Math 4

Revised Edition

Class

4

Author
Shyam Datta Adhikari

M.Sc (Maths), TU

Oasis School Mathematics Book-4 1

Name : ....................................................

Class : ................... Roll No. : ..........

Section : ...................................................

School : ...................................................

Publisher
Oasis Publication Pvt. Ltd.
Copyright
The Publisher
Edition
First Edition : 2067
Re print : 2068, 2069, 2070, 2071, 2072. 2073
Third Edition : 2075 (2018 A.D.) (Completely Revised)
Contributors
Megh Raj Adhikari
Madan Kumar Shrestha
Shanta Kumar Sen (Tamang)
Layout
Oasis Desktop Publishing
Ramesh Bhattarai

Printed in Nepal

2 Oasis School Mathematics Book-4

Preface Oasis School Mathematics is an activity-oriented and interactive series
intended for the students of the primary level. It has been designed in
compliance with the latest curriculum of the Curriculum Development
Centre (CDC), the Government of Nepal, with a focus on child psychology
of requiring mathematical knowledge and skill. The major thrust is on
creating an enjoyable experience in learning mathematics through the
inclusion of a variety of problems which are closely related to our daily
life. This book is expected to foster a positive attitude among children and
encourage them to enjoy mathematics. A genuine attempt has been made
to present mathematical concepts with ample illustrations, assignments,
activities, exercises and project works to students so as to encourage them
to participate actively in the process of learning.

Key Features Unit test evaluates
knowledge, understanding
Assignment provides students an and skill of the mathematical
opportunity for immediate practice for concepts learnt in the
retention of mathematical concepts. respective unit.

Illustration facilitates easy groups of Worksheet helps students
logic behind the mathematical concepts. grasp the basic principles of
mathematical concepts in a
Exercise helps students have fun way.
additional practice for reinforcement of
mathematical knowledge and skill. Objective questions help
students analyse the correct
Activity provides opportunities for from multiple choices.
students to relate mathematical concepts
to everyday life.
Project work helps students in learning
by doing.

I am highly grateful to principals, administrators, experts and mathematics teachers
who have provided me with opportunities to anticipate in workshops, teachers, training
programmes and interaction programmes as a resource person. Their invaluable
feedback has helped me immensely to thoroughly revise and comprehensively update
the series.

I am deeply indebted to my students who are the source of encouragement for me to go
ahead with this project.

I am extremely grateful to Mr. Bijay Kumar Basnet for painstakingly editing the content
and the language of the series.

Grateful thanks go to chairman Sanjaya Kumar Chaudhary and Managing Director
Mr. Harish Chandra Bista for their invaluable support and cooperation in getting this
series published in this shape.

At the end, constructive and practical suggestions of all kinds for further improvement
of the book will be appreciated and incorporated in course of revision.

– Shyam Datta Adhikari

Oasis School Mathematics Book-4 3

Contents 5
30
1. Geometry 69
2. Number System 103
3. Four Fundamental Operations 133
4. Fraction 155
5. Decimal 166
6. Percentage and Unitary Method 183
7. Time 192
8. Money Matters 214
9. Metric Measurement 230
10. Perimeter, Area and Volume 245
11. Graphs, Bills, Temperature and Sets 264
12. Algebra
13. Model Test Paper

4 Oasis School Mathematics Book-4

UNIT

1 Geometry

12 Estimated Teaching Hours: 15
93

6

Contents • Point, line, line segment and ray
• Angles
• Types of angles
• Triangles
• Types of triangles
• Solid figures

Expected Learning Outcomes

Upon completion of the unit, students will be able
to develop the following competencies:

• To identify the point, line, line segment and ray
• To measure the given line segment using a ruler
• To draw a line segment of given length
• To identify the vertex and arms of an angle
• To measure the given angle with the help of a protractor
• To construct the angle of given measurement with the help of

protractor
• To categorise the angle
• To categorise the triangle on the basis of its sides
• To categorise the triangle on the basis of its angles
• To identify the corners, edges and faces of solid figures

Materials Required: Paper cutting of angles having different shapes, ruler,

protractor, compass, models of solid objects like cube,
cuboid, cylinder, sphere and glue, cryons, etc.

Oasis School Mathematics Book-4 5

Point, line, line segment and ray (review)
Point:

This is a point. A point is represented by a dot. It has no dimension.
It is denoted by capital letters A, B, C etc.

Line:

A line has no end points which extend to any length on both sides.
It is a line.

Point
Line
Line segment
Ray

Line Segment:

A line segment is a part of a line, which has a definite length.
AB is a line segment.

Ray:

A ray is a type of line which has only one end point. It is half of a line
It is a ray.

6 Oasis School Mathematics Book-4

Class Assignment

1. Identify whether the given figures are point, line, line segment or ray.
a. b. c. d.

2. Fill in the blanks.
a. A point is represented by………………..
b. A……………….has no dimension.
c. A……………….has no end point.
d. A part of a line is a………………..
e. A……………….has only one end point.

3. Find the number of line segments used in the following figures:

a. b. c. d. e.

Measurement of a line segment P Q

PQ represents a line segment. Length of a line
segment is measured with the help of a ruler.

This is a ruler. Each number in the ruler represents centimeter. Each
centimeter is divided into 10 small sub-divisions. They represent
millimetre (mm).

Oasis School Mathematics Book-4 7

How to measure the line segment? Steps:
AB
• Place the ruler along the line
Remember ! segment AB such that the
• 1 cm = 10 mm zero mark is on the ruler at
• 5 cm 6 mm = 5.6 cm point A.

• Read the mark on the ruler
which corresponds to the
point B. The reading of
B gives the length of line
segment AB.

\ AB = 2.5 cm

Note: A divider can also be used to measure the line segment.

Class Assignment

Write the reading of the given points.

