Prime Mathematics 3

Prime

Mathematics
Series
3

Raj Kumar Mathema

Dirgha Raj Mishra Bhakta Bahadur Bholan

Uma Raj Acharya Yam Bahadur Poudel

Naryan Prasad Shrestha Bindu Kumar Shrestha

Prime

Mathematics
Series

3

Approved by
Government of Nepal, Ministry of Education, Science and
Technology Curriculum Development Centre Sanothimi,

Bhaktapur as and additional learning materials.

Raj Kumar Mathema Authors
Dirgha Raj Mishra Bhakta Bahadur Bholan
Uma Raj Acharya Yam Bahadur Poudel
Naryan Prasad Shrestha Bindu Kumar Shrestha

Editors
Anil Kumar Jha
Dhurba Narayan Chaudhary
Hari Krishna Shrestha

Language Editor
Mrs. Tara Pradhan

Pragya Books & Distributors Pvt. Ltd.

Printing history
First Edition 2074 B.S.
Second Edition 2077 B.S.

Authors
Raj Kumar Mathema
Dirgha Raj Mishra
Bhakta Bahadur Bholan
Uma Raj Acharya
Yam Bahadur Poudel
Naryan Prasad Shrestha
Bindu Kumar Shrestha

Editors
Anil Kumar Jha
Dhurba Narayan Chaudhary
Hari Krishna Shrestha

Layout and design
Rabi Man Shrestha

© Publisher
All rights reserved. No part of this book, or designs and illustrations here within, may be
reproduced or transmitted in any form by any means without prior written permission.
ISBN : 978-9937-0-2221-7
Printed in Nepal

Published by
Pragya Books & Distributors Pvt. Ltd.

Lalitpur, Nepal
Tel : 5200575
email : [email protected]

Preface

Prime Mathematics Series is a distinctly outstanding mathematics series
designed in compliance with Curriculum Development Centre (CDC) to meet
international standards. The innovative, lucid and logical arrangement of the
content makes each book in the series coherent. The presentation of ideas
in each volume makes the series not only unique, but also a pioneer in the
evolution of mathematics teaching.

The subject matter is set in an easy and child-friendly structure so that
students will discover learning mathematics a fun thing to do.A lot of research,
experimentation and careful gradation have gone into the making of the series
to ensure that the selection and presentation is systematic, innovative and both
horizontally and vertically integrated.

Prime Mathematics Series is based on child-centered teaching
and learning methodologies, so the teachers will find teaching this series
equally enjoyable. We are optimistic that this series shall bridge the existing
inconsistencies between the cognitive capacity of children and the course matter.

We owe an immense debt of gratitude to the publishers for their creative,
thoughtful and inspirational support in bringing about the series. Similarly, we
would like to acknowledge the tremendous support of teachers, educationists
and well-wishers for their contribution, assistance and encouragement in making
this series a success.

We hope the series will be another milestone in the advancement of teaching
and learning mathematics in Nepal. We solicit feedback and suggestions from
teachers, students and guardians alike so that we can refine and improvise the
series in the future editions.

Our team would like to express our special thanks to Mr. Nara Bahadur
Gurung, Mr. Ram Narayan Shah, Mr.Tulsi Kharel, Mr. Mani Ram Khabas, Mr. Umesh
Acharya, Mr., J. Phuldel, Mr. Kamal Raj Tripathee, Mr. Rudra Prasad Pokharel, Mr.
Uttam Prasad Panta, Mr. L.N. Upadhyaya, Mr. Shakti Prasad Acharya, Mr. Upendra
Subedi, Mr. Kul Narayan Chaudhary, Mr. Bishonath Lamichhane, Mr. Harilal
Lamichhane, Mr. Govinda Paudel, Mr. Krishna Aryal, Mr. Nim Bhujel, Mr. Santosh
Simkhada, Mr. Pashupati Upadhyaya, Mr. Dipak Adhikari, Mr. Mukti Adhikari, Mr.
Dipendra Upreti, Mr. Dipak Khatiwada, Mr. Narayan Nepal, Mr. Raj Kumar Dahal,
Mr. Bhim Raj Kandel, Mr. Prem Giri,Mr. Iswor Khanal, Mr. Balram Ghimire, Mr. Om
Kumar Chhetri, Mr. Ram Hari Bhandar, Mr. Krishna Kandel, Mr. Madhav Atreya,
Deep Raj Nigam Unai, Sangita Thapa, Shiva Devkota, Harihar Adhikari, Chandra
Dev Tiwari, Chura Gurung, Sagar Dhakal, Baikuntha Marahatha, Subash Bidari
Raghu Kandel, Sudip Poudel, Roshan Sapkota Sujan Dhungana, Tara Bahadur
Bhandari and Jiwan K.C. for their Painstaking effort in peer reviewing of this
book.

Contents Page

Unit Topic 1
23
1. Geometry 61
2. Four Digit Numbers 77
3. Addition 89
4. Subtraction 105
5. Multiplication 119
6. Division 135
7. Time 141
8. Money 151
9. Length 165
10. Area and Volume 173
11. Weight 195
12. Fraction and Decimal 201
13. Unitary Method and Bill 205
14. Statistics 211
15. Set 221
16. Algebra
Model Question

Unit

1

Estimated periods − 13

GEOMETRY

Objectives
At the end of this unit, the students will be able to

• measure the length of the given line segments and draw the line segments of the given
measurements using ruler.

