Vedanta Excel in Mathematics Books 4 Final (2079)

Approved by the Government of Nepal, Ministry of Education, Curriculum
Development Centre, Sanothimi, Bhaktapur as an Additional Material

vedanta

Excel in

Mathematics

4Book

Author
Hukum Pd. Dahal

Editor
Tara Bahadur Magar

vedanta
Vedanta Publication (P) Ltd.
jb] fGt klAns];g k|f= ln=

Vanasthali, Kathmandu, Nepal
+977-01-4982404, 01-4962082
[email protected]
www.vedantapublication.com.np

vedanta

Excel in

Mathematics

4Book

All rights reserved. No part of this publication may
be reproduced, copied or transmitted in any way,
without the prior written permission of the publisher.

First Edition: B.S. 2077 (2020 A. D.)
Second Edition: B.S. 2078 (2021 A. D.)
Third (Revised and Updated) Edition: B.S. 2079 (2022 A. D.)

Price: Rs 380.00

Published by:
Vedanta Publication (P) Ltd.

j]bfGt klAns;] g k|f= ln=

Vanasthali, Kathmandu, Nepal
+977-01-4982404, 01-4962082
[email protected]
www.vedantapublication.com.np





Preface

The series of 'Excel in Mathematics' is completely based on the contemporary pedagogical teaching
learning activities and methodologies extracted from Teachers' training, workshops, seminars and
symposia. It is an innovative and unique series in the sense that the contents of each textbooks of
the series are written and designed to fulfill the need of integrated teaching learning approaches.
Excel in Mathematics is an absolutely modified and revised edition of my three previous series:
'Elementary mathematics' (B.S. 2053), 'Maths In Action (B. S. 2059)' and 'Speedy Maths' (B. S. 2066).
Excel in Mathematics has incorporated applied constructivism. Every lesson of the whole series
is written and designed in such a manner, that makes the classes automatically constructive and
the learners actively participate in the learning process to construct knowledge themselves, rather
than just receiving ready made information from their instructors. Even the teachers will be able
to get enough opportunities to play the role of facilitators and guides shifting themselves from the
traditional methods of imposing instructions.
Each unit of Excel in Mathematics series is provided with many more worked out examples.
Worked out examples are arranged in the hierarchy of the learning objectives and they are reflective
to the corresponding exercises. Therefore, each textbook of the series itself is playing a role of a
‘Text Tutor’. There is a well balance between the verities of problems and their numbers in each
exercise of the textbooks in the series.
Clear and effective visualization of diagrammatic illustrations in the contents of each and every
unit in grades 1 to 5, and most of the units in the higher grades as per need, will be able to integrate
mathematics lab and activities with the regular processes of teaching learning mathematics
connecting to real life situations.
The learner friendly instructions given in each and every learning contents and activities during
regular learning processes will promote collaborative learning and help to develop learner-
centred classroom atmosphere.
In grades 6 to 10, the provision of ‘General section’, ‘Creative section - A’ and ‘Creative section - B’
fulfills the coverage of overall learning objectives. For example, the problems in ‘General section’
are based on the Knowledge, understanding and skill (as per the need of the respective unit)
whereas the ‘Creative sections’ include the Higher ability problems.
The provision of ‘Classwork’ from grades 1 to 5 promotes learners in constructing knowledge,
understanding and skill themselves with the help of the effective roles of teacher as a facilitator
and a guide. Besides, teacher will have enough opportunities to judge the learning progress and
learning difficulties of the learners immediately inside the classroom. These classworks prepare
learners to achieve higher abilities in problem solving. Of course, the commencement of every
unit with 'Classwork-Exercise' may play a significant role as a 'Textual-Instructor'.
The 'project works' given at the end of each unit in grades 1 to 5 and most of the units in higher
grades provide some ideas to connect the learning of mathematics to the real life situations.
The provision of ‘Section A’ and ‘Section B’ in grades 4 and 5 provides significant opportunities
to integrate mental maths and manual maths simultaneously. Moreover, the problems in ‘Section
A’ judge the level of achievement of knowledge and understanding and diagnose the learning
difficulties of the learners.
The provision of ‘Looking back’ at the beginning of each unit in grades 1 to 8 plays an important
role of ‘placement evaluation’ which is in fact used by a teacher to judge the level of prior
knowledge and understanding of every learner to make his/her teaching learning strategies.

