Maths Zone book 4 2077

Approved by Government of Nepal, Ministry of Education, Curriculum Development
Center(CDC), Sanothimi, Bhaktapur, Nepal

Maths Zone
With 4Grade

Maths for Fun
and

Practice Zone

Authors
Sthir Babu Subedi
Bishnu Prasad Poudel

Shubharambha Publication Pvt. Ltd.

KKaatthhmmaanndduu, NNeeppaall

Published by:

Shubharambha Publication Pvt. Ltd.

Kathmandu, Nepal
URL: www.shubharambhapublication.com.np
E-mail: [email protected]

www.facebook.com/shubharambhapublication

Book : Maths Zone Grade: 4

Authors : Sthir Babu Subedi

Bishnu Prasad Poudel

Layout Design : Zeeta Computer Service Pvt. Ltd.

Ghantaghar, Kathmandu

Phone : 01-4263459, 9841418545

Copyright © : Publisher

Edition : First: 2075 B.S.

Second Revised : 2077 B.S.

No part of this book may be reproduced or transmitted by means(electronic,
photocopying, recording or otherwise) without prior written permission from the
publisher. Any breach of this condition will entail legal action and prosecution.

Printed in Nepal

Preface

Maths Zone with Maths for Fun and Practice Zone is developed according to
the curriculum of Nepal Government. It is the textbook with new design and
layout. The lessons are designed as per innovations. A colourful presentation
is made so that this description should look as interesting. This may lead to an
interactive approach. Our efforts are to make textbooks teachable with quality,
i.e. maintaining of standards. We have made specific endeavours to publish the
text and illustrations in much effective form.
The textbook is student-friendly and easy to practise and understand. It doesn’t
contain only the exercises, as in traditional textbooks. It is all mixed together
with the explanation, exploration, examples, exercises, etc. It is designed for
students to learn in a small collaborative group setting, where students practise
together, helping each other to learn the material. Ideally, the instructor would
not necessarily lecture, but would act more as a facilitator, and be available to
clarify ideas.
This Series is the complete program to help children practice the essential math
skills they learn. Matches the math curriculum so the children will reach their
full potential and on important standardized tests ! It applies interesting and
successful way to improve the child’s math. It comprises explanation in simple
language, examples with clear instruction, worksheets to increase the child’s
confidence, enjoyment, and success.
We are hopping for the positive and constructive comments and suggestions
from our respected teachers, guardians and well-wishers to improve our series
in the days to come. Any comments or suggestions for the improvement of the
book will be always welcome.

Authors

Contents

Unit 1 Geometry 5

29

Unit 2 Concept of Numbers

58

Unit 3 Basic Operation of Mathematics

88

Unit 4 Time and Money



Unit 5 Measurement 117



Unit 6 Mensuration 144

164

Unit 7 Fraction, Decimal and Percentage

216

Unit 8 Unitary Method

223

Unit 9 Bill and Budget



Unit 10 Statistics 228

Unit 11 Set 245

Unit 12 Algebra 255

M odel Question 268

1 Geometry

Specific Objective Prescribed by CDC

 To recognize and distinguish the vertices, edges and surfaces of some
simple solid objects.

 To draw the angles from 0° to 180° (in the difference of 10) by using
protractors.

 To distinguish acute, right and obtuse angles comparing with a right
angle.
Maths Zone Grade-4 5

Warm-up Questions

1. Identify the following figures & write their name in the
box.

2. What is the length of given line segment? B

P QA

PQ = cm AB = cm

3. Draw line segment AB of 5 cm.

4. Tick (√) the greatest angle. X

A P

B CQ R Y Z

5. Write the vertices, arms & angle of given triangle.

Vertices : P
...................., ...................., ....................

Arms : ...................., ...................., ....................

Angles : Q R ...................., ...................., ....................

6. Measure the length of each side of given Quadrilateral.

A AB = cm

BC = cm
B D CD =
cm

C DA = cm

6 Maths Zone Grade-4

Solid Shapes

Class Discussion

Solid Shapes Details/Description Physical Models

Cuboid ‰‰ All six surfaces are
rectangular.

‰‰ All six surfaces are
square.

Cube

Cylinder ‰‰ Two circular bases.
Sphere ‰‰ One curved surface.

‰‰ Round solid shapes.
‰‰ Only one curved

surface.

‰‰ One circular base.

‰‰ One curved surface.

Cone

‰‰ Two triangular

surface.

Triangular Prism ‰‰ Three rectangular

surface.

Maths Zone Grade-4 7

Exercise - 1.1 Physical Models

1. Match the following:
Solid Shapes

1. Cuboid

2. Cube

3. Cylinder

4. Sphere

5. Cone

6. Triangular prism

8 Maths Zone Grade-4

Solid Shapes, Skeleton and Nets

Class Discussion Nets of Solid Shapes

Solid Shapes Skeleton of Solid Shapes

Cuboid

Cube

Cylinder

Sphere

Cone

Triangular Prism

Note the teacher

Introduce skeleton and nets of solids to identify faces, vertices and edge only.