• name the angles and draw angle using ruler.
• identify the parts (angles, sides, vertices) of triangles and quadrilaterals.
• identify circles, its centre, radius, diameter and circumference.
• identify and name the regular solids like cubes, cuboids, cylinders, cones, sphere etc.

and count their faces, edges and corners.
• find the perimeter of the given figure or plane objects.

Teaching Materials
• Instrument box, geoboard, models of triangles, quadrilaterals, circles and solid objects

(cubes, cuboids, spheres, cylinder, cones etc)

Activities
It is better to:

• demonstrate the process of measuring lengths of line segments using scale or measuring
tape.

• demonstrate the models of triangles, quadrilateral and other shapes to teach the
concept of plane figures.

• show the corners of different objects to give the concept of angles and discuss about
the sides, vertices and angles of triangles and quadrilaterals.

• demonstrate the models of solid objects and explain their parts (vertices, edges, faces)

Geometry

Great pyramid of Giza
of Egypt was built 4900

years ago.
The shape is pyramidal.

Learn the following:

Point QA
• Two rays PQ and RS, if produced meet at A P S

which is a point.

• A point is a position supposed to have no R
size.

• In geometry a point is denoted by a dot.

• A point is denoted by capital letter like A,
B, C etc.

Line B
• A line is a long narrow mark either straight D

or curve. B
Q
• A line is supposed to have only one A N
dimension, length.

• A line is read by marking the end points C
with capital letters.
For example: AB is a straight line and CD

is a curve line.

• The arrow heads are used at both ends of a A
straight line which can be extended to both
the directions. AB is a straight line.

• A straight line which can be extended in only P
one direction is a ray. PQ is a ray. M

• A line segment is a part of a line. It has fixed
length. MN is a line segment.

2 Prime Mathematics Book − 3

Exercise - 1.1

A) Match the following:
a curve line

a ray

a line segment

straight line

a point

B) Identify whether the following are line, ray,curve line
or line segment as given in the example:

AB D MN

C

Line segment AB. CD is MN is

P X Z Y
Q SY is Y
PQ is
ZY is

Prime Mathematics Book − 3 3

C) Draw the following in the given box.

AB a line segment PQ ray MN
a line AB

a point a curve line CD a straight line GH

Measuring line segments

Learn the following:
• We need to measure long as well as short lengths.
• Long distances are measured by using meter scales and measuring

tapes.

a metre scale measuring tapes

• Short lengths are measured by using a ruler

10 mm = 1cm centimeters

Inches

• Our geometric box (instrument box) 10 mm = 1 cm
contains a short ruler. One edge of it is 100 cm = 1 m
scaled with centimetres (cm) and other
edge with inches. It is 15 cm long.

• 1 cm is divided into 10 small parts and
each part is equal to 1 millimetre (mm).
100 cm is equal to 1 metre (m)

4 Prime Mathematics Book − 3

Measuring lengths

AB Place the starting point at 0 (zero)
and read the scale showing
the end point.

Here, the length of the line segment AB is 5 centimetres.
We write AB = 5cm
M N Here, the length of the line segment MN

is 5cm and 5mm. We write MN = 5cm
and 5mm = 5cm and 0.5 cm = 5.5cm.

PQ

Here, the length of the line segment PQ is 3 cm and
7 mm. We write PQ = 3cm and 7mm = 3.7cm.

Exercise - 1.2

A) Measure the following line segments and fill in
the boxes.

AB PQ

a) AB = 4cm E b) PQ = cm
D M N

c) DE = cm H d) MN = cm D
G C

e) GH = cm f) CD = cm

Prime Mathematics Book − 3 5

B) Measure the following line segments and fill in
the boxes.

ABP Q

a) AB = cm b) PQ = cm
D cm EM
N
c) DE =
G d) MN = cm

HC D

e) GH = cm f) CD = cm

C) Draw the line segments of the following measures
in your exercise book .

(a) 3cm (b) 7cm (c) 9cm
(d) 8cm (e) 2cm 9mm (f) 11.5cm

D) Join the given pair of points using a ruler and write
their measures.

BM N
A

AB = MN =

Q Y

P X
PQ = XY =

6 Prime Mathematics Book − 3

E) Measure and write their measurement:
(a) What is the length of your mathematics book?

(b) Write the measure of your pencil.

(c) What is the length of your geometry box?

(d) What is the length of your sharpener?

Angles

Learn the following:

• If two straight lines AB and BC meet at the point B, angle is formed
at B with line AB and BC.
• Here, at the point B where the lines AB and BC meet is called the
vertex and straight lines AB and BC are called arms of ∠ABC.
• We write angle ABC or angle CBA or ∠ABC or A
arm
∠CBA with vertex in the middle.

B angle C
Vertex arm

Angles

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

Prime Mathematics Book − 3 7

Exercise - 1.3

A)Write the names of the following angles.Also name
the vertex and the arms as gaven in the example.