A B C DE F G

A = .......... cm
B = .......... cm
C = .......... cm
D = .......... cm
E = .......... cm
F = .......... cm
G = .......... cm

8 Oasis School Mathematics Book-4

Construction of a line segment of given length

We use a ruler to draw a line Steps:
segment.
• Mark any point A, which
Eg draw a line segment of 3.5 corresponds to the 0 mark of the
cm. ruler.

AB • At the point which corresponds
to 3.5 cm, mark point B.

• Join AB with the help of the
ruler.

AB is the required line segment of length 3.5 cm.

Exercise 1.1

1. Find the length of the following line segments.
a. B b.

A C D
H
c. d.

E G

F

2. Find the length of line segments AB, BC, CD, DE, AC and CE.

A B C D EF

3. Measure the length of the sides of the following figures and find their
perimeters (Sum of the length of their sides).

a. A b. P c. M

Q NP
S

BC R
O

Oasis School Mathematics Book-4 9

4. Draw line segments with the given lengths: c. CD = 6.2 cm
a. AB = 6 cm b. XY = 5.5 cm f. MN = 5.2 cm
d. EF = 3.6 cm e. PQ = 6.3 cm
g. OP = 3.8 cm h. GH = 4.3 cm Consult your teacher.

Angles

Two rays OA and OB meet at point O to form an angle in fig (i).
Two line segments OA and OB meet at point O to form an angle

in figure (ii)

Hence two rays or line segments form an angle at their common end

point. A

A

Angle B Angle B
O O
Fig. (ii)
Fig. (i)

angle angle

Vertex and arms of angles A

In the given figure, two line segments OA arm
and OB meet at O to form an angle.
OA and OB are the arms of the angle and O O angle B
is the vertex. vertex arm

The common end point of two line segments is called vertex and the
line segments are called arms.

10 Oasis School Mathematics Book-4

Notation of angle O A
The angle is represented by ∠. B
So angle AOB is denoted as ∠AOB. ∠AOB.
It can also be written as ∠BOA.

Note:
arm
∠AOB and ∠BOA can simply be written as ∠O

Remember !

• When you write the name of an angle, write in such P
a way that the letter given for the vertex comes in
the middle. angle
arm
• Name of the angle is ∠POQ or ∠QOP. O Q
• Vertex is O. vertex
• Arms are OP and OQ.

Class Assignment

P Name of angle = or
Vertex =

O Q Arms = and

Exercise 1.2

1. Write the names of the following angles in both ways.

a. P b. X c. A

Y C

Q B
Z

Oasis School Mathematics Book-4 11

2. Write the names of angles, vertices and arms of the following angles.

a. A b. P c. X

Q

B C R Y Z
N Q
d. O e.

M PO

AC

3. Two straight lines AB and CD O
intersect at O. Write the names of

all the angles formed at O. D B

4. Write the names of three objects having angles in their structure.

Consult your teacher.

Measurement of angles Line of base

Angles are usually measured in degrees. Centre Inner scale
The symbol for degree is o. There are 360° Outer scale
in a circle and 180° in a straight line.
An instrument named protractor is used to
measure its angles.

A protractor has numbers 0° to 180° marked
on it from both sides.

Steps:
• Place a protractor in such a way that the centre of the base of the

protractor is placed on the vertex of the angle and the base arm of the
angle should be on the line of the base of the protractor as shown in
the figure.
• Start measuring from the side which the base arm is facing.

• If the base arm coincides with 0° of inner scale, use inner scale and if
it coincides with 0° of outer scale, use outer scale.

12 Oasis School Mathematics Book-4

In the given figure, base arm QP is I have to use the inner
facing the right side, start measuring scale.
from the right. Use inside scale to
measure the angle. 0° of inner scale is on
\ ∠ PQR = 40° the base arm.

R

Q P

In the given figure, base arm BC is 0° of outer scale is on
facing the left side, start measuring the base arm.
from the left. Use outside scale to
measure the angle. I have to use the outer
\ ∠ ABC = 30 scale.

A

CB

Exercise 1.3

1. Write down the size of the angle in each of the given figures.

a. b. X c.

A

P

B C YZQ R

d. e. f.

M PE

O N O QF G

Oasis School Mathematics Book-4 13

2. Measure the following angles.

a. A b. P

O B O Q

E d. O

c. X

OD C Y
A
Construction of angles, using protractor 60°
B
Construction of an angle 60°.

Steps:
• Draw a line AB.
• Place the protractor in such a way that its centre is

exactly on B and the 0° – 180° line on AB.
• Count the inner or outer scale which starts from 0°.

Mark point C at 60°.
• Remove the protractor and join BC.
Now, ∠ABC = 60°.

Exercise 1.5 f. 70°
l. 140°
Draw the specified angles with the help of a protractor. r. 135°
a. 20° b. 30° c. 40° d. 50° e. 60°
g. 80° h. 90° i. 110° j. 120° k. 130°
m. 150° n. 160° o. 45° p. 75° q. 105°

Consult your teacher.

14 Oasis School Mathematics Book-4

Types of angles C

There are different types of Acute angle
angles according to their sizes. BA
i. Acute angle:
An angle which is less than B

90° is called an acute angle. Right angle
Example: 30°, 50°, 70°, 75° OA
P
ii. Right angle:
An angle that is exactly 90° Obtuse angle
OQ
is called right angle.

iii. Obtuse angle:
An angle which is more

than 90° and less than 180°
is called an obtuse angle.
Example: 120°, 130°, 145°,
160°, etc.

iv. Straight angle: A Straight angle
OB
An angle that is exactly 180°
is called a straight angle.

v. Reflex angle: Reflex angle O M
N
An angle that is more than
180° but less than 360° is
called a reflex angle.