Maths Zone Grade-4 9

Vertices, Edges and Faces of Solid Shapes

Class Discussion Number of Number of Number of
Solid Shapes
Vertices Edges Faces
Edge
Vertex 8 12 6
Face

Cuboid

Edge
Vertex
Face
8 12 6

Cube

Edge

Curved Cibrcauselar 0 2 3
surface

Cylinder

cuOrnveed 0 0 1
surface

Sphere 112

Vertex
Curved

Edge
Edge

Circular base

Cone

Rectangular surface

Edge

Trsiuanrfgauclear 695

Triangular Prism

10 Maths Zone Grade-4

Exercise - 1.2

1. Draw the following shapes.

Cuboid Cube Triangular Prism

2. Color the different surfaces by different colors of the
following shapes. Write the number of surfaces.

Cylinder Sphere Cone

No. of Surfaces No. of Surfaces No. of Surfaces

............................. ............................. .............................

3. Write the number of faces, edges and vertices of the cube
and cuboid.

Cube Faces Edges Vertices

Cuboid

4. Fill the appropriate word in the blanks from the word banks.

a. A solid shape which has no vertices and no edge is called
......................

b. A solid shape which has one vertex and one edge is called
......................

c. A solid shape which has no vertices and three faces is called
......................

Word Bank Cube Cuboid Sphere Cone Cylinder

Maths Zone Grade-4 11

Angles

Review

An angle is defined as a figure formed by two lines that meet at
a common point.
‰‰ The common point of two lines is called vertex. A
Arm

‰‰ The two lines are called arms of the angle. O AngleB
In the given figure, 'O' is vertex and AO & OB Vertex Arm
are arms of the angle AOB.

Angles can be measured by the protector in degree.

Measurement of Angles

Outer scale
70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
50˚ 90˚ 130˚

40˚ Inner scale 140˚
30˚ 150˚

20˚ 160˚

10˚ 170˚

0˚ 180˚ 0˚ 180˚

Base line Base line
(Left side) (Right side)

This is protractor. ‰‰ In general, inner scale is in
It is used to measure ascending order from right to left
the angles. and 0° to 180°.

‰‰ Outer scale is also in ascending
order from left to right 0° to 180°.

‰‰ Always use the scale with 0° on one of the base arms of the angle.

‰‰ Always count round the edge from 0°.

12 Maths Zone Grade-4

Let's measure an angle PQR using Inner scale.

‰‰ Place the centre point of the protractor on P
the vertex 'Q' of the angle PQR.

‰‰ Adjust the protractor so that one arm 'QR'
of the angle PQR is along the base line.

‰‰ 'QR' arm is along the right side base of the Q R

protractor line so use inner scale.

‰‰ Count round the measure of the angle PQR where the other arm

QP crosses the scale. P
Here, ∠PQR = 50°.

QR

Let's measure an angle ABC using Outer scale.

‰‰ Place the centre point of the protractor on the vAertex 'B' of the
angle ABC.

‰‰ Adjust the protractor so that one arm 'BC' of
the angle ABC is along the baseline.

‰‰ 'BC' arm is along the leftside base of the C B
protractor so use outerscale.

‰‰ Count round the measure of the angle ABC where the other arm
'BA' crosses the scale.

Here, ∠ABC = 40°

A

CB
Maths Zone Grade-4 13

Exercise - 1.3

1. See the measure of the angle and write in the box.
a. A b.
70˚ 80˚ 90˚ 100˚ 110˚ R 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°
10° 170˚
10˚ 170° B C P 10˚ 170° Q 10° 170˚
0˚ 180˚ 0˚ 180˚ 0˚ 180˚
0˚ 180˚

∠ABC = ∠PQR =

c. Z d. Y

70˚ 80˚ 90˚ 100˚ 110˚ 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°

10˚ 170° Y 10° 170˚ X R 10˚ 170° A 10° 170˚
0˚ 180˚ 0˚ 180˚ 0˚ 180˚ 0˚ 180˚

∠XYZ = ∠RAY =
e. f.
G A
70˚ 80˚ 90˚ 100˚ 110˚ 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚ 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70° 50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚ 120° 60° 130˚
130° 50° 130° 50°
40˚ 140˚ 40˚ 140˚

30˚ 140° 40° 150˚ 30˚ 140° 40° 150˚

20˚ 150° 30° 160˚ 20˚ 150° 30° 160˚
160° 20° 160° 20°

10˚ 170° H 10° 170˚ I P 10˚ 170° R 10° 170˚
0˚ 180˚ 0˚ 180˚ 0˚ 180˚ 0˚ 180˚

g. ∠G HI = h. ∠PRA =

10˚ 20˚ 30˚ 40˚ 50˚ 60˚ 70˚ 80˚ 90˚ 100˚ 110˚ 120˚ 130˚ 140˚ 301°502˚0°16100˚°
180˚ 170° 160° 150° 140° 130° 120° 110° 100° 90˚ 90˚ 80° 70° 60° 50° 40°
S0˚ R90˚ 170˚
80° 100˚ 110˚ 0˚ 180˚
80˚
70° 120˚ 506˚0˚70˚13102°01°10°100°
60° 130˚

50°
40° 140˚
0˚ 10°203°01°701˚6105˚0˚ 40˚ 140°
180˚ A 302˚0˚10˚115600°1°701°80˚
A

U 0˚

D

∠USA = ∠DRA =

14 Maths Zone Grade-4

2. Measure the following angles by using inner scale of the
protractor. Fill in the boxes.
P
a. A b.

BC Q ∠PQR = R
c. X ∠ ABC = D d.