AP N

Q

B CR MO

Angle: ∠ABC Angle: Angle:
or ∠CBA or or

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

and and

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

Arms: and and

8 Prime Mathematics Book − 3

B) Name the angles indicated in the following figures:

A AD K

C BB L M
C N
∠ABC

D C HZ Y
E X
C D G W
A B F
E

C) Put the correct letters in the following figures
from the given names and vertices.

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

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

Prime Mathematics Book − 3 9

Comparison of angles: Wide space
(Big angle)
Narrow space
(Small angle)

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

Exercise - 1.4

A) Compare the following pairs of angles and write
smaller or bigger accordingly.

a) A b) c) d) L
PX Z

B CQ R YM N

bigger smaller

e) D X f) g) R h) M

E FY ZS TO N

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

a) A P P

b) L

C BQ R M NQ R

∠ABC ∠PQR ∠LMN ∠PQR

10 Prime Mathematics Book − 3

c) W A d) U X

X YB CV WY Z

∠WXY ∠ABC ∠UVW ∠XYZ

Plane figures

Learn the following:

Triangle: A
Given figure ABC has three sides AB, BC Corners or Vertex or Angle

and CA. C
A
It has three vertices A, B and C.

It has three angles. B

∠ABC, ∠BCA, ∠BAC formed at the

vertices B, C and A respectively. ABC is a

triangle. Triangle ABC is also written as

∆ABC. Sides C
A triangle is a closed figure enclosed by B

three line segments.

Quadrilateral A
Given figure ABCD has four sides AB, BC, CD D

and AD.

It has four corners or vertices A, B, C and Corners or Vertex or Angle

D. Quadrilateral C A
It has four angles. ∠ABC, ∠BCD, ∠ADC,B Sides

∠BAD formed at the vertices B, C, D and D
A respectively.

ABCD is a quadrilateral.

BC

Prime Mathematics Book − 3 11

If the opposite sides of a quadrilateral A D

are equal and angles are also equal, it is

known as a rectangle. Corners or Vertex or Angle

Here, ABCD is a rectangle. It’s opposite AD

sides are equal i.e. AB = DC and BC = AD. B Square C
And all the angles are equal i.e.
∠ABC = ∠BCD = ∠CDA = ∠DAB Sides

A quadrilateral is a closed figure B Square C
D
enclosed by four line segments. A

If all the four sides and angles of a Corners or Vertex or Angle

quadrilateral are equal, it is known as

a square. B Rectangle C
Here, ABCD is a square. Its sides
A D
AB = BC = CD = DA and angle

∠ABC = ∠BCD = ∠CDA = ∠DAB = 90o. Sides

Exercise - 1.5 B Rectangle C
X
A) Join the dots using ruler to make a triangle

a) A b)

B CY Q Z
c) N d) J

Q P

12 Prime Mathematics Book − 3 S

B. Construct 2 different triangles using a ruler
a) b)

C. Write the name, sides, vertices and angles of the

following triangles:

A a) P

R

B C Q
Name: ∆ABC Name:
Sides:
Sides: AB, BC, CA Vertices:
Angles:
Vertices: A, B and C

Angles: ∠ABC, ∠BCA, ∠BAC

b) L c) W

M N XY
Name: Name:
Sides: Sides:
Vertices: Vertices:
Angles: Angles:

Prime Mathematics Book − 3 13

D. Fill in the blanks:

(a) The side of the triangle is the longest. P
Q
(b) Vertices of the triangle are ,

and . R

(c) The angle is the biggest.

(d) Name of this triangle is .

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

K N AB W ZP S

LM DC XY QR
(a) (b) (c) (d)

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

(a) KLMN KL

(b)

(c)

(d)

14 Prime Mathematics Book − 3

A B
C
F. In the given quadrilateral ABCD, sides AB = BC = CD = DA S
and ∠ABC = ∠BCD = ∠CDA = ∠DAB. R

So, ABCD is a ....................................... D
G. In the given quadrilateral PQRS, PQ = SR and P

QR = PS and ∠PQR = ∠QRS = ∠RSP = ∠SPQ.

So, PQRS is a ....................................... Q

G) Name the shape of following objects.

A blackboard A carom board A Set square A book

H. Provide the correct name for the rectangle ABCD,
square PQRS, square KLMN and rectangle WXYZ
given below:

Prime Mathematics Book − 3 15

Circle

Read the following:

• A circle has no corners. D
• Length of the complete boundary of the circle is called the
circumference.
• Each point on the circumference is at same distance from OA
a fixed point. The fixed point is called the centre of the B
circle. C
• Distance of a point on the circumference from the centre is S
called the radius.
• Here, in the figure, O is the centre and OA is the radius. OP
• A circle is a round plane region bounded by a curve line.
• A line passing through the centre of the circle from a point
of circumference to other point of circumference is called
diameter. RS is a diameter. R

Exercise - 1.6

A. Name the centre and radius or diameter of the given circle.

a B bY c d

AX P O
Z Q X

Centre: .......... Centre: .......... Centre: .......... Centre: ..........