The socially communicative approach by language and literature in every textbook especially in
primary level of the series will play a vital role as a ‘textual-parents’ to the young learners and
help them in overcoming maths anxiety.

The Excel in Mathematics series is completely based on the latest curriculum of mathematics,
designed and developed by the Curriculum Development Centre (CDC), the Government of Nepal.

I do hope the students, teachers and even the parents will be highly benefited from the ‘Excel in
Mathematics’ series.

Constructive comments and suggestions for the further improvements of the series from the
concerned will be highly appreciated.

Acknowledgments

In making effective modification and revision in the Excel in Mathematics series from my previous
series, I’m highly grateful to the Principals, HOD, Mathematics teachers and experts, PABSON,
NPABSAN, PETSAN, ISAN, EMBOCS, NISAN and independent clusters of many other Schools
of Nepal, for providing me with opportunities to participate in workshops, Seminars, Teachers’
training, Interaction programmes and symposia as the resource person. Such programmes helped
me a lot to investigate the teaching-learning problems and to research the possible remedies and
reflect to the series.

I’m proud of my wife Rita Rai Dahal who always encourages me to write the texts in a more
effective way so that the texts stand as useful and unique in all respects. I’m equally grateful to
my son Bishwant Dahal and my daughter Sunayana Dahal for their necessary supports during the
preparation of the series.

I’m extremely grateful to Dr. Ruth Green, a retired professor from Leeds University, England
who provided me very valuable suggestions about the effective methods of teaching-learning
mathematics and many reference materials.

Grateful thanks are due to Mr. Tara Bahadur Magar for his painstakingly editing of the series and
I am thankful to Dr. Komal Phuyal for editing the language of the series.

Moreover, I gratefully acknowledge all Mathematics Teachers throughout the country who
encouraged me and provided me the necessary feedback during the workshops/interactions and
teachers’ training programmes in order to prepare the series in this shape.

I’m profoundly grateful to the Vedanta Publication (P) Ltd. to get this series published. I would
like to thank Chairperson Mr. Suresh Kumar Regmi, Managing Director Mr. Jiwan Shrestha,
Marketing Director Mr. Manoj Kumar Regmi for their invaluable suggestions and support during
the preparation of the series.

Last but not the least, I’m heartily thankful to Mr. Pradeep Kandel, the Computer and Designing
Senior Officer of the publication house for his skill in designing the series in such an attractive
form.

Hukum Pd. Dahal

Contents

Unit Topics Page No.

1 Number System 7 - 29

1.1 Counting and writing numbers - Looking back, 1.2 Number, numeral
and digit, 1.3 Hindu - Arabic number system, 1.4 Place, Place value
and Face value, 1.5 Expanded form of numbers, 1.6 Six-digit numerals,
1.7 Seven-digit numerals, 1.8 Eight-digit numerals, 1.9 International place
value system, 1.10 Use of commas, 1.11 The greatest and the least numbers,
1.12 The greatest and the least numbers formed by given digits, 1.13 Rounding
off numbers - Estimation, 1.14 Roman number system, 1.15 Natural numbers
- The counting numbers, 1.16 Whole Numbers, 1.17 Odd and even numbers,
1.18 Prime and Composite Numbers