Example: 210°, 240°, 300°,
etc.

Oasis School Mathematics Book-4 15

Exercise 1.4

1. Categorise the following angles as acute, right, obtuse, straight and
reflex angle.
35°, 45°, 165°, 90°, 210°, 180°, 315°, 175°, 80°, 25°

2. Answer the following questions.
a. How many degrees are there in a right angle?
b. How many degrees are there in a straight angle?
c. What do you call an angle which is less than 90°?
d. What do you call an angle which is greater than 90° and less
than 180°?
e. What do you call an angle which is greater than 180°?

3. Without measuring the angle, guess the type of the given angles?

a. b. c.

d. e . f.

g. h . i.
16 Oasis School Mathematics Book-4

4. Observe the angle between the hands of given clocks and guess their
type.

a. b. c. d.

5. Measure the size of each of the following angles and name their type.

a. A b. P

OB O Q

c. d. M

C O

O DN

e. f. E

Y

XO FO

Oasis School Mathematics Book-4 17

6. Name of each angle of the given figures and classify them into acute,

obtuse and right angle.

a. A b. A E

H

ED BD G

BF CF
C

7. Who am I?

a. I am an angle, my size is less than 90°.
b. I am an angle, my size is exactly 90°.
c. I am an angle, my size is between 90° to 180°.
d. I am an angle, I am 180°.
e. I am an angle, I am greater than 180° and less than 360°.

Consult your teacher.

Triangles

This is a triangle ABC. A
It is bounded by three line segments AB, BC and
AC. These are called the sides of the triangle. It has B C
three vertices A, B and C.

P Vertices : P, Q and R
Sides : PQ, QR and PR
Angles : ∠P, ∠Q and ∠R

Q R Name of triangle : ∆PQR, ∆PRQ, ∆RQP etc.

Note: ∠BAC can be simply written as ∠A.

18 Oasis School Mathematics Book-4

Class Assignment

X Name of given triangle = ....................................
Its sides are .............., .............., and ...................
Its angles are .............., .............., and ................

Y Z Its vertices are .............., .............., and ..............

Types of triangles on the basis of sides

Scalene Triangle: Let’s measure the length of all three sides of triangle ABC.

AB = 5.5 cm 5.5 cm A3 cm
BC = 4.5 cm
AC = 3 cm In this triangle, not any two sides
are equal in length. Such triangle
is known as scalene triangle.

B 4.5 cm C

Isosceles Triangle: Let’s measure the length of all three sides of triangle PQR.

PQ = 4.5 cm P
PR = 4.5 cm
QR = 5 cm 4.5 cm 4.5 cm In this triangle, the length of two
sides is same. Such triangle is
known as isosceles triangle.

Q 5 cm R

Here, length of PQ = length of PR.
Again,

Equilateral Triangle: Let’s measure the length of the sides of triangle DEF.

DE = 4.5 cm D4.5 cm4.5 cm In this triangle, the length of all
DF = 4.5 cm E 4.5 cm three sides is equal. Such triangle
EF = 4.5 cm is known as equilateral triangle.

F

Oasis School Mathematics Book-4 19

Remember !

• In scalene triangle, all sides are unequal.
• In isosceles triangle, any two sides are equal.
• In equilateral triangle, all sides are equal.

Class Assignment

1. Write the type of triangle according to the given features.

Feature Type of triangle
Triangle having all sides unequal
Triangle having any two sides equal
Triangle having all three sides equal

2. Who am I?
a. I am a triangle. All my sides are unequal in length. ...................
b. I am a triangle. Two of my sides are equal in length. . ...................
c. I am a triangle. All of my sides are equal in length. ...................

Exercise 1.6

1. Name the triangles, their sides, their angles and their vertices.

a. A b. P c. X

B CQ RY Z
X
2. Classify the triangles into scalene, isosceles or equilateral.

a. A b.

4 cm 4 cm 6.5 cm

4 cm

B 4.5 cm C Z 4.5 cm Y

20 Oasis School Mathematics Book-4

c. P d. 5 cm
D
E

3.5 cm 3.5 cm

4 cm 6 cm
F
Q 3.5 cm R

3. Write the type of the following triangle whose three sides have measurement:

a. 5cm, 7 cm, 6cm b. 7cm, 6cm, 7cm
c. 4 cm, 4cm, 4 cm, d. 3.8 cm, 5.7cm, 6.4 cm

Consult your teacher.

Types of Triangle on the Basis of Angle

Let’s measure all three angles of the A
triangle ABC.
∠A = 500, ∠B = 600,­ ∠C = 70° B C
Here all three angles are acute angles.
Such triangle is known as acute angled
triangle.

Let’s measure all three angles of triangle P R
PQR. Q

∠P = 30­0, ∠R = 400, ∠Q = 110°

Here, ∠Q = 1100, i.e. an angle is
obtuse.
Such triangle is known as obtuse angled
triangle.

Let’s measure all three angles of triangle X Z
XYZ. Y

∠X = 600, ∠Y = 900, ∠Z = 30°
Here, ∠Y = 90° i.e. an angle of ∆XYZ is
right angle.
Such triangle is known as right angled
triangle.

Oasis School Mathematics Book-4 21

Remember !

• In acute angled triangle, all three angles are acute.
• In obtuse angled triangle, one angle among three is obtuse.
• In right angled triangle, one angle among three is 90°.

Class Assignment

1. Write the type of triangle according to the given features.

Feature Type of triangle

Triangle in which all three angles are
acute.

Triangle in which any one angle is
obtuse.

Triangle in which any one angle is right
angle.

2. Classify the triangles into acute angled, obtuse angled or right angled.

a. A b. D c. X

45°

110° 25° C E FY Z
B

Exercise 1.7

1. Measure the angles of the given triangles and classify them on the
basis of their angles.

a. b.