Y Z E ∠DEF = F
∠XYZ =

3. Measure the following angles by using outer scale of the
protractor & fill in the boxes.
a. b. B

K

ML S ∠BDS = D
∠KLM = L

c. Xd.

Z Y N M
∠XYZ = ∠LMN =

Maths Zone Grade-4 15

4. Measure the following angles and fill in the boxes.

a. X b. P

Z R Q
X
Y ∠PQR =
∠XYZ = I
c. N d.

L

Z Y
∠XYZ =
M
H
∠LMN =

e. f.
EF

D G
∠DEF = ∠GHI =

16 Maths Zone Grade-4

5. Measure the angles (Inner) of the triangles.

a. A b. L c. P

B CM NQ R
∠A = ∠L =
∠B = ∠M = ∠P =
∠C = ∠N = ∠Q =
∠R =

6. Write the name and size of the angles which are colored
in the given figures. (In your exercise copy)

a. A b. P S

R

CB

QT
ED

F

Maths Zone Grade-4 17

Construction of Angles OB

Let's draw an angle of 50° using 70˚ 80˚ 90˚ 100˚ 110˚
inner scale. [Consider the zero is in the 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
inner scale to the right hand side.] 120° 60° 130˚
130° 50°
‰‰ Draw a line segment 'OB'. 40˚ 140˚

‰‰ Place the protractor such that its centre 30˚ 140° 40° 150˚
is at 'O' and its baseline is on OB.
20˚ 150° 30° 160˚
‰‰ Count round the edge 0° to 50° (using 160° 20°
inner scale) and mark 'A'.
10˚ 170° O 10° 170˚ B
‰‰ Remove the protractor. Join the points 0˚ 180˚ 0˚ 180˚ B
O and A by using scale.
70˚ 80˚ 90˚ 100˚ 110˚ A
∠AOB = 50° 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
Let's draw an angle of 120° using 120° 60° 130˚
outer scale. [Consider the zero is in the 130° 50°
40˚ 140˚
outer scale to the left hand side.]
30˚ 140° 40° 150˚
‰‰ Draw a line segment XY.
20˚ 150° 30° 160˚
‰‰ Place the protractor such that its centre 160° 20°
is at 'Y' and its baseline is on XY.
10˚ 170° O 10° 170˚
‰‰ Count round the edge 0° to 120° (using 0˚ 180˚ 0˚ 180˚
outer scale) and mark 'Z'
A
‰‰ Remove the protractor. Joint the points
Y and Z by using scale. OB

\ ∠XYZ = 120° XY

18 Maths Zone Grade-4 70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚
130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

X 10˚ 170° 10° 170˚
X
0˚ 180˚ Y 0˚ 180˚

70˚ 80˚ 90˚ 100˚ 110˚ Z

60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚
130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

10˚ 170° 10° 170˚

0˚ 180˚ Y 0˚ 180˚

Z

120°
XY

Exercise - 1.4

1. Draw the following angles using inner scale of the
protractor. (If the zero is in the innerscale to the right hand side.)

a. 20° b. 60° c. 80°

d. 90° e. 130° f. 150°

2. Draw the following angles using outer scale of the
protractor. (If the zero is in the outerscale to the left hand side.)

a. 30° b. 50° c. 70°

d. 90° e. 120° f. 160°

3. Draw the following angles using protractor.

a. 10° b. 45° c. 75°

d. 110° e. 140° f. 135°

Note to the teacher :

In the market we may find different protractors. They may
start 'O' from inner or outer scale to the right hand side. Here
we have consider the 'O' is in right hand side of inner scale
and left hand side of outer scale. If you found the different
than this structure then guide the students accordingly.

Maths Zone Grade-4 19

Types of Angles:

Class Discussion

Name the given figures.

70˚ 80˚ 90˚ 100˚ 110˚
60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
120° 60° 130˚
130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

10˚ 170° 10° 170˚

0˚ 180˚ 0˚ 180˚

� Identify the angle made by the corner of the set-square with the

help of protractor.

 The angle made by the corner of the set square is exactly ..............

degree.

Right Angle A

� An angle that measures exactly 90° is

a right angle. In the adjoining figure,

∠ABC is a right angle.

BC
� Give any two real life examples that show the right angle in our

surroundings.

20 Maths Zone Grade-4

‰‰ Join the corner of both set-
squares.

‰‰ Identify the angle made by
them.