2 Fundamental Operations - I (Addition and Subtraction) 30 - 40

2.1 Addition and Subtraction - Looking back , 2.2 Relation between addition and
subtraction, 2.3 Adding and regrouping

3 Fundamental Operations - II (Multiplication and Division) 41 - 67

3.1 Multiplication - Looking back, 3.2 Multiplier, multiplicand and
product, 3.3 Row and column multiplication, 3.4 Multiplication facts,
3.5. Multiplication of 10, 100, 200, 3000, ... and so on, 3.6 Multiplication
of bigger numbers, 3.7 Division - Looking back, 3.8 Dividend, divisor,
quotient and remainder, 3.9 Division as repeated subtraction, 3.10 Relation
between multiplication and division, 3.11 Division by row and column,
3.12 Dividing tens, hundreds, thousands, ... by 10, 20, 300, 4000, ...,
3.13 Division facts, 3.14 Division of bigger numbers, 3.15 Divisibility test,
3.16 Factors and multiples, 3.17 Prime Factors, 3.18 Process of finding multiples
of a given number

4 Order of Operations 68 - 73

4.1 Simplification - A single solution of a mixed operation, Order of operations,
4.3 Use of brackets in simplification

5 Fraction 74 - 92

5.1 Fraction - Looking back, 5.2 Reducing fractions to their lowest terms, 5.3 Like
and unlike fractions, 5.4 Comparison of like fractions, 5.5 Proper and improper
fractions, 5.6 Mixed numbers, 5.7 Process of changing improper fraction to
mixed number, 5.8 Process of changing mixed number to improper fraction,
5.9 Addition and subtraction of like fractions, 5.10 Repeated addition of like
fractions 5.11 To find the value of fraction of a number in a collection

6 Decimal and Percent 93 - 110

6.1 Tenths and hundredths - Looking back, 6.2 Mixed number and decimal,
6.3 Place and place value of decimal numbers, 6.4 Comparison of decimal
numbers, 6.5 Conversion of a decimal number into a fraction, 6.6 Conversion of a
fraction into a decimal number, 6.7 Addition and subtraction of decimal numbers,
6.8 Percent - How many out of 100?, 6.9 Conversion of fraction into percent,
6.10 Conversion of percent into fraction, 6.11 Fraction, decimal and percent,
6.12 To find the value of the given percent of a quantity, 6.13 Fraction, decimal
and percent

7 Measurement - Time and Money 111 - 140

7.1 Measurement of Time - Looking back, 7.2 24 - hour clock system, 7.3
The calendar - Days, weeks, months and year, 7.4 Conversion of units of
time, 7.5 Addition and subtraction of time, 7.6 Measurement of money,
7.7 Changes of Nepali rupees note, 7.8 Conversion between rupees and paisa,
7.9 Addition and subtraction of money, 7.10 Money related multiplication
division, 7.11 Rate of cost

8 Measurement - Length, Weight and Capacity 141 - 176

8.1 Measurement of length - Looking back, 8.2 Standard units of length,
8.3 Conversion of units of length, 8.4 Addition and subtraction of lengths,

8.5 Map and distance, 8.6 Measurement of weight - Looking back, 8.7 gk] fnL
k/Dk/fut tf}nsf OsfO{, 8.8 Conversion of units of weight, 8.9 Addition and
subtraction of weights, 8.10 Measurement of capacity - Looking back, 8.11 gk] fnL
k/Dk/fut Ifdtfsf OsfO,{ 8.12 Conversion of units of capacity, 8.13 Addition and

subtraction of capacities,

9 Measurement - Perimeter, Area and Volume 177 - 188

9.1 Perimeter - The distance all the round, 9.2 Perimeter of rectangle and
square, 9.3 Area - Space covered by a surface, 9.4 Area of rectangle and
square, 9.5 Volume - space occupied by an object, 9.6 Volume of cube,
9.7 Volume of cuboid

10 Algebra 189 - 217

10.1 Mathematical sentence, 10.2 Mathematical sentences on addition and
subtraction, 10.3 Mathematical sentences on multiplication and division, 10.4
Mathematical sentence using letters, 10.5 Finding the value of letter, 10.6
Use of mathematical sentences, 10.7 Constant and variable - Introduction,
10.8 Operation on constant and variable, 10.9 Like and unlike terms,
10.10 Addition and subtraction of like terms