22 Oasis School Mathematics Book-4

c. d.

2. Identify the type of triangle having three angles with following
measurement.

a. 600, 700, 500 b. 1050, 300, 450

c. 900, 600, 300, d. 750, 700, 350

Consult your teacher.

Activity

• Take a sheet of paper.
• Fold it into half.

• Fold it once again.

• Open the last fold.

• Take one corner of the paper and get it to meet the crease
line.

• Find out acute, obtuse, right angle and straight angle in
the last fold.

Solid figures

Look and learn:

Square face It is a cube.
It has 6 sqaure faces.

Oasis School Mathematics Book-4 23

It is a cuboid.
It has 6 rectangular faces.

Rectangular face

It is a cylinder .
It has two circular faces.
It has a curved surface.

Circular face

It is a cone.
It has a circular face and a curved
surface.

Circular face

It is a sphere.
Its surface is curved.

Curved face

Class Assignment

1. Name the shape of the given solid figures.

24 Oasis School Mathematics Book-4

Vertices, edges and faces of solid objects

Take a box of ink. It is a cuboid. It has six
rectangular faces.

If we draw 6 faces on a plane paper as shown in
the figure, we can get a net of cuboid.
If we paste all the faces, we can get a similar
shape.

A B Vertex The lines of two rectangular faces meet in an
D Edge edge.

F C Face AB, BC, AD, DC, AF, BG, DE, CH, FG, GH,
E G EH and FE are the edges of the given cuboid.

H

The meeting points of 3 edges of a cuboid are called vertices.
A, B, C, D, E, F, G and H are the vertices of the given cuboid.

A cuboid has 6 rectangular faces, 8 vertices and 12 edges.

Exercise 1.8

1. Write the number of vertices, edges and faces for each of the following figures.
a. b. c.

2. Write the names of the vertices, edges and faces of the given figures.

a. A B b. F
ED
D A
C Consult your teacher.
H
E G
B

FC

Activity

Collect the objects of different shapes and count their faces, vertices and edges.

Oasis School Mathematics Book-4 25

Objective Questions

Colour the correct alternatives.

1. I have a circular face and a curved face, who am I?

Cylinder Sphere Cone

2. Given figure has

8 vertices and 12 edges 12 vertices and 8 edges. 6 vertices and 12 edges.

3. Given letter is made by

1 curved line and 1 straight line. 1 curved line and 2 straight lines.

1 curved line and 3 straight lines. P

4. The name of given angle is

∠PQR ∠QPR ∠PRQ Q R

5. Among the following, which is not the correct name of the given angle?

∠ABC ∠CBA ∠ACB A

6. If the measurement of an angle is more than 180° and B
less than 360° then the angle is

acute angle obtuse angle reflex angle
A
7. In the given figure, ∠ABC is C

an acute angle an obtuse angle a reflex angle

8. What is a triangle, none of whose sides are equal? B C

equilateral triangle scalene triangle isosceles triangle

9. In DABC, AB = 5.6cm, BC = 5.6 cm, AC = 6 cm then the triangle is

scalene triangle isosceles triangle equilateral triangle

10. Which of the following statements is not true?

all angles of an acute none of the angles of a one of the angles of an
angled triangle are right-angled triangle is obtuse-angled triangle

acute. acute. is obtuse.

Total number of correct answers

26 Oasis School Mathematics Book-4

Worksheet

Match the three boxes that mean the same by colouring them alike.

Acute angle An angle more than 900° and less
than 1800.

Obtuse angle An angle equal to 90°.
Right angle
An angle more than 1800° and less
than 3600°.

Straight angle An angle equal to 180°.

Reflex angle An angle less than 90°.

Project Work

Cut triangles of different shapes from the colour paper. Paste them
on the chart paper and investigate to identify their type on the basis of
their sides and angles.

Oasis School Mathematics Book-4 27

Unit Test Full marks -25
2
1. Measure the lengths of the given line segments.
a. B b. Q

P 3
A
Z
2. Measure the following angles. b.
a.

A

B CX Y

3. Measure each side of the given triangles and classify them on the basis

of their sides. 3

a. A b. P c.

XY

B CQ RZ

4. Classify the given triangles on the basis of their angles. 3

a. b. c. A

PX

Q RY ZC B

28 Oasis School Mathematics Book-4

5. Construct the following angles with the help of a protractor. 3
4
a. 30° b. 70° c. 50° d. 120°

6. Fill in the blanks.
a. A cuboid has…………… rectangular faces.

b. A………..has no dimension.

c. A part of a line is a …………………

d. A triangle has…………….sides and ……………angles.

7. Answer the following questions. 4

a. What is a triangle called in which all three sides are equal?

b. What is a triangle called in which all three angles are acute?

c. How many edges and vertices does a cuboid have?

d. What is an angle called which measures exactly 180°?

8. Write the number of edges, faces and vertices of the given solid. 3

AB

DC

FG
EH

Oasis School Mathematics Book-4 29

UNIT

2 Number System

12 Estimated Teaching Hours: 15
93

6

Contents • Place value system of numbers (upto
crore)

• Use of comma
• Building of numbers
• Roman numerals
• Comparison of numbers
• Odd and even numbers
• Rounding off the number to its nearest

tens and hundreds
• Prime factorisation
• H.C.F. and L.C.M.

Expected Learning Outcomes

Upon completion of the unit, students will be able
to develop the following competencies:

• To read and write the numbers and their names up to crore
• To use the comma (,) according to Nepali as well as

international system of numeration
• To compare the numbers and arrange them in ascending and

descending order
• To build the smallest and the greatest number using the given

digits
• To identify odd and even numbers using the given digits
• To round off the number to its nearest tens and hundreds
• To factorise the given number
• To find the H.C.F. and L.C.M. of its given numbers

Materials Required: Abacus, place value chart, playcards, gluestick, cryons, etc.