 It is exactly.............. degree. 70˚ 80˚ 90˚ 100˚ 110˚
‰‰ Check the angle in a base line of 60˚ 120˚
50˚ 110° 100° 90˚ 80° 70°
the protractor. 120° 60° 130˚
 It is also .................. degree. 130° 50°
40˚ 140˚

30˚ 140° 40° 150˚

20˚ 150° 30° 160˚
160° 20°

10˚ 170° 10° 170˚

0˚ 180˚ 0˚ 180˚

Straight Angle

An angle whose measure is exactly 180° is a straight angle. In
the adjoining figure, ∠PQR is a straight angle.

P QR

‰‰ Give any two real life examples that show the straight angle in
our surrounding.

Oh! I understand that;
Angle exactly 90° is  Right angle
Angle exactly 180° is Straight angle

Let's discuss the angles which are less than 90°.
They are 89°, 75°, 40°, 30°, 10°, 5° etc.

Maths Zone Grade-4 21

Acute Angle X

An angle which is less than 90° is called an
acute angle. In the adjoining figure ∠ XYZ
is an acute angle.
YZ

� Check the following angle using set square whether they
are acute or not? Write Yes or No in the box.
a. b. c.

� Recheck them using protractor whether their size
(Measurement) is smaller than 90° or not?

Guess the angle which is greater 90° but smaller than 180°.

Obtuse Angle R

An angle which is more than 90° but less A M
180° is an obtuse angle. In the adjoining
figure ∠RAM is an obtuse angle.

� Check the following angle using set square whether they
are obtuse or not? Write 'Yes' or 'No' in the box.
a. b. c.

� Recheck them using protractor to identify their size.
22 Maths Zone Grade-4

Reflex Angle

An angle whose measure is more than 180° M L
but less than 360° is a reflex angle. In the
adjoining figure ∠LMN is a reflex angle.
L
Complete Turn

An angle whose measure is exactly 360° is O A
complete turn. In the adjoining figure, line
OA makes 360°.

Exercise - 1.5

1. Fill in the gaps in the table with the appropriate answer.

S.N. Types of angles Size (Measurement) Examples

1. Acute Angle greater than ............ 40°, 50°, 60°
and smaller than ..... etc.

2. ...................... exactly 90° 90°

3. Obtuse Angle greater than ........... ......., .........,
and less than ..........
............

4. Straight Angle .............................. 180°

5. Reflex Angle .................... 180° 185°, 210°,
and .................... 275°
360°

6. ...................... exactly 360° 360°

Maths Zone Grade-4 23

2. Classify the angles measuring by the protractor.

a. b. c.

d. e. f.

3. Match the following angles with their examples.

Acute Angle 90°

Right Angle 185°

Obtuse Angle 45°

Straight Angle 175°

Reflex Angle 180°

4. Identify and write the angles made by the minute hand
and the hour hand in the following clocks.

24 Maths Zone Grade-4

Maths Fun

A. Name acute angle, obtuse angle, right angle and reflex
angle in the route map of a city.
CD

A BE F
N MJ I

LK G
Acute Angles H


Obtuse Angles


Right angles


Reflex angles



Maths Zone Grade-4 25

B Prepare acute angle, right angle, obtuse angle and
straight angle with fold as given.
‰‰ Take a sheet of square paper.
‰‰ Fold it into half vertically and horizontally.
‰‰ O pen the last fold.
‰‰ Take one corner of the paper and get it to meet the crease
line.
‰‰ Find out acute angle, right angle, obtuse angle and straight
angle in the last fold.

(i) (ii) (iii)
(iv)
A

BE

C D

(v)

26 Maths Zone Grade-4

Practice Zone

Group 'A'

1. Tick the right answer of the followings.
a. An acute angle measures.
i. equal to 90°
ii. equal to 180°
iii. smaller than 90°
iv. greater than 90° and less than 180°

b . A right angle measures

i. equal to 90°

ii. equal to 180°

iii. greater than 90 and smaller than 180°

iv. smaller than 90°

c. A straight angle measures

i. two right angle ii. 180°

iii. Both (i) & (ii) iv. None of them

2. Choose the correct word and complete the following.
a. Cube has all .............. face (Rectangular, Square, Triangular)

b. The point where three or more than three edges of a solid meet
is called the .............. of the solid. (origin, vertex, common point)

c. The line segment where two faces of a solid meet is called the
.............. of the solid. (common side, edge, face)

d. A solid that has only one curved and smooth surface is ..............
(sphere, cone, cube).

e. A device used to measure the size of an angle is called ..............
(degree, centimeter, protractor)

Maths Zone Grade-4 27

f. I n a set square, one angle is right angle, and the other two are
both .............. angles. (acute, right, obtuse)

3. Find and circle the shapes from the 3 possibilities.

Face = 6
Edges = 12
Vertices = 8

Faces = 5
Edges = 9
Vertices = 6

Faces = 5
Edges = 8
Vertices = 5

Faces = 2
Edges = 1
Vertices = 1

Group 'B'

1. Draw an acute angle and obtuse angle of your choice in
your copy and measure its size.

2. Measure the given angles.

a. P b. X c. H

QR Z IJ
Y
∠PQR ∠ HIJ
∠ XYZ
28 Maths Zone Grade-4

2 Concept of
Numbers

Specific Objective Prescribed by CDC

 To count, read and write numbers up to 1 crore using Hindu Arabic
number system (both in numerals and in words) and their place value.