11 Geometry: Lines and Angles 218 - 225

11.1 Point, line and line segment - Looking back, 11.2 Measuring the length
of line segments, 11.3 Angle - Looking back, 11.4 Measurement of angles,
11.5 Construction of angles

12 Geometry: Shapes 226 - 234

12.1 Plane figures (or shapes), 12.2 Triangle, 12.3 Quadrilaterals, 12.4 Circle,
12.5 Solid figures (or shapes)

13 Statistics 235 - 243

13.1 Bill, 13.2 Budget, 13.3 Bar graph - Looking back

Answers 244- 253

Evaluation Model 254- 256

Unit Number System

1

1.1 Counting and writing numbers - Looking back
Classwork - Exercise
1. Let's read these interesting facts. Rewrite the number names in

numerals.

a) The highest peak of the world 'Sagarmatha' is about eight thousand
eight hundred forty-nine metres high.

b) The highest lake of Nepal 'Tilicho lake' is situated at an altitude of four
thousand nine hundred nineteen metres.

c) Mariana Trench is the deepest trench in the world. It is about ten
thousand nine hundred ninety-four metres deep.

d) At the equator, the earth rotates at a speed of about one thousand seven
hundred kilometres in 1 hour.

2. Let's count Nepali rupees notes. Say and write how many rupees altogether.

a) Rs

rupees.

b) Rs

rupees.

c) Rs

rupees.

3. Let's read the price of these articles. Say and write the price in words.

Rs 750.00 Rs 1,589.00 Rs 4,999.00 Rs 999.00 Rs 7,625.00

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 7 vedanta Excel in Mathematics - Book 4

Number System

a) Calculator:
b) Watch:

c) Mobile:

d) Headphone:

e) Sound box:

4. Let's say and write how many digits there are in these numerals.
2 a) 70 is a
digit numeral. b) 306 is a digit numeral.

c) 5080 is a digit numeral. d) 73014 is a digit numeral.

5. Let's listen to your teacher! Write 4 digit numerals said by your teacher.



6. It's your time! Let's write a numeral of the given number of digits. Then,
write the name of numerals in words.

a) A 2-digit numeral

b) A 3-digit numeral

c) A 4-digit numeral

7. Let's count the blocks of hundreds, tens, and ones. Then, write in the
place value table. Say and write the numeral and number name.

a) H T O 101

1 0 1 One hundred one

b)
HTO

c)
HTO

vedanta Excel in Mathematics - Book 4 8 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

d)
HTO

9. Let's count the blocks of thousands, hundreds, tens, and ones. Then
write in the place value table. Say and write the numerals and number
in words.

a) Th H T O 1001

1 0 0 1 One thousand one
b)

Th H T O

c)

Th H T O

d)

Th H T O

1.2 Number, numeral, and digit

A number is a count of objects or quantities. For example, five fingers, five
children, five litres of water, and so on.
A numeral is a symbol that represents a number. For example, 5 fingers, 5
children, 5 litres of water, and so on.

A digit is a single symbol used to make numerals. For example, 2 and 7 are
two digits of the numeral 27.

1.3 Hindu - Arabic number system

The Hindu-Arabic number system was first developed by the Hindus.
Later, this number system was spread by the Arabs all over the world. This
system has ten basic symbols: they are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. These
symbols are called digits. All the numbers from smaller to larger are formed
by using these ten digits.

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 9 vedanta Excel in Mathematics - Book 4

Number System

Devanagari number system is also similar to the Hindu-Arabic number
system. However, it has a bit different symbols of digits.

Hindu-Arabic digits 0 1 2 3 4 5 67 8 9
Devanagari digits
Devanagari number names ) ! @ # $ % ^& * (
z"Go Ps bO' { tLg rf/ kfFr 5 ;ft cf7 gf}+

1.4 Place, Place value, and Face value 2 tens = 2 × 10 = 20
7 ones = 7 × 1 = 7
Let's take a number 27.

In this number, 2 is at tens place and 7 is at
ones place. The place value of 2 is 20 and the
place value of 7 is 7.