Radius: .......... Diameter: ........ Radius: .......... Radius: ..........

B. Provide the correct name in the given figures takes:

ab cd

Centre: O Centre: K Centre: P Centre: M
Radius: OP Radius: KS Diameter: PQ Radius: MX

C. Perform the following tasks:

Draw radius XY in the given circle and measure XY. X
Centre: ...............
Radius XY = .............. cm

16 Prime Mathematics Book − 3

b. Draw a radius.
Name and measure its length.
Centre: ..................
Radius: ................. = .............. cm

D. Choose any two circular objects and draw its outline to get a circle
in your exercise book.
(a) Object: A two rupees coin
(b) Object: A striker of a carom board

Regular solid objects Face

Learn the following:
Cube
A cube is a solid having 6 square faces.
• It has 8 vertices or corners.
• It has 12 equal edges or sides.

Edge Vertex

A die An ice cube A puzzle cube Edge Vertex

Cuboid
A cuboid is a solid having 6 rectangular faces.
• It has 8 vertices or corners. Face
• It has 12 edges.

A book A brick An instrument box

Cylinder curved
A cylinder is a solid having two equal circular surface
bases and a curved surface.
• It has two circular edges. circular circular
edge face

• It has no vertices.

Log of wood Can Pipe

Prime Mathematics Book − 3 17

Cone Vertex
A cone is a solid having a circular base and a
curved surface. Circular
• It has one circular edge. surface
• It has one vertex.
Circular Circular
edge base

Ice cream cone A birthday paper cap Sharpened part of a pencil

Sphere and hemisphere Sphere Hemisphere
A sphere is a solid formed by a single curved
surface.
• It has no edge.
• It has no vertex.
• Half of a sphere is called the hemisphere.

A ball A marble A half orange

Exercise - 1.7

A. Name the following solid shapes .

B.Give examples of the following shapes.
(a) A cube: For example
(b) A cylinder: For example
(c) A sphere: For example
(d) A cone: For example
(e) A cuboid: For example
(f) A hemisphere: For example

18 Prime Mathematics Book − 3

C.Complete the following (providing the correct number):
A cuboid has ..................... vertices.
It has .................................. edges.
It has ................................. faces.

A cone has ........................ vertex.
It has ........................... circular edge.
It has circular base and ......................
curved surface.

A cylinder has ...................... vertex.
It has ........................... circular bases.
It has ............................. curved surface.

A sphere has ....................... vertex.
It has .......................... curved surface.
It has ............................ plane face.

Perimeter

Learn the following:

Total length of the boundary of a closed figure is called perimeter (p).
P (ii) A 4cm
(i) 6.5cm 5cm
5cm D
3cm
Q 8.5cm R B 7cm C

Perimeter of the figure (i) = PQ + QR + RP = 6.5cm + 8.5cm + 5cm = 20cm
Perimeter of the figure (ii) = AB + BC + CD + DA = 5cm + 7cm + 3cm + 4cm = 19cm

Exercise - 1.8
A) Find the perimeter of the following figures:

a. A b. A 8cm D
3cm 6cm 6cm
5cm

B 4cm C B 8cm C
Perimeter = AB + BC + CD + AD
Perimeter = AB + BC + AC
= ........ cm + ........ cm = ...... cm + ...... cm +
+ ........ cm ...... cm + ...... cm
= ........ cm
= ...... cm

Prime Mathematics Book − 3 19

E 6cm I 6cm E 4cm
4cm 5cm A D
5cm 5.5cm
F
4cm B 6.5cm C

G 7cm H

Perimeter (P)= + + ++ Perimeter (P) = + + + +
= .......cm + .......cm +
= ...... cm + ...... cm + ......cm .......cm +.......cm
+ ...... cm + ...... cm + .......cm

= ........ cm = ........... cm

B) If all the sides of the following figures are equal,

find their perimeter.

A P Q ON WZ

PM

B 4cm C S 4cm R K 3cm L X Y

Perimeter (P) Perimeter (P) Perimeter (P) 6cm

=4+4+4 = = Perimeter (P)
= 3 × 4cm = =
= 12cm = = =
=
=

C) Measure the sides of the following figures and find

their perimeter:
A PS

CB QR

AB = ......., BC = ......., AC = ....... PQ = ......., QR = .......,
Perimeter (P)= AB + BC + AC RS = ......., PS = .......
= ......cm + ......cm + ...... cm Perimeter (P) = ............................
= = ............................

AD = .................
H

E

Perimeter (P)= ......B..................C..... Perimeter (P)= ....F....................G......
= ............................. = ..............................
= ................. = .................

20 Prime Mathematics Book − 3

Unit Revision Test-I

A. Identify whether the following are
line, line segment or a ray:

a. B b. c. M N
AP Q

B. Measure the length of the given line segments. Y
a. Q b.

X
P

C.Name the given angles. Write the vertex and the arms:

a. A b. X

B C W Y
Name: Vertex : Name: Vertex :

Arms: and Arms: and

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

a. A D b. X P

CE FY Z R
Q
B
∠ABC ∠DEF ∠XYZ ∠PQR

E. Name the following triangles, their vertices, sides

and angles.

a. A b. X

B CY Z
Name:
Name: and
Vertices : , and Vertices : , and
Sides: ,
and Sides: , ,
Angles:
, and Angles: and

Prime Mathematics Book − 3 21

Unit Revision Test-II

Identify the centre and radius of the circle.