 To round off the numbers up to 999 to the nearest hundred.
 To distinguish the prime and composite numbers from 1 to 50.
 To find the prime factors of the numbers from 1 to 99 by prime

factorization method.
Maths Zone - Grade 4 29

Concept of Number

Class Discussion

In the ancient time, people didn't have any numerals for
counting. They used to count things by using stones, small
sticks, lines on the walls and later fingers. Along with the
development of human civilization people of different places
used different symbols for number system.
The Roman Numerals
Roman numerals was originated in ancient Rome. The Roman
numeral system is a cousin of the Etruscan numerals and the
letters derive from earlier non-alphabetical symbols. The first
ten Roman numerals are I, II, III, IV, V, VI, VII, VIII, IX, X.
The Hindu-Arabic numerals
The Hindu-Arabic numerals system is a decimal place-value
numeral system. Digits 0,1, 2, 3, 4, 5, 6, 7, 8, 9 were developed
by Hindu and spread by Arabian all over the world. So, this
number system is called Hindu Arabic Numerals.

Devanagari numerals : The digits are ), !, @, #, $, %, ^, &, *, (

Counting/Natural numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
Whole numbers : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ...
Even numbers : 2, 4, 6, 8, 10, 12, ...
Odd numbers : 1, 3, 5, 7, 9, 11, ...

30 Maths Zone - Grade 4

Revision of 6-digit numbers

Let's take a 6-digit number.

235794

Put comma according to National System.

2,35,794, then

Study the numbers in different forms

Lakhs Ten Thousands Hundreds Tens Ones Place
Thousands

2 3 5 7 9 4 Face value

200000 30000 5000 700 90 4 Place value

2×100000 3 × 10000 5 × 1000 7 × 100 9 × 10 4×1 Expanded
form

Two lakhs thirty five thousands seven hundred and Number
ninety four. Names

@,#%,&($ Devanagari
Number

bO' { nfv kQ} L; xhf/ ;ft ;o rf}/fgAa] Devanagari
Number
name

Exercise - 2.1

1. Complete all the questions as shown in the example. (Use pencil to

write in the given spaces.)

a. 325798  3,25,798  Three lakh, Twenty five thousand
seven hundred and ninety eight

b. 182734  

c. 492799  

d. 882625  

Maths Zone - Grade 4 31

2. Complete all the questions as shown in the example.

a. Three lakh Forty three thousand eight hundred and thirty
three.

L T-Th Th H T O  3,43,833
343 8 3 3

b. Five lakh Seven thousand Nine hundred twenty six.



c. Four lakh Three thousand Six hundred Fifty.



3. Complete all the questions as shown in the example.

a. 235726  200000 + 30000 + 5000 + 700 + 20 + 6

b. 479812  + + + + +

c. 479812  + + + + +

4. Complete all the questions as shown in the example.

a. 345796  3 × 100000 + 4 × 10000 + 5 × 1000 +
7 × 100 + 9 × 10 + 6 × 1

b. 543782  + + +
+ +

c. 818012  + + +

+ +

5. Complete all the questions as shown in the example.

a. 300000 + 40000 + 5000 + 700 + 60 + 8  3,45,768

b. 800000 + 70000 + 4000 + 300 + 90 + 7 

c. 900000 + 0 + 3000 + 400 + 70 + 0 

d. 7×100000+4×10000+3×1000+5×100+0+9×1

e. 8 × 100000+3×10000+0+4×100+6×10+8×1 

32 Maths Zone - Grade 4

6. Complete all the questions as shown in the example.

a. 2 , 3 5 7 9 8 Face value 7
Place value 700

b. 8 1 5 7 2 9 Face value
Place value

c. 9 3 7 9 1 8 Face value
Place value

d. 8 1 2 9 1 0 Face value
Place value

7. Complete all the questions as shown in the example.
a. Three lakh seven hundred fifty.

tLg nfv ;ft ;o krf;

b. Four lakh thirty two thousand nine hundred and seventy.


c. Nine lakh forty five thousand seven hundred.



8. Complete all the questions as shown in the example.

a. kfrF nfv bO' { xhf/ tLg;o kt} fnL;

Five lakh two thousand three hundred forty five

b. tLg nfv Ps xhf/ ;ft ;o ;}tL;



c. ;ft nfv krf; xhf/ kfFr



Maths Zone - Grade 4 33

The smallest and the greatest numbers

Let's complete the table

Number formed Smallest Greatest
with number number
1 digit
1 9
2 digits
10 99
3 digits

4 digits
5 digits

6 digits
7 digits

8 digits

1. Find the difference of the greatest number of 7 digits and
the smallest number of 8 digits.

10000000 – 9999999 =
2. Find the sum of the greatest number of 6 digits and 1.

9999999 + 1 =

3. Write the conclusion from these two questions.


34 Maths Zone - Grade 4

National System of Numeration

Numbers up to crore

Periods Crores Lakhs Thousands Ones
Ten Ten
Place Name Crore Lakh Lakh Thousand Thousand Hundred Ten One

42987653 4 29 87 65 3

Four crore twenty nine lakh eighty seven thousand six hundred
and fifty three.