27 20 blocks 7 blocks

Ones place = 7 × 1 = 7 -Pssf] :yfgdf & Ö &_
Tens place = 2 × 10 = 20 -bzsf] :yfgdf @ Ö @)_

Let's take another number 213.

In this number, 2 is at hundreds 2 hundreds = 2 × 100 = 200
1 ten = 1 × 10 = 10
place; 1 is at tens place; and 3 is at

ones place. The place value of 2 is 3 ones
200; the place value of 1 is 10; and =3×1=3

the place value of 3 is 3. 200 blocks 10 blocks 3 blocks

213

Ones place = 3 × 1 = 3 -Pssf] :yfgdf # Ö #_
Tens place = 1 × 10 = 10 -bzsf] :yfgdf ! Ö !)_
Hundreds place = 2 × 100 = 200 -;osf] :yfgdf @ Ö @))_

Again, let's take any two numbers 3405 and 16072.

3405

Ones place = 5 × 1 = 5 -Pssf] :yfgdf % Ö %_
Tens place = 0 × 10 = 0 -bzsf] :yfgdf ) Ö )_
Hundreds place = 4 × 100 = 400 -;osf] :yfgdf $ Ö $))_
Thousands place = 3 × 1000 = 3000 -xhf/sf] :yfgdf # Ö #)))_

Vedanta ICT Corner
Please! Scan this QR code or
browse the link given below:

https://www.geogebra.org/m/ymmyeusm

vedanta Excel in Mathematics - Book 4 10 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

16072

Ones place = 2 × 1 = 2 -Pssf] :yfgdf @ Ö @_
Tens place = 7 × 10 = 70 -bzsf] :yfgdf & Ö &)_
Hundreds place = 0 × 100 = 0 -;osf] :yfgdf ) Ö )_
Thousands place = 6 × 1000 = 6000 -xhf/sf] :yfgdf ^ Ö ^)))_
Ten-thousands place=1×10000=10000 -bz xhf/sf] :yfgdf !Ö!))))_

The face value of each digit of any number is the digit itself.
For example, the face value of 6 in 16072 is 6. The face value of 9 in 28914
is 9, and so on.

1.5 Expanded forms of numbers

Let's learn about the expanded forms of numbers from the given illustrations.

45 = = Forty + Five
= 40 + 5
4 × 10 5 × 1 = 4 × 10 + 5 × 1

236 = 3 × 10 6 × 1 = Two hundred + Thirty + Six
= 200 + 30 + 6
2 × 100 = 2 × 100 + 3 × 10 + 6 × 1

3104 = = Three thousand + One hundred + Four

3 × 1000 1 × 100 4 × 1 = 3000 + 100 + 4
= 3 × 1000 + 1 × 100 + 4 × 1

Similarly, 28973 = 2 × 10000 + 8 × 1000 + 9 × 100 + 7 × 10 + 3 × 1
40307 = 4 × 10000 + 0 × 1000 + 3 × 100 + 0 × 10 + 7 × 1
= 4 × 10000 + 3 × 100 + 7 × 1
Again, let's learn to write numbers in the short forms.
7 × 10 + 2 × 1 = 72
3 × 100 + 6 × 1 = 3 × 100 + 0 × 10 + 6 × 1 = 306
4 × 1000 + 2 × 10 + 3 × 1 = 4 × 1000 + 0 × 100 + 2 × 10 + 3 × 1 = 4023
5 × 10000 + 2 × 1000 + 1 × 100 + 8 × 10 + 4 × 1 = 52184

11Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

Exercise - 1.1
Section A - Classwork

1. Let's say and write the answer as quickly as possible.

a) The digits of the numeral 2058 are
b) How many digit are there in the numeral 70502?
c) What is the place name of 9 in 6945?
d) What is the place name of 4 in 41860?
e) Which digit of the numeral 6037 is at hundreds place?
f) Which digit of numeral 52930 is at thousands place?
g) What is the place value of 7 in the numeral 3705?
h) What is the place value of the digit at thousands place

in 95135?
i) What is the face value of 3 in the numeral 7325?
j) What is the face value of the digit at tens place of the

numeral 856?