30 Oasis School Mathematics Book-4

Hindu Arabic numbers and Devanagari number system

Hindus first invented the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The Arabs
learnt it from the Hindus and spread the system all over the world. So
the system is called Hindu Arabic system.

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are the
Hindu Arabic numbers.

The symbols ), !, @, #, $, %, ^, &, * and ( are used in Devanagari system
to represent the numbers.

Hindu Arabic Numerals 0 1 2 3 4 5 6789

Number name Zero One Two Three Four Five Six Seven Eight Nine

Devanagari Numerals )!@#$%^&*(
Number name
z"Go Ps bO' { ltg rf/ kfFr 5 ;ft cf7 gf}

Note:

The system of counting in both Hindu Arabic and Devanagari system is the same.

Class Assignment

1. Write the following numbers in Devanagari number system.

a. 87 b. 307 c. 4283

d. 7586 e. 5412

2. Write the following Devanagari numbers in Hindu Arabic number system.

a. &$ b. #*% c. ^$%#

d. $##( e. @(%)

Before the invention of zero, there was no place value
system. Ancient Egyptians used the notation of:

• Stick ( | ) for 1 • Heel bone ( ∩ ) for 10

• Coiled rope ( )for 100 • Lotus flower ( )for 1000

Oasis School Mathematics Book-4 31

Place value of up to 5 digit numbers (Review)

Let's take a five digit number, Place value of a digit =
Digit its place
37214
Place value
Ones place
Tens place 4×1=4
Hundreds place 1 × 10 = 10
Thousands place 2× 100 = 200
Ten thousands place 7 × 1000 = 7000
3 × 10000 = 30000

Expanded form

37214 = 30000 + 7000 + 200 + 10 + 4

37214 = 3 × 10,000 + 7 × 1000 + 2 × 100 + 1 ×10 + 4 × 1

Standard Expanded form
form

Given number in the place value chart

Let's keep the number 37214 in the place value chart.

Thousands period Ones period

Ten thousands Thousands Hundreds Tens Ones
4
3 7 21

How to read this number? Read the number along
While reading a number of 5 digits with their periods.

37 , 214

Thirty seven thousand Two hundred and fourteen

32 Oasis School Mathematics Book-4

How to use a comma?
Comma separates the period, starting from the right after 3 digits: 37, 214

Remember ! We have to use a comma
after three digits from the
• A five digit number begins with the
ten thousands place. right.

• We use comma to separate the period.

Exercise 2.1

1. Write the place value of each of the digits of the given numbers.

a. 27861 b. 50018

2. Write the place value of coloured digits

a. 37284 b. 18064 c. 40312

3. Write the following numbers in expanded form.

a. 84 b. 374 c. 3819 d. 57214

e. 56192 f. 63752 g. 25014

4. Write the following numbers in standard form.
a. 2 × 10000 + 5 × 1000 + 3 × 100 + 2 × 10 + 1
b. 50000 + 6000 + 400 + 50 + 3
c. 6 × 10000 + 2 × 1000 + 1 × 100 + 2 × 10 + 5
d. 70000 + 5000 + 400 + 70 + 9

5. Write the numerals for the following number name.

a. Thirty two thousand six hundred and twenty three

b. Sixty nine thousand three hundred and thirty one

c. Eighteen thousand and thirteen

d. Six thousand two hundred

6. Write the number name of the following numbers.

a. 37842 b. 23169 c. 84379 d. 18064

e. 5232 f. 6872 g. 20539 h. 4072

7. Show the following numbers in the place value chart, put comma and
write their number names.
a. 26418 b. 30214 c. 56398 d. 62193 e. 54150

Consult your teacher.

Oasis School Mathematics Book-4 33

Place value system of 6-digit numbers

Nepali place value system
In Nepali place value system of numeration, a 6-digit number moves

into new period called lakhs period. Take a 6-digit number 258143.

Lakhs periods Thousands periods Ones periods
Lakhs
2 Ten thousands Thousands Hundreds Tens Ones

5 8 1 43

In this number: Place value of 3 1×3=3
L T.Th Th H T O Place value of 4 4 × 10 = 40
2 5 8 1 4 3 Place value of 1 1 × 100 =100




Place value of 8 8 × 1000 = 8000

Place value of 5 5 × 10000 = 50000

Place value of 2 2 × 1000000 = 200000

\ Expanded form of this number
258143 = 200000 + 50000 + 8000 + 100 + 40 + 3

How to read the number? Read the number with
2 58 143 periods separately.

Two lakh fifty eight thousand one hundred and forty three

In international place value system of numeration, there are only two periods
in 6-digits number.

Thousands periods Ones periods
Hundreds Tens Ones
Hundred Ten thousands Thousands
thousands 8 1 43

25

34 Oasis School Mathematics Book-4

How to read the number?

258 143 Read the number with
periods separately.

Two hundred fifty eight thousand one hundred and forty three

Remember !

A 5-digit number is read in the same way in both the systems. A 6 digit number
is read differently. We call a lakh in Nepali system and hundred thousands in
international system.

\ 1 lakh = 1 hundred thousand

Class Assignment

1. Show the following numbers in the place value chart according to
Nepali and international place value system of numeration and write
their number name.

a. 326459 b. 928431

c. 652376 d. 1057237

2. Write the place value of the digits in the given number.

3741925

3. Write the place value of the following digits in both the system.

271463

In Nepali system In International system
2 - …La…kh…s ….......... 2 - …H…und…re…d th..o..u..s.a..n.d

Oasis School Mathematics Book-4 35

7 - ………….......... 7 - …………..........
1 - ………….......... 1 - …………..........
4 - ………….......... 4 - …………..........
6 - ………….......... 6 - …………..........
3 - ………….......... 3 - …………..........