42987653
Ones
Thousands
Lakhs
Crores

Use of Commas

To indicate periods in the National system of Numeration, at
first we place a comma after three digits from the right and
then after every two digits.

Example 1

Rewrite the number using comma and write in words.
a. 4791823 b. 58132437

Solution:
a. 4791823  47,91,823
Forty seven lakh ninety one thousand eight hundred

and twenty three.
b. 58132437  5,81,32,437
Five crore eighty one lakh thirty two thousand four

hundred and thirty seven.

Maths Zone - Grade 4 35

Example 2

Write down the number using place value chart for : Four
crore sixty two lakh thirty seven thousand two hundred
and seventeen.

Solution:
5 crore 62 lakh 37 thousand 2 hundred and 17

Crores T. Lakhs Lakh T.Th Th H T O
5 6 2 3 72 1 7

∴ It is 5,62,37,217

Example 3

Write down the number using place value chart for three
crore five lakh and two thousand and five.

Solution:
3 crore 5 lakh 2 hundred and 5

Crores T. Lakhs Lakh T.Th Th H T O
3 0 5 0 020 5

∴ It is 3,05,00,205.

Alternative:

3 crore 5 lakh 2 hundred and 5

__ __ __ __ __ __ __ __

3 5, ,2 5

Then,

3, 0 5, 0 0, 2 0 5

∴ It is 3,05,00,205

36 Maths Zone - Grade 4

Example 4

Write five lakh three thousand and four.

Solution:
5 lakh 3 thousand and 4

5 lakh ⇒ 5,00,000 Alternative Method for
Writing the Words in
3⇒ 3,000
Thousands Number
4 Ones 4 5,03,004
⇒+

5, 03, 004

∴ 5, 03, 004

National System of Numeration in Devnagari

lkl/o8 s/f8] nfv xhf/ Ps

:yfg gfd s/f]8 bz nfv nfv b=xhf/ xhf/ ;o bz Ps

#$%^@*#% # $ % ^ @ * # %

∴ tLg s/f8] k}tfnL; nfv a;} 7\7L xhf/ cf7 ;o kt} L; .

Example 1

Write in Devanagari number.

bO' { s/f8] krf; nfv tLg ;o ;ft .

Solution:

bO' { s/f]8 krf; nfv tLg ;o ;ft . Ö @,%),)),#)&

Maths Zone - Grade 4 37

Face Value and Place Value

Let's take 8 digit number 45792812

 Each digit of this number has two types of values.

Face value : The actual value of a digit is called its face value.

Place value : The value of a digit according to its position is
called its place value.

So, the face value of 4 in 45792812 is 4.

and the place value of 4 is 4,00,00,000 or four crore.

The smallest and the greatest numbers formed by the given digits.

Let's take the digits 2, 4, 3, 5, 7 and 9.
First, arrange them in increasing order 234579  Smallest number.

Arrange them in decreasing order 975432  Greatest number.

Now,

The greatest number and the smallest number formed by

3, 0, 7, 2, 5, 8, 9 9875320 Do not write 'o' at first
The greatest number = 2035789 because 20 is two
The smallest number = digit number but 02
is one digit number.

Exercise - 2.2

1. Rewrite and complete the following.
a. The greatest number of 5 digits ...........................
b. The smallest number of 7 digits ...........................
c. The greatest number of 8 digits ...........................
d. The smallest number of 6 digits ...........................

38 Maths Zone - Grade 4

2. Rewrite the given numbers and write the face value

and place value of colored digit.

a. 3587923 b. 27898255

c. 45279811 d. 81278432

3. Re-write the number using comma and in words.

a. 43279811 b. 4200972

c. 42345678 d. 20253040

4. Write down the number using place value chart.
a. Fifty five lakh thirty three thousand two hundred and
twenty two.
b. Two crore twenty five lakh, thirty four thousand four
hundred fifty five.
c. Thirty seven lakh three hundred forty six.
d. Seven crore fifty five thousand nine hundred and
twenty six.
e. Four crore twenty two lakh and five.

5. Write the number in Devnagari numerals.

a. ;f7L nfv k}t+ fnL; xhf/ tLg ;o c;L

b. Ps s/f]8 krf;L nfv rf}tL; xhf/ 5 ;o ;q

c. kfFr s/f8] krkGg nfv c7f;L xhf/ tLg;o t]TtL;

6. Write the numerals in Nepali words.

a. %$,^&,#@% b. #%,$#,@!# c. %,^(,*&,@!%

7. Write the smallest and the greatest number formed by

the given digits (using once.)

a. 2, 4, 1, 3, 5 and 7 b. 6, 9, 3, 4, 7 and 8

c. 2, 4, 0, 3, 5, 9 and 7 d. 8, 6, 7, 2, 4, 0 and 3

Maths Zone - Grade 4 39

International System of Numeration

Numbers upto Millions

Periods Millions Hundred Thousand Thousand Ones
Millions Thousand Ten 1 Hundred Tens Ones
Place
Name 2 3 Thousand 7 34

2351734 5

Two million three hundred fifty one thousand seven hundred
and thirty four.