2. tnsf k|Zgx?sf] pQ/ hlt;Sbf] rf8F f] egf}+ / n]vf}+ x} t .
s_ krf;L ;+Vofgfdsf] c+u|]hL ;V+ ofgfd / ;+Vof slt x'G5 <
v_ &%^$ nfO{ cu+ |]hL ;+Vofdf nv] f}+ .
u_ 9328 nfO{ gk] fnL ;V+ ofgfddf n]vf}+ .
3_ 8140 nfO{ g]kfnL ;+Vofdf nv] f+} .
ª_ ^#%* df ;osf] :yfgdf s'g c+s 5 / To;sf] :yfgdfg slt x'G5 <
r_ %@(# df % sg' :yfgdf 5 / o;sf] :yfgdfg slt x'G5 <

3. a) How many ones make 1 ten?

b) How many tens make 1 hundred?

c) How many hundreds are there in 1 thousand?

d) How many thousands are there in 1 ten-thousand?

4. a) What is the digit at ones place in 7 × 10?

b) What is the digit at tens place in 3 × 100 + 5 × 1?
c) What is the digit at hundreds place in 4 × 1000 + 6 × 10 + 8 ×1?

vedanta Excel in Mathematics - Book 4 12 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

Section B

5. Let's count the number of ones, tens, hundreds, and thousands blocks.
Then, write the numerals. Rewrite them in the expanded forms.

a) b)

c) d)

6. Let's write the numerals shown by the abacus. Then rewrite them in

the expanded forms.

TO HT O Th H T O T-th Th H T O

a) b) c) d)



7. Let's draw abacus to show these numerals.

a) 45 b) 362 c) 2017 d) 34258

8. Let's find the place value of each digit of the following numerals:

a) 672 b) 4853 c) 51491

9. Let's write the short forms of numerals of these expanded forms:

a) 8 × 10 + 4 × 1 b) 7 × 100 + 2 × 10 + 5 × 1

c) 4 × 100 + 8 × 1 d) 2 × 1000 + 7 × 10 + 7 × 1

e) 5 × 1000 + 3 × 100 + 4 × 10 + 6 × 1

f) 3 × 10000 + 6 × 1000 + 1 × 100 + 8 × 10 + 7 × 1

10. Let's work out these problems and find the correct answers.

a) Calculate the difference between the place values of 5 of the numerals
352 and 325.

b) Calculate the difference between the place values of 2 of the numerals
4218 and 4128.

c) Calculate the difference between the place value of 1 of the numerals
1560 and 160.

13Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

11. Write the number names of the numerals used in these statements.
a) The population of a village is 9075.
b) The cost of a mobile is Rs 15009.
12. Write the numerals of the number names used in these statements.
a) Mrs. Chaudhari donated seven thousand eleven rupees to the

earthquake victims.
b) In the Gandaki Pradesh, ten thousand eighty-six children got the

polio vaccination last year.
13. How many ten-thousands are there in these numerals?
a) 10650 b) 21540 c) 36907 d) 74215 e) 99999

Vedanta ICT Corner
Please! Scan this QR code or
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1.6 Six-digit numerals
Classwork - Exercise

1. Let's say and write the answer as quickly as possible.

(a) How many digits are there in 10000 (Ten thousand)?

(b) How many digits are there in 50000 (Fifty thousand)?

(c) Howmanydigitsaretherein90000(Ninetythousand)?