Centre: OP Centre: A B
Radius: Radius:

Complete the following sentences:

(a) The shape of a brick is .

(b) A cube has vertices, edges and

faces.

(c) Half of a sphere is called .

(d) A cylinder has circular bases and

curved surface.

Name the angles indicated in the following figure:

a. M b. P S

ON R
Q

Find the perimeter of the given figure.

a. b. 5cm
6cm
10cm 4.5cm

4cm

8cm 6cm
Perimeter =
Perimeter =

Draw the line segment of the following length:

(a) 3.5cm (b) 7.8cm

22 Prime Mathematics Book − 3

Unit

2

Estimated periods − 33

FOUR DIGIT NUMBERS

Objectives

At the end of this unit, the students will be able to:
• count, read and write the numbers upto 6 digits in the Devanagari and Hindu-Arabic

System.
• use of comma in correct places.
• write the numbers in words and vice versa.
• say the place value of the digits of a six digit number and to represent in place value

table.
• arrange six digit numbers in ascending order and descending order.
• round off the numbers to the nearest 10 and to the nearest 100.
• recognize the odd and even numbers.
• write the number in Roman numerals and vice versa.

Teaching Materials
• Number line, number chart
• Place value chart, Roman numeral chart

Activities

It is better to:
• give the concept of 1000 through discussion and have the students write 1000, 2000,

3000 .........., 9000
• teach students to put comma in between hundred place and thousand place and after

every two digits in Devanagari and Hindu-Arabic System.
• represent the given number in place value chart.

Four digit numbers

We have learnt that 10 ones make
1 ten and 10 tens make 1 hundred.
Could you say how many hundreds

make 1 thousand?

Thank you. Yes, I know. 10 hundreds
make 1 thousand.
10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand=1000

Complete the table given below:

500 501 509
610 611 619
721 722 730
832 833 841
991 992 999 1000
1001 1002 1010

Could you say the smallest number
made of two digits?
The smallest number made
of two digit is 10.

What is the greatest number of two
digits? Is 999 the greatest number

of three digits?

I know the greatest number of two digits is 99.
Yes, 999 is the greatest number of three digits.
Good!
Thank you.

24 Prime Mathematics Book − 3

Thus, we have learnt that the greatest number of three
digits is 999, the smallest number of two digits is 10 and the

smallest number of three digits is 100.
If we observe the table given above, the number
that comes just after 999 is 1000 which is a four digit
number. It is the smallest number of 4 digits and 9999
is the greatest number of four digits. Let’s show some

four digit numbers in place value table.

Four digit numbers in place value table.

Thousands Hundreds Tens Ones Thousands Hundreds Tens Ones
1 0 21 2 4 03
1021 2403

One thousand and twenty one. Two thousand four hundred and
three.

Thousands Hundreds Tens Ones Thousands Hundreds Tens Ones
3 1 20 4 3 19
3120 4319

Three thousand one hundred and Four thousand three hundred and
twenty. nineteen.

Exercise - 2.1

A.Write the vehicles' number.

a. b.

Prime Mathematics Book − 3 25

c. d.

A.
B.
C.
D.

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

Th H T O 3452 Three thousand four hundred
3452 and fifty two.

Th H T O
4513

Th H T O
5679

Th H T O
6790

Th H T O
7099

Th H T O
9001

Th H T O
9059

26 Prime Mathematics Book − 3

C. Represent the given numerals in the place value

table and write in words as shown in the example:
Th H T O Two thousand three hundred
2347 2347 and forty seven.

5408 Th H T O

7059 Th H T O

8918 Th H T O

9400 Th H T O

1098 Th H T O

9999 Th H T O

D. Represent the following number name in the place value

table and write in numeral as shown in the example:
Three thousand and forty two. Four thousand one hundred
and nine.

Th H T O Th H T O

3042

3042 Six thousand four hundred and
Five thousand two hundred ninety.

and twenty eight. Th H T O
Th H T O

Seven thousand nine hundred Eight thousand five hundred
and forty three. and eight.

Th H T O Th H T O

Prime Mathematics Book − 3 27

E.Write in expanded form as shown blank below:

4253 = 4000 + 200 + 50 +3

9999 = + + +

6048 = + + +

5219 = + + +

8195 = + + +

7450 = + + +

F.Write in short form as shown below:

5000 + 000 + 00 + 3 = 5003
6000 + 700 + 90 + 7 =
7000 + 500 + 80 + 6 =
8000 + 400 + 70 + 5 =
9000 + 300 + 60 + 4 =
4000 + 200 + 50 + 3 =

G.Count by 100s and fill up the blank as shown below.

9240 9340 9440 9540 9640

8150

7395

6475

9501

4285

H.Count by 1000s and fill up the blank as shown below.