2 , 3 5 1 ,7 3 4

Ones

Thousands

Millions

Use of Commas: To indicate periods in international system,
we place a commas after every three digits from the right.

Example 1

Rewrite the number in international system using commas
and in words.
8351724

Solution: 8,351,724
Eight Million three hundred fifty one thousand seven
hundred and twenty four.

Example 2

Write down the number using place value chart for
Five million two hundred forty six thousand eight hundred
and twenty seven.

Solution: 5 Million 246 thousand 827

M H.T T.Th T H T O
5246827

∴ It is 5,246,827.
40 Maths Zone - Grade 4

Exercise - 2.3

1. Rewrite the given numbers in international system

using commas and in words.

a. 426719 b. 223345

c. 1872436 d. 7740826

e. 234459 f. 1586402

2. Write down the number using place value chart for:
a. Three hundred forty six thousand five hundred and twenty
four.

b. Eight Million, four hundred fifty two thousand nine
hundred and seventeen.

c. Seven Million four hundred twelve thousand and fifty
nine

d. Five Million two hundred and sixty three.

e. Seven million four hundred ninteen thousand two
hundred and sixty two.

3. Find the place value of the underlined digits in the

following numbers and write in words.

a. 347, 598 b. 234, 982

c. 4, 332, 468 d. 8, 257, 999

e. 8, 986, 752 f. 2, 43, 7987

4. Write the smalllest number of 7 digits and greatest
number of 6 digits. Find their sum and rewrite the
number names in international system of numeration.

Maths Zone - Grade 4 41

Rounding off Numbers

Class Discussion

Rounding means making a number simpler but keeping its
value close to what it was. The result is less accurate, but
easier to us.
Rounding whole numbers is the process by which we change
the number to the nearest 10, 100 or 1000 to make calculation
easier.

Round off the given numbers nearest to 10.

14 is nearer to 10 16 is nearer to 20

10 11 12 13 14 15 16 17 18 19 20

We can write 14 as 10 and 16 and 20 round off nearest to
10.

What is about 15?

15 is in middle (equidistant
from 10 and 20)

10 11 12 13 14 15 16 17 18 19 20

In this case we rounded up 15 to 20 to the nearest 10

Round off the given numbers nearest to 100.

300 310 320 330 340 350 360 370 380 390 400

We can write 320 as 300, 370 as 400 and 350 as 400
rounded off nearest to 100.
42 Maths Zone - Grade 4

Round off the given numbers nearest to 1000.

4000 4100 4200 4300 4400 4500 4600 4700 4800 4900 5000

We can write 4300 as 4000, 4800 as 5000 and 4500 as
5000 rounded off nearest to 1000.

Rules for Round off Numbers

Lets take a number 26574

‰‰ Find the place to which you wish to round and underline it.

26574 26574 26574
∴ Tens ∴ Hundreds ∴ Thousands

‰‰ If the digit to the right is 5 or greater, add 1 to the underlined
digit.

‰‰ If the digit to the right is less than 5, leave the marked digit
unchanged.

‰‰ Replace each digit to the right of the marked place with zero.

26574 26574 26574

4<5 4>5 5=5

∴ 26570 ∴ 26600 ∴ 27,000

Exercise - 2.4

1. Round off the number to the nearest Ten e. 75645
a. 24 b. 45 c. 315 d. 4444

2. Round off the number to the nearest hundred
a. 345 b. 564 c. 5555 d. 47865 e. 67349

3. Round off the number to the nearest thousand
a. 4375 b. 6666 c. 274821 d. 74268 e. 75633

4. The number of students in Rara Boarding School is 1275.
Round off it to the nearest tens, hundred and thousands.
Maths Zone - Grade 4 43

Compare and Learn

Even Numbers Odd Numbers
The numbers that can be The numbers which are not
divided by 2 are called even even are called odd numbers.
numbers. e.g. : 2, 4, 6, ....., e.g.: 1, 3, 5, 7, ......, 21, 23,
20, 24, ..... ......

Factors Multiples
The numbers which can divide The numbers which can be
a number without leaving divided by a number are called
remainder are called factors multiples of the number.
of the number.
The number 1 is neither prime
Factors of 6 are 1, 2, 3 and 6. nor composite.

Prime and Composite Numbers

Now, let's investigate the ideas for prime and composite numbers.

Numbers Arrangements Factors/Products
1
1 1×2
1×3
2

3

4 1 × 4, 2 × 2

5 1×5

6 1 × 6, 2 × 3, 3 × 2

7 1×7

44 Maths Zone - Grade 4

8 1 × 8, 2 × 4, 4 × 2

9 1 × 9, 3 × 3

From the table we can see that the numbers 2, 3, 5 and 7 have
only one arrangement. So, these numbers are prime numbers.
Prime Numbers: The numbers that have 1 and the number
itself as factor are prime numbers. eg: 2, 3, 5, 7 ......