2. Let's count by 10 thousands and write the missing numerals.

(a) 10000, 20000, 30000, , , 60000

(b) 70000, , 90000, then

After 90000, it comes 100000 (Hundred thousand). One lakh!
One hundred thousand = 1 lakh ⇒ 100000 100000
Two hundred thousand = 2 lakh ⇒ 200000 and so on. It is a 6-digit
numeral.

100000, 200000, 300000, ... 900000 are 6-digit numerals.

4, 1, 6, 2, 8 and 0 are the 6-digits of the numeral 416280.

1.7 Seven-digit numerals

Now, can you say what number comes after 900000 (Nine hundred
thousand)?

vedanta Excel in Mathematics - Book 4 14 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

Of course, it is 1000000 (Ten hundred thousand).
Ten hundred thousand = 10 lakh = 1000000
Twenty hundred thousand = 20 lakh = 2000000 and so on.
1000000, 2000000, 3000000, ... 9000000 are 7-digit numerals.
5, 8, 0, 3, 4, 9 and 6 are the 7-digits of the numeral 5803496.

1.8 Eight-digit numerals

Classwork - Exercise

1. Let's say and write the missing lakhs.

a) 10 lakh, 20 lakh, , , 60 lakh

b) 70 lakh, , 90 lakh, then

Of course, after 90 lakh (9000000) it comes 100 lakh (10000000).

One hundred lakh = 1 crore ⇒ 10000000

Two hundred lakh = 2 crore ⇒ 20000000 and so on.

10000000, 20000000, ... 90000000 are 8-digit numerals.

2. Let's write these numerals in place value tables and name them.

a) 254876

L T-th Th H T O Two lakh fifty-four thousand eight
2 5 4 8 7 6 hundred seventy-six.


b) 4791038

T-L L T-th Th H T O Forty-seven lakh ninety-one thousand
thirty-eight.
4 7 9 1 038

c) 36825940

C T-L L T-th Th H T O Three crore sixty-eight lakh twenty-
3 6 8 2 5 9 4 0 five thousand nine hundred forty.

1.9 International place value system

Let's compare the places of digits of numerals between Nepali and

International system.

15Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

Nepali place International place Place values Number of digits
names names
Ones
Tens Ones 1 One
Hundreds
Thousands Tens 10 Two
Ten-thousands
Lakhs Hundreds 100 Three
Ten-lakhs
Crores Thousands 1000 Four

Ten-thousands 10000 Five

Hundred-thousands 100000 Six

Millions 1000000 Seven

Ten-millions 10000000 Eight

In this way, only after ten-thousands, the place names of digits are
different in Nepali and International system.

Classwork - Exercise
1. Let's read the above table. Say and write the answers as quickly as

possible.
a) How many hundred-thousands are there in 1 lakh?
b) How many lakhs are there in 2 hundred thousands?
c) How many millions are there in 40 lakhs?
d) How many lakhs are there in 5 millions?
e) How many ten-millions are there in 1 crore?

1.10 Use of commas

It is easier to read and write the bigger numbers by separating the digits
at thousands and greater than thousands places by using commas (,).

Remember! We start to use commas only in 4-digit and greater than
4-digit numerals.

vedanta Excel in Mathematics - Book 4 16 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

In Nepali and International place value system, we use commas in different
ways.

7000 7, 000 Use of commas up to ten-thousands place of Nepali and
70000 70, 000 International systems are the same.

700000 7, 00,000 In Nepali system, each pair of digits greater than
700000 hundreds place is separated by commas.

700,000 In International system, each group of 3-digits greater
than hundreds place is separated by commas

Numerals Use of comma in Nepali Use of commas in International
5200000 system System

52,00,000 5,200,000
Fifty-two lakh Five million two hundred thousand

32500000 3,25,00,000 32,500,000
Three crore twenty-five Thirty-two million five hundred
lakh thousand

Classwork - Exercise

1. Let's rewrite these numerals using commas in Nepali and
International systems.

Numerals Use of comma in Nepali Use of commas in International

system System

15327

804930

6831400

32495600

17Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

1.11 The greatest and the least numbers
Classwork - Exercise

1. Let's read and learn from the given examples. Then, write the

remaining numbers.