5500 6500 7500 8500 9500
1240
5690
3746
2919
4905

28 Prime Mathematics Book − 3

Face value and place value of numbers

Could you say what is the I don’t know. Sir!
place value of 7 in the
number 7465.

The digit 7 is in thousands place. So, its place value is 7
thousand (7000). Similarly, 4 is in the place of hundred.
So, its place value is 400. 6 is in the place of ten so, it’s
place value is 6 tens i.e. 60. The place of 5 is one so, it's
place value is 5. But the face value of 7, 4, 6 and 5 in the

number 7465 are 7, 4, 6 and 5 respectively.

Exercise - 2.2

A.Write the place value of digit 3 of each number given below:

7430 4673
3450 9368

B.Write the place value and face value of the underlined digit.

Place value Face value Place value Face value

9943 4901

8956 3249

6740 2195

7845 1957

5495 2451

Request to the teacher:
Please show more examples of this type.

Prime Mathematics Book − 3 29

Comparison of four digit numbers

Can you say that among the numbers No, sir!
9,456 and 8,956; which one is greater?

Let’s represent them in place Please, could you explain
value table. which one is greater?

Th H T O Th H T O

9456 8956

First compare the digits of thousands place. As 9 is greater than 8. So,
9456 is greater than 8956.

Let’s compare the numbers 7256 and 7568. Represent them in place
value table.

Th H T O Th H T O

7256 7568

The digits of thousands place are equal. Now, compare the digits of
hundreds place. As 5 is greater than 2. So, 7568 is greater than 7256.

Compare the numbers 8947 and 8974.

Th H T O Th H T O

8947 8974

As the digits of thousands place and hundreds place are equal. Now,
compare the digits of tens place. As 7 is greater than 4. So, 8974 is
greater than 8947.

Compare the numbers 9458 and 9453.

Th H T O Th H T O

9458 9453

The digits of thousands place, hundreds place and tens place are equal.
So, compare the digits of ones place. As 8 is greater than 3. So, 9458 is
greater than 9453.

Thus, to compare four digit numbers, first compare the digits of

thousands place. If they are equal, compare the digits of hundred's

place. If they are also equal, then compare the digits of tens place. If

they are also equal, then compare the digits of ones place.

30 Prime Mathematics Book − 3

Compare the numbers 9437 and 9437

Th H T O Th H T O
9437 9437

The digits of thousands place, hundreds place, tens place and ones
place are equal. So, 9427 is equal to 9437 i.e. 9437=9437.

Exercise - 2.3

A. Put > or < or = sign in the boxes:

9487 8487 1248 1448 8709 8700
2308 2408 3097 3097 7600 7700
1574 1584 9908 8908 6850 6840
2708 2705 3459 3559 5746 5749
5008 5008 5709 5809 7999 8000

B. Arrange in ascending order.

9100 8200 6400 4500 7120
,
,, ,

7240 7340 7570 7119 7941
,
,, ,

8912 9920 7634 5349 4614
,
,, ,

6720 8900 9990 7800 4530
,
,, ,

4750 9845 8940 7670 1260

,, , ,

Prime Mathematics Book − 3 31

C. Arrange in descending order:

4140 7814 6709 8950 9140
7980
,, , ,
8267
6940 5496 9450

,, , ,

9190 8645 1240 5685 3490

,, , ,
6240 3847 9350 2595 1460

,, , ,

Five digit numbers

Do you know the number one
more than 9999?

Yes, I know. That is
9999
+1

10000 It is ten thousand
Could you count the number of

digits in 10,000?
10,000 contains five digits. The
digits are 1,0,0,0 and 0.

Could you say the smallest
and greatest number of five
digits? Yes, sir!
10000 is the smallest and
99999 is the greatest number
of five digits.

32 Prime Mathematics Book − 3

Some five digit numbers are:

T−Th Th H T O We put comma
45206 between thousands
45,206
and hundreds.
Forty five thousand two hundred
and six.

T−Th Th H T O
69300
69,300

Sixty nine thousand and three
hundred.

Exercise - 2.4

Perform the task as shown below:

T−Th Th H T O 78,909 Seventy eight thousand
7 8909 nine hundred and nine.

T−Th Th H T O
9 0000

T−Th Th H T O
8 4001

T−Th Th H T O
7 9100

T−Th Th H T O
8 5214

T−Th Th H T O
6 9487

Prime Mathematics Book − 3 33

B. Represent the given numerals in place value
table and write in words as shown below:

24,500 T−Th Th H T O
24 5 0 0

42,857 Twenty four thousand and five hundred.
T−Th Th H T O

53,941 T−Th Th H T O

89,020 T−Th Th H T O

99,999 T−Th Th H T O

T−Th Th H T O
90,102

C. Represent the following number names in place
value table and write in numeral as shown below.

Fifty six thousand and nine Sixty seven thousand eight
hundred. hundred and eight.

T−Th Th H T O T−Th Th H T O
56900

56,900

34 Prime Mathematics Book − 3

Seventy thousand two hundred Ninety nine thousand nine
and twenty two. hundred and ninety nine.
T−Th Th H T O
T−Th Th H T O

Twenty five thousand and Thirty nine thousand eight
twenty five. hundred and seventeen.