Place value system of numbers (Up to Crores)

Nepali place value system of 7, 8 and 9-digit numbers
The following table shows Nepali place value system of numeration.

Period's name Place name Place value

Ones 1

Ones Tens 10
Hundreds 100
Thousands Thousands 1000
Lakhs Ten thousands 10000
Crores Lakhs 100000
Ten Lakhs 1000000
Crores 10000000
Ten Crores 100000000

Let’s write a number of 7 digits in Nepali place value chart.

Take a 7-digit number 2146375.

Ten lakhs Lakhs Ten Thousands Thousands Hundreds Tens Ones
2 1 4 63 7 5

Lakhs Thousands Ones

How to read a 7-digit number? Read the periods separately.

21 46 375

Twenty one lakh forty six thousand three hundred and seventy five

36 Oasis School Mathematics Book-4

Remember !

A 7 digit number begins with ten lakhs.

8-digit number in place value chart
Let's write a number of 8 digits in Nepali place value chart.
Take a number of 8 digits 47231639.

Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones
4 7 2 3 16 3 9

Crores Lakhs Thousands Ones

How to read the number? Read the periods separately.

4 72 31 639

Four crore seventy two lakh thirty one thousand six hundred and thirty nine

Remember !

9-digit number begins with crore. Its periods are crores, lakhs, thousands
and ones.

Let’s take a 9 digit number and write it in Nepali place value chart.
Ten crores Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones

3 2 15 7 4 3 29

Crores Lakhs Thousands Ones

How to read the number? Read the periods separately.

32 15 74 329

Thirty two crore fifteen lakh seventy four thousands three hundred and twenty nine

Remember !

9 digit number begins with ten crores.

Oasis School Mathematics Book-4 37

Class Assignment

Show the following numbers in place value chart according to Nepali system
of numeration and write their names.

a. 3741698

Ten lakhs Lakhs Ten Thousands Thousands Hundreds Tens Ones

Number name: …………………….........................................................…………..
b. 78432607

Crores Ten lakhs Lakhs Ten Thousands Thousands Hundreds Tens Ones

Number name: …................................................................................….....………..
c. 496275132

Ten crores Crores Ten lakhs Lakhs Ten thousands Thousands Hundreds Tens Ones

Number name: …................................................................................….....………..

International place value system of 7, 8 and 9-digit numbers
The following table shows the international place value system of numeration:

Period's name Place name Place value

Ones 1

Ones Tens 10

Hundreds 100

Thousands 1000

Thousands Ten thousands 10000

Hundred thousands 100000

Millions 1000000

Millions Ten millions 10000000

Hundred millions 100000000

38 Oasis School Mathematics Book-4

7-digit number in International place value chart

Let's take a number of 7 digits and show it in the international place value chart.

3461493.

Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones
3 4 6 14 9 3

Millions Thousands Ones

How to read the number?

Read the periods separately.

3 461 493

Three million four hundred and ninety three
Four hundred sixty one thousand

8-digit number in International place value chart

Lets take an 8-digits number 54321568.

Ten millions Millions Hundred thousands Ten thousands Thousands Hundreds Tens Ones

54 3 2 1 5 68

Millions Thousands Ones

How to read it?
Fifty four million three hundred twenty one thousand five hundred and sixty
eight.
9-digit number in place value chart
Take a 9-digit number 467304219.

Hundred Ten Millions Hundred Ten Thousands Hundreds Tens Ones
Millions Millions 7 thousands thousands 4 2 9
1
46 3 0

Millions Thousands Ones

How to read it?
Four hundred sixty seven million, three hundred four thousand, two
hundred and nineteen

Oasis School Mathematics Book-4 39

Class Assignment

Write the following numbers in the place value chart of international system
of numeration and write their number name.

4763215

Millions Hundred Ten thousands Thousands Hundreds Tens Ones
thousands

Number name: …………………….......................................................................…………..

98426156 Hundred Ten thousands Thousands Hundreds Tens Ones
thousands
Millions

Number name: …………………….......................................................................…………..

346712753 Hundred Ten thousands Thousands Hundreds Tens Ones
thousands
Millions

Number name: …………………….......................................................................…………..

Comparison of Nepali and international place value chart

Let's see the given table and compare two system of numeration.

Nepali system International system Place value

Ones Ones 1

Tens Tens 10

Hundreds Hundreds 100

Thousands Thousands 1000

Ten thousands Ten thousands 10000

Lakhs Hundred thousands 100000

Ten Lakhs Millions 1000000

Crores Ten millions 10000000

Ten Crores Hundred millions 100000000

40 Oasis School Mathematics Book-4

Class Assignment

Place value
Write the place value of each digit of the given number.
2 3 7 4 2 5 4 2 1

Place value of 1 = 1 × 1 =1
Place value of 2 = 2 × 10 = 20
Place value of 4 = 4 × 100 = 400
= 5000
Place value of 5 = 5 × 1000 = 20000
= 400000
Place value of 2 = 2 × 10000 = 7000000
= 30000000
Place value of 4 = 4 × 100000 = 200000000

Place value of 7 = 7 × 1000000

Place value of 3 = 3 × 10000000
Place value of 2 = 2 × 100000000

\ 237425421 = 2 × 100000000 + 3 × 10000000 + 7 Place value = Digit ×
× 1000000 + 4 × 100000 + 2 × 10000 + 5 × 1000 + 3 its place.
× 100 + 2 × 10 + 1 × 1.

This is the expanded form of the number.

How many lakhs are there in one million? .................................................
How many thousands are there in one lakh? .................................................
How many millions are there in one crore? .................................................
How many millions are there in ten crores? .................................................