The numbers which are exactly divisible by 1 or itself
are called prime number.
Composite numbers: The numbers that have more than two
factors are composite numbers. eg: 4, 6, 9, 12, .......
The numbers which are exactly divisible by a number
other than 1 and itself are called composite number.

Prime Number from 1 to 50
Do the following activities:

Step 1 : Write down the numbers from 1 to 50 as shown
Table - 1

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50

Maths Zone - Grade 4 45

Step 2 :

‰‰ Cross 1 because it is not prime.

‰‰ Encircle 2 and 5 then cross all the numbers of the column 2 and 5.

‰‰ Encircle 3 and 7.

‰‰ Cross all the numbers of the column 4, 6, 8 and 10.

Step 3
Rewrite the remaining numbers in Table 2.

(Table - 2)
23 5 7 9

11 13 17 19

21 23 27 29

31 33 37 39

41 43 47 49

Step 4:
Cross the multiples of 3 and 7 respectively and rewrite the
remaining numbers in Table 3.
(Table - 3 )
23 5 7

11 13 17 19

23 29

31 37

41 43 47

Step 5:
Write all the prime numbers from 1 to 50.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
Note to the teacher: Teachers can use Sieve of Eratosthenes
method to find prime number.

46 Maths Zone - Grade 4

Exercise - 2.5

1. Answer the following questions
a. Write the smallest even number.

b. Write the smallest prime number.
c. Which number is neither prime nor composite?
d. How many factors are there in a prime number?
2. Answer the following questions.
a. Identify the prime and composite numbers that are given

below.
4, 7, 13, 18, 27, 37, 41, 49

b. Write down the first four prime numbers.
c. List out the prime numbers from 30 to 50.
d. How many prime numbers are there from 1 to 50.
e. List out the composite numbers from 20 to 40.
f. List out all the prime numbers from 1 to 50.
3. Make a grid of numbers from 1 to 100 and do the same
activity as given on pages 45 and 46 to find the prime
numbers from 1 to 100.
a. How many prime numbers are there? List all the prime

numbers.
b. How many composite numbers are there?
c. How many prime numbers are there between 50 and 100?

Note to the teacher: Teachers can use Sieve of Eratosthenes method
to solve question no. 3.
Sieve of Eratosthenes is a simple, ancient algorithm for finding all
prime numbers up to any given limit. It does so by iteratively marking as
composite (i.e., not prime) the multiples of each prime, starting with the
first prime number, 2.

Maths Zone - Grade 4 47

} Prime Factorization

} Class Discussion
A prime number has exactly two factors 1 and itself.

1×7=7
Factors Product

The first four prime numbers are 2, 3, 5 and 7

Divisibility test of first four prime numbers

By 2 : All even numbers that end with 0, 2, 4, 6 and 8.
eg: 10, 14, 44, 88, etc.
By 3 : If the sum of its digits is divisible by 3, then the number

is also divisible by 3.
eg: 54 ⇒ 5 + 4 = 9, 9 is divisible by 3
So 54 is divisible by 3.
By 5 : If the last digit of a number is 5 or 0.
eg: 50, 65, 105, etc.
By 7 : Double the last digit and subtract it from the remaining

number. If the result is divisible by 7,then the number
is also divisible by 7.
e.g: 315 ⇒ 31 - ( 2 × 5) = 21
and 21 ÷ 7 = 3
So, 315 is divisible by 7.

The word composite means made up of various part.
Each composite number is made up of a single set of prime
factors.

48 Maths Zone - Grade 4

Let's investigate the number up to 15. 4 5
=2×2
123 10
9 =2×5
6 78 =3×3
=2×3 =2×2×2 15
14 =3×5
11 12 13 =2×7
=2×2×3

The process of resolving a number into factors such that all of its
factors are prime is known as prime factorization.

Factors Tree Method Successive Division method

Example 1

Find the prime factors of 36 by factor tree method.

Solution:

36 36

2 18 Composite 2 18
Composite
29 No Composite 9

Start with the 33 3
smallest prime
factor of the 36 = 2 × 2 × 3 × 3
given number.
Factor Tree Method

Restate the prime factors: 36 = 2 × 2 × 3 × 3

Using Index/exponential notation 36 = 22 × 32

Maths Zone - Grade 4 49

It doesn't matter how you can split your composite
numbers you always get same prime factors.

36 36 Note: It is better
approach to write
66 4 ×9 prime numbers in
2×3 2×3 ascending order.
2× 2× 3 × 3
∴ 24 = 2 × 3 × 2 × 3
24 = 2 × 2 × 3 × 3

Example 2

Find the prime factors of 18 by successive division method.

Solution: 12 is even so it is divisible by smallest prime number 2.
2 12 2 × 6 = 12, write the quotient below the divided and repeat
39 the same process until not getting 1 in quotient.
33
1

\ 12 = 2 × 2 × 3

Exercise 2.6

1. Identify the number which are divisible by 2, 3, 5 and 7.
40, 57, 77, 90, 205, 324, 210, 105, 343, 147

Divisible by 2 Divisible by 3 Divisible by 5 Divisible by 7

50 Maths Zone - Grade 4