T−Th Th H T O T−Th Th H T O

D.Write in expanded form as shown below:

20453 = 20000 + 0000 + 400 + 50 + 3

69742 = ++ ++

48960 = ++ ++

52871 = ++ ++

83400 = ++ ++

99999 = ++ ++

E.Write in short form as shown below:

20000 + 3000 + 400 + 90 + 5 = 23,495

40000 + 5000 + 600 + 80 + 4 =

60000 + 7000 + 700 + 70 + 3 =

90000 + 6000 + 800 + 50 + 2 =

50000 + 1000 + 900 + 40 + 1 =

70000 + 2000 + 100 + 30 + 2 =

Prime Mathematics Book − 3 35

Place and face value in five digit numbers

Let’s find the place value and face value of the
digits used in the number 32,498. First represent

it in a place value table.

Ten thousands Thousands Hundreds Tens Ones
3 2 4 98

3 is in ten thousands place so, its place value is 3 ten thousands that means
30,000. But its face value is 3.

2 is in thousands place so, its place value is 2 thousands that means 2,000.
But its face value is 2.

4 is in hundreds place. Therefore its place value is 4 hundred or 400. Its
face value is 4. 9 is in tens place. So, its place value is 9 tens or 90. Its face
value is 9.

Similarly, 8 is in ones place so, its place value is 8 ones or 8. Its face value
is also 8.

Exercise - 2.5

Write the place value and face value of the underlined digits.

Place value Face value Place value Face value

24536 4000 4 64985

52697 75806

69780 12405

92984 25900

85007 39452

Comparison of numbers
(5 digit numbers)

Could you compare the numbers 59,264 and 68,975?

Yes, I can. First I have to represent the
numbers in place value table.

T−Th Th H T O
5 9264
6 8975

36 Prime Mathematics Book − 3

First compare the digits in ten thousands place. 6 is greater than 5. So, 68975 is greater
than 59264.
Also, while comparing if the digits of ten thousands place are equal, then compare the
digits of thousand place. If they are also equal, compare the digits of hundreds place. If
they are also equal, compare the digits of tens place. If they are also equal, then compare
the digits of ones place.
If the digits of ten thousands place, thousands place , hundreds place, tens place and ones
place are equal, then the numbers are equal to each other.

Exercise - 2.6

A. Put > or < or = sign in the boxes:

98,405 98,505 64,902 64,903
24,820
49,801 59,801 24,810 45,850
98,400
60,100 60,100 35,850

73,125 73,129 99,400

B. Arrange the given numbers in descending order:

38920 , 43200 94345 84620
94210
, , ,
15850 89200 75,810

, , , ,
96400 74210 52960
24750

,, , ,

46954 98475 12960 34497

,, , ,

C. Arrange the given numbers in ascending order:

60805 70019 90010 59987 49999

,, , ,

76250 78005 79319 70259 71099

,, , , 87081
87310 87095 87901 87199

, , ,, 98799
98725 98790 98708 98701

, , ,,

Prime Mathematics Book − 3 37

Six digit numbers The sum of 99999 and
1 is 100000, that is
Can you add 99999 and 1 ? one lakh.
What is the sum?

100000 is a six digit number. It is
the smallest number of six digits.
Let’s represent 100000 in place value table.

Lakh Ten Thousands Thousands Hundreds Tens Ones
L T – Th Th H T O
1 00 0 0 0

1,00,000 = One lakh
While writing a six digit number, we put comma between the digits of
hundreds place and thousands place. Also, we put comma between the
digits of ten thousands place and lakh.

Exercise - 2.7

A. Show the given numerals in place value table and
write in words.

6,21,100 L T – Th Th H T O
621100

Six lakh twenty one thousand and one hundred.

7,40,958 L T – Th Th H T O

5,24,109 L T – Th Th H T O

38 Prime Mathematics Book − 3

9,99,999 L T – Th Th H T O

8,41,356 L T – Th Th H T O

5,10,002 L T – Th Th H T O

B.Represent the given number names in a place value
table and write the numeral.

Six lakh forty two thousand Seven lakh ninety thousand
and four hundred. five hundred and ten.

L T – Th Th H T O L T – Th Th H T O
6 4 2400
Nine lakh three thousand nine
6,42,400 hundred and sixty seven.

Eight lakh two thousand six L T – Th Th H T O
hundred and four.

L T – Th Th H T O

Five lakh and four thousand. Three lakh fifty two thousand
L T – Th Th H T O nine hundred and five.

L T – Th Th H T O

Prime Mathematics Book − 3 39

C. Count by 10,000s and complete the boxes:

310500 320500 330500 340500 350500
425004
509605
615200
845900
731402

D. Count by 1,00,000s and complete the boxes:

200305 300305 400305 500305 600305

342904

595806

418400

319200

Place value and face value in six digit numbers

Could you represent 627495 Yes, sir! I can
in a place value table?

L T – Th Th H T O
6 2 7495

Digit Place value Face value
6 6 lakh = 6,00,000 6
2 2 ten thousands = 20,000 2
7 7
4 7 thousands = 7,000 4
9 4 hundreds = 400 9
5 9 tens = 90 5
5 ones = 5

40 Prime Mathematics Book − 3

Exercise - 2.8

A.Represent the given numerals in a place value table
and write in words.