Class Assignment

1. Write the place value of the coloured digit.

a. 4 3 2 7 1 6 b. 5 7 1 8 4 3 6 c. 1 6 4 2 1 5 7
d. 3 9 2 1 5 8 6 4
2 × 1000 = 2000

d. 9 2 5 8 4 3 7 4 c. 2 5 0 2 1 7

Oasis School Mathematics Book-4 41

2. Write the following numbers in expanded form.
2743162

4320421
31245607

3. Write in the short form:

a. 2 × 1000000 + 3 × 100000 + 5 × 10000 + 4 × 1000 + 3 × 100 + 8 × 10 =

b. 4 × 1000000 + 2 × 10000 + 5 × 1000 + 9 × 100 + 7 × 10 =

c. 2 × 10000000 + 4 × 1000000 + 9 × 100000 + 7 × 1000 + 8 × 10 + 5 =

Use of Commas

When a number is very large, the place of the numbers is separated by
commas. There are different ways of using commas in Nepali place value
system and international place value system of numeration.
In both the system, comma separates the periods.
Use of comma in Nepali place value system

Use comma after three digits starting from the last and then after each two digits.

27, 84, 63, 785 use of commas in Nepali place value system of numeration

Separate the periods ones, thousands, lakhs and crores by commas.

Use of comma in international place value
In international place value system of numeration, use comma to separate
the periods ones, thousands, millions. Use commas (,) after three digits
each starting from the last.
347, 893, 214 use of comma in the international place value system
of numeration.

Use comma after three digits each starting from the last
Separate the periods millions, thousands and ones by commas

42 Oasis School Mathematics Book-4

Class Assignment

1. Use commas in appropriate place according to Nepali system of
numeration and write their name.
a. 7482961

b. 17372452

c. 18046134

2. Use commas in appropriate place according to international system of
numeration and write their names.
a. 37652841

b. 1896304

c. 371428839

Exercise 2.2

1. Draw the place value chart of Nepali system of numeration. Show the
following numbers in place value chart and also write their names.
a. 1354627 b. 3701945 c. 28653907

d. 39126509 e. 572416321 f. 392157264

2. Draw the place value chart of international system of numeration.

Show the following numbers in place value chart and also write their

number names. b. 17922352 c. 36126157
a. 2638145

d. 82357428 e. 392563195 f. 64853842

3. Write the numerals for the following number names:
a. Seventy eight lakh thirty two thousand six hundred and
twenty three

Oasis School Mathematics Book-4 43

b. Eighty seven lakh twelve thousand four hundred and ninety
two

c. Three crore forty two lakh eighty seven thousand six hundred
and twenty three

d. Eighteen crore seventy eight lakh thirty seven thousand five
hundred twenty nine

e. Thirty two crore forty eight lakh sixty four thousand and eighty

4. Write the numerals for the following number name:

a. Three million five hundred twenty three thousand six hundred
and eighty nine

b. Twelve million three hundred twenty seven thousand eight
hundred and sixty nine

c. Four hundred thirty nine million six hundred eight thousand
seven hundred and thirty seven

d. Six hundred ninety two million four hundred ninety two

thousand six hundred and forty nine.

5. Put commas in appropriate places according to Nepali system of

numeration and write the number names. d. 37189274
a. 4628795 b. 1864723 c. 123742169

6. Put commas in appropriate places according to international system of

numeration and write their number names:

a. 4782674 b. 3241962 c. 938427536 d. 38570825

7. Write the place value of the coloured digit.

a. 4728143 b. 18923745 c. 283963521 d. 632542

e. 984126579 f. 47843219 g. 54289316

8. Write the following numbers in expanded form.

a. 478253 b. 3789014 c. 19757321

d. 52691842 e. 30593201 f. 567829321

44 Oasis School Mathematics Book-4

9. Write the number in short form.

a. 3 × 1000000 + 5 × 100000 + 3 × 10000 + 2 × 1000 + 6 × 100 + 2 × 10 + 5
b. 6 × 10000000 + 5 × 1000000 + 4 × 10000 + 3 × 10000 + 2 × 1000 + 1 × 100

+ 9 × 10 + 8
c. 9 × 100000000 + 5 × 10000000 + 3 × 1000000 + 1 × 100000 + 7 ×

10000 + 2 × 1000 + 5 × 100 + 2 × 10 + 6
d. 4 × 100000 + 3 × 10000 + 2 × 1000 + 1 × 100 + 5 × 10 + 6

10. Answer the following questions:

a. How many thousands are there in 1 lakh?
b. How many lakhs are there in 1 million?
c. How many lakhs are there in 1 crore?
d. How many millions are there in 1 crore?

Consult your teacher.

Greatest and the smallest numbers of given digits

The given table shows the smallest and the greatest numbers of one, two
... nine digits.

Look at the table:

Number of Digits Smallest number Greatest number

One 1 9
Two 10 99

Three 100 999
Four 1000 9999

Five 10000 99999
Six 100000 999999

Seven 1000000 9999999
Eight 10000000 99999999

Nine 100000000 999999999

Oasis School Mathematics Book-4 45

How to form the smallest and the greatest number using the given digits?
Take the digits 3, 7, 4
The greatest number using these digits is 743. Digits are in descending order

The smallest number using these 3 digits is 347 Digits are in an ascending order

The greatest number can be I understand!
formed by arranging the given The smallest number can be
formed by arranging the given
digits in descending order. digits in an ascending order.

Look at one more example,

Let's form the greatest number of 2, 3, 7, 6, 0, 9

Greatest number = 976320

Smallest number = 023679 Note: While forming the smallest
(It is not a six digit number) number containing 0, do not
start from 0.
Smallest number = 203679

Class Assignment

Use the given digits to write the greatest and the smallest number.

