6 4 5
cost of both items?

∴ The total cost of both items is Rs. .

b) The price of a shirt is Rs. 1375 and the price of

a jacket is Rs. 2948. What is the total price of 1 3 7 5
+ 2 9 4 8
both items?

∴ The total price of both items is Rs. .

142 Approved by CDC Mathematics 3

c) There are 5342 men and 4697 women in a

village. How many people are there altogether? 5 3 4 2
+ 4 6 9 7
∴ There are people altogether.

d) A man earns Rs. 3750 from house rent, Rs.

4375 from farming and Rs. 5275 from business

in a month. How much money does he earn

altogether?

∴ He earns Rs. altogether.

e) A truck carried 1285 kg of mangoes on Sunday,

2435kg on Monday and 2527kg on Tuesday.

How many kgs of mangoes are carried by the

truck altogether?

∴ It carried kgs of mangoes.

f) A fruit seller bought 2587kg apples, 1735kg

mangoes and 643kg guavas. How many kgs of

fruits did he buy?

∴ He bought kgs of fruits.

Mathematics 3 Approved by CDC 143

5.2 Subtraction

Relation between addition and subtraction.

See, feel, learn and do.

Dorje has 24 oranges and Ram Lakhan has 12 oranges. They kept them in a
same basket.

+=

24 12 36

There are 36 oranges in the basket.
If Suniva takes 12 oranges from the basket, how many oranges will left?

–=

12 24

36 There will 24 oranges left in the basket.

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Dolma has 18 apples and Ram Gopal has 15 apples. They kept them in a same
basket.

+ =
18
15

33

There are 33 apples in the basket.
If Sumina takes 18 apples from the basket, how many apples will left?

–= 15
18

33 There will be 15 apples left in the basket.
Mathematics 3
Approved by CDC 145

Simplification of addition and subtraction

See, feel and learn.

Mohan, you have 12 pencils.

I give you 15 pencils more. From which,

you gave 14 pencils to your friends.

How many pencils will be left

with you now? I think I have to add

12 + 15 – 14 first and then subtract,
= 27 – 14 shouldn't I ?

Yes, very good. = 13

See, feel and do.

1. Simplify A:

6+4–3 7+3–5 7+3–5
= 10 - 3 = =
= 7 = =

6–2–3 7–8+5 8–9+7
= = =
= = =

2. Simplify B: 29 + 14 – 12 35 – 27 + 18
= − 12 = − 27
17 + 12 – 15 = =
= − 15
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146

a) 18 – 12 + 37 – 32 b) 16 – 14 + 43 – 12
= 18 + 37 – 12 + 32 = –
= 55 – 44 = –
= 11 =

c) 24 – 13 + 37 – 22 d) 21 – 15 + 38 – 29
= – = –
= – = –
= =

Simplification of addition and subtraction by machines

See, feel and do.

Simplify the following by machine as shown in the example:

12 15 8

7 +8 −5 10 9 +2 −4

24 27 3

4 5 +10 −8
3
8 7 147
+9 −5

4

Mathematics 3 Approved by CDC

20 15
30 +5 −10 12
40
+8 −13
20 10
30 +5 −10
40 15
12

+8 −13
10

Subtraction upto 3 digit numbers without borrowing

1. Perform the following task as shown in the example:

T O T O T O H T O
4 6 5 7 6 9 3 5 4
− 2 5 − 3 4 − 2 7 − 2 4 3

2 1

H T O H T O H T O H T O
5 7 3 7 5 6 6 4 3 8 7 5
− 3 4 1 − 4 3 4 − 3 2 1 − 4 5 2

148 Approved by CDC Mathematics 3

2. Perform the following task as shown in the example:

76 − 34 = 35 − 24 = 567 − 52 =

89 − 56 = 67 − 34 = 734 − 222 =

54 − 23 = 257 − 124 = 654 − 431 =

60 − 40 = 435 − 214 = 965 − 425 =

Subtraction upto 3 digit numbers with borrowing

Mohan, can you subtract Yes, sir! Let me try.
246 from 362?

Good Mohan! 6 can’t be subtracted from 2.
So, 2 borrows 1 ten from 6 tens.
1 ten + 2 ones = 12 ones
12 ones − 6 ones = 6 ones
6 tens has left 5 tens.
Then we subtract 4 tens from 5 tens.

H T O
3 6 2
− 2 4 6

1 1 6

1. Perform the following task as shown above in the example:

T O T O T O T O
5 2 6 4 8 1 9 4
− 2 7 − 3 6 − 4 5 − 5 9

Mathematics 3 Approved by CDC 149

H T O H T O H T O H T O
4 6 2 5 7 4 3 6 3 4 3 5
− 2 3 5 − 2 4 7 − 1 4 8 − 2 7 2

Subtraction of 4 digit numbers without borrowing

See, feel and learn.

Meena, do you know the
process of subtraction of 4

digit numbers?

Oh! I think I have an idea.
Yes, sir! The process is same as
the process of subtraction of 3

digit numbers, isn’t it?

Can you subtract 3245
from 5469?

Yes, good. Of course sir !
First we arrange the given
numbers according to their
place value.Then subtract

one by one.

Th H T O
5 4 6 9
− 3 2 4 5
2 2 2 4

150 Approved by CDC Mathematics 3