6,70,405 L T – Th Th H T O
670405

Six lakh seventy thousand four hundred and five

4,38,950 L T – Th Th H T O

6,79,801 L T – Th Th H T O

9,81,254 L T – Th Th H T O

7,45,690 L T – Th Th H T O

B.Write the numerals in expanded form:

8,45,623 = 8,00,000 + 40,000 + 5,000 + 600 + 20 + 3

9,18,415 = + + + ++
7,23,495 =
6,92,780 = + + + ++
5,19,769 =
4,21,596 = + + + ++

+ + + ++

+ + + ++

Prime Mathematics Book − 3 41

C.Write in short form:

8,00,000 + 20,000 + 4,000 + 500 + 20 + 3 = 8,24,523
9,00,000 + 40,000 + 6,000 + 700 + 50 + 4 =
7,00,000 + 30,000 + 9,000 + 800 + 70 + 5 =
4,00,000 + 50,000 + 5000 + 600 + 80 + 9 =
5,00,000 + 70,000 + 7,000 + 900 + 10 + 3 =
6,00,000 + 90,000 + 8,000 + 400 + 20 + 7 =

D.Write the face and place value of underlined digits:

Face value Place value Face value Place value

9,87,253 8 80000 8,92,415

7,84,269 7,19,694

9,81,345 6,20,184

Comparison of six digit numbers

Could you find Yes, Sir! I can. First I have to
which one is greater represent the numbers in place value
6,97,132 or 7,87,145? table and start to compare the digits

in highest place value
and so on.

L T – Th Th H T O

697132

787145

When we compare the digits of lakh place value, 7 is greater than
6 so, 7,87,145 is greater than 6,97,132.

Exercise - 2.9

A. Put the sign >, < or = in the boxes:

7,89,432 8,89,432 4,83,450 4,83,350

6,72,504 6,62,504 5,96,451 5,96,568

9,99,999 6,56,900 2,13,497 4,13,497

9,99,999 9,99,999 3,59,600 3,29,600

42 Prime Mathematics Book − 3

B. Arrange the numbers in increasing order:

245800 645800 954008 108918

,, , ,
612500 642698
609418 619400
, ,
,, 245528 245499
,
245698 245600 , 721564
732598 ,
,, 948148
, ,
741265 736985 948168

,, ,

948100 948150

,,

C. Arrange the numbers in decreasing order:

293481 993481 793481 593481

,, , ,
369658 399658
349658 329658

,, , ,
429713 425713
428713 421713

,, , ,
523641 521498
526536 523694

,, , ,
632730 632430
632830 632930

,, ,,

Prime Mathematics Book − 3 43

The greatest and smallest numbers made up of
certain number of digits

Could you form the greatest and smallest
number of digits 1, 0, 3, 4?

Sorry sir, I don’t know. Could
you help me properly?

To form the greatest number, Let’s keep the digits in
descending order i.e. 4310. So, 4310 is the greatest

number formed by the digits 1, 0, 3 and 4.

Similarly, to form the smallest number, let's arrange the digits in increasing
order i.e. 0134. But it is a number of three digits. So, if there is 0, we have
to take it as second digit. So, the smallest number is 1034 formed by the
four digits 1, 0, 3 and 4.

Exercise - 2.10

A.Form the greatest number and the smallest number
of the given digits.
Greatest number Smallest number

4, 3, 5, 7 7543 3457

6, 0, 1, 9

1, 2, 0, 5

9, 1, 6, 7

2, 3, 4, 8

8, 6, 5, 0

B.Form the greatest number and the smallest number

of the following digits. Smallest number
Greatest number 10348
84310
3, 1, 0, 4, 8

9, 3, 2, 1, 4

4, 0, 1, 3, 7

1, 2, 3, 4, 5

6, 4, 2, 8, 0

44 Prime Mathematics Book − 3

D.Form the greatest number and the smallest number
of the following digits.

0, 2, 4, 6, 8, 9 Greatest number Smallest number
986420 204689

1, 0, 3, 5, 7, 9

2, 4, 5, 7, 8, 1

3, 4, 6, 7, 8, 9

1, 0, 2, 4, 8, 7

Use of comma while writing numbers

Do you know where to put
commas in the number 245639?

Yes, sir, I know. We have to put comma after counting
3 digits from the right and the another comma after 2
digits from the first comma and so on. That means we

write the number in the form: 2,45,639.

Thank you! You are absolutely correct. But it is
Devanagari or Hindi Arabic or Local system. There is Hindu
Arabic of English or international system too. In Hindu Arabic System
we put comma after counting three digits from right and next comma
after next three digits and we put comma in between the digits 5 and
6. So, we read it as two hundred and forty five thousand six hundred

and thirty nine. In Hindu Arabic System there is no lakh.

A. Use comma:

International System Local System

573491 573491

24560 24560

674951 674951

9650 9650

53270 53270

704578 704578

8194 8194

34589 34589

123456 123456

598976 598976

Prime Mathematics Book − 3 45