Digits Greatest number Smallest number
2, 3, 0, 4

1, 2, 8, 9, 4

6, 3, 1, 2, 0

5, 2, 1, 6, 4

Remember !

• One more than the greatest number of 4 digits = the smallest
number of 5 digits

46 Oasis School Mathematics Book-4

Exercise 2.3

1. Answer the following questions.
a. Which is the greatest number of 6 digits?
b. Which is the smallest number of 5 digits?
c. Write the greatest and the smallest number of 7 digits.
d. Write the greatest and the smallest number of 8 digits.

2. Write the greatest and the smallest number formed by the digits 2, 1, and 6.

3. Write the greatest and the smallest number formed by the given digits.
a. 2, 3, 8, 4, 6 b. 3, 0, 1, 5, 8, 9, 7 c. 4, 0, 8, 2, 3, 5, 9 d. 5, 3, 2, 6, 1

Consult your teacher.

Roman Number System

Before Hindu Arabic system came into existence, the Romans had
invented their own symbols to represent various numbers. They had
seven basic symbols represented by the letters I, V, X, L, C, D and M.

Roman Numerals I V X L C DM
Hindu Arabic Numerals 1 5 10 50 100 500 1000

Remember !

In Roman numeral system,

• There is no symbol for zero.

• There is no place value system.

Roman palace

Conversion of Roman numbers into Hindu Arabic numbers

Rule: 1
When any smaller number comes to the right of the larger one, the value of
the smaller number is added to the value of the larger one.

Examples: VI = 5 + 1 = 6
XII = 10 + 1 + 1 = 12
XV = 10 + 5 = 15
LXVI = 50 + 10 + 5 + 1 = 66

Oasis School Mathematics Book-4 47

Rule: 2

When any smaller number comes before the larger one, the value of the

smaller number is subtracted from the value of the larger one.

Examples: IV = 5 – 1 = 4

IX = 10 – 1 = 9

XL = 50 – 10 = 40

XC = 100 – 10 = 90

Remember !

Smaller number can be placed before the greater number only once.
• I is subtracted from V and X only.
• X is subtracted from L and C only.
• C can be subtracted from D and M only.
• V, L, D cannot be subtracted.

Rule: 3

The symbol I, X, C and M can be repeated only up to three times.

Repeatition of the symbols represents addition.

Examples: III = 1 + 1 + 1 = 3

XXX = 10 + 10 + 10 = 30

CC = 100 + 100 = 200

Remember !
• The symbols V, L, and D never repeat.

Rule: 4
Bar ( – ) over a symbol is 1000 times the value of the symbol without bar.

Example: V = 5 × 1000 = 5000

X = 10 × 1000 = 10000

XV = 15 × 1000 = 15000

Conversion of Hindu Arabic numbers into Roman numbers

To convert the Hindu Arabic numbers into Roman number system, we
have to follow the given steps:

48 Oasis School Mathematics Book-4

Example :

Convert 67 into Roman numerals.

67 = 50 + 10 + 7 Steps:
= LXVII
42 = 40 + 2 • Expand the numbers which are greater
= XLII than 10.
28 = 10 + 10 + 8
= XXVIII • Recall the Roman symbols and convert the
expanded numbers into corresponding
Roman numerals.

452 = 400 + 50 + 2

= CDLII

Example 1:

Convert the following numbers into Roman numerals.

a. 76 b. 34 c. 125 d. 364 e. 4696

76 = 50 +10 +10 + 5 + 1

= LXXVI

34 = 10 + 10 + 10 + 4

= XXXIV

125 = 100 + 10 + 10 + 5

= CXXV

364 = 100 + 100 + 100 + 50 + 10 + 4

= CCCLXIV

4696 = 4000 + 500 + 100 + 9 0 + 6

= IV DCXCVI

Example 2:

Convert the following Roman numerals into Hindu Arabic numerals:

a. VIII b. XIX c. XXVI d. XCVI e. DCCLXV f. V DCCLII
Solution:

a. VIII = 5 + 1 + 1 + 1 = 8

b. XIX = 10 + (10 - 1) = 19

c. XXVI = 10 + 10 + (5 + 1) = 26

d. XCVI = (100 – 10) + (5 + 1) = 96

e. DCCLXV = 500 + 100 + 100 + 50 + 10 + 5 = 765

Oasis School Mathematics Book-4 49

f. V DCCLII = 5 × 1000 + 500 + 100 + 100 + 50 +1 +1
= 5000 + 500 + 100 +100 + 50 + 2 = 5752

Exercise 1.8

1. Convert the following Hindu Arabic numerals into Roman numbers:

a. 8 b. 17 c. 26 d. 39 e. 48 f. 59
g. 67 h. 74 i. 82 j. 98 k. 107 l. 132
m. 191 n. 246 o. 477 p. 510 q. 723 r. 1217

s. 2714 t. 3524 u. 6412 v. 7303 w. 8496

2. Convert the following Roman numbers into Hindu Arabic numbers:

a. VII b. XIII c. XVII d. XXVIII e. XXIX

f. XLIV g. XLVIII h. XLIX i. LXXXVI j. XCIII

k. XCIX l. CXXIV m. DCXXXII n. MDCXIV o. VICCXX

Consult your teacher.

Comparison of two numbers

• If the numbers of digits are • If the numbers of digits are
different same.

Take any two numbers Height of Mount Everest is
8,848m.
34631 and 8362
Height of the Mount Manaslu
Which is greater? is 8,163 m.

Greater the number of digits,
greater the number.

34631 is greater than 8362.

Which mountain is more higher?

Start to compare from the left until you find two different digits.

Similarly, I can
compare 5, 6, 7, 8 digit

numbers also.

8848 8163

=
>
\ 8,848 > 8,163

Height of Mount Everest is more than the height of Mount Manaslu.

50 Oasis School Mathematics Book-4