The least 1-digit number 1 The greatest 1-digit number 9

The least 2-digit number 10 The greatest 2-digit number 99

The least 3-digit number 100 The greatest 3-digit number

The least 4-digit number The greatest 4-digit number

The least 5-digit number The greatest 5-digit number

The least 6-digit number The greatest 6-digit number

The least 7-digit number The greatest 7-digit number

The least 8-digit number The greatest 8-digit number


2. Let's say and write the 'greatest' or 'least' in the blank spaces. Also
write the number of digits.

a) 999999 is the number of digits.

b) 1000000 is the number of digits.
c) 10000000 is the number of digits.

1.12 The greatest and the least numbers formed by given digits

Classwork - Exercise

Let's say and write the answer as quickly as possible.

1. a) All possible 2-digit numbers formed by the digits 2 and 3 are
and .

b) Between 23 and 32, the greater number is and the smaller
number is

c) So, the greatest 2-digit number formed by 2 and 3 is

d) And, the least 2-digit number formed by 2 and 3 is

vedanta Excel in Mathematics - Book 4 18 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

2. a) All possible 3-digit numbers formed by the digits 1, 0, and 4 are

,, and

b) Between 104, 140, 410, and 401, the greatest number is
and the smallest number is

c) So, the greatest 3-digit number formed by 1, 0, and 4 is

d) And, the least 3-digit number formed by 1, 0, and 4 is

Remember! 014 and 041 are not 3-digit numbers. They are 2-digit
numbers. Because 041 is 41 and 014 is 14.

3. Let's take two digits 5 and 8. Now, answer these questions.

a) Arrange them in descending and in ascending order to make 2-digit
numbers.

descending order Ascending order

b) The greatest 2-digit number formed by 5 and 8 is

c) The least 2-digit number formed by 5 and 8 is

d) Did you investigate the rule to write the greatest and the least numbers
formed by the given digits?

4. Now, let's practise to write the greatest and the least numbers formed
by these digits.

Digits Greatest Least Digits Greatest Least
numbers numbers numbers numbers

4, 7 5, 0, 1, 2

2, 8, 0 7, 3, 9, 4, 6

6, 3, 9 2, 8, 5, 0, 7

Exercise - 1.2

Section A - Classwork

1. Let's say and circle the correct answer as quickly as possible.

a) How many ten-thousands are there in 25690?

(i) 2 (ii) 5 (iii) 25

b) How many lakhs are there in 1 crore?

(i) 10 (ii) 100 (iii) 1000

19Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

c) The number name of the numeral 40700000 is

(i) forty crore seventy lakh (ii) four crore seventy lakh

(iii) four crore seven lakh

d) The numeral for thirty lakh six thousand five is

(i) 3006005 (ii) 3060005 (iii) 30060005
e) What is the next number in 10800, 10900,

(i) 11000 (ii) 101000 (iii) 110000

f) How many lakhs are there in 1 million?

(i) 1 (ii) 10 (iii) 100

g) How many millions are there in 1 crore?

(i) 1 (ii) 10 (iii) 100

h) What is the least number of 6-digit?

(i) 900000 (ii) 10000 (iii) 100000

i) The greatest 4-digit number formed by the digits 1, 9, 4 and 0 is

(i) 9401 (ii) 9410 (iii) 9041

j) The least 4-digit number formed by the digits 2, 5, 0 and 8 is

(i) 0258 (ii) 5082 (iii) 2058

2. Let's say and write the answer as quickly as possible.

a) The place name of 3 in 17345800 is

b) The place name of 5 in 25967040 is
c) Using commas in Nepali system, 3254016 is written as
d) Using commas in International system, 3254016 is
e) How many thousands are there in 1 lakh?
f) How many lakhs are there in 1 crore?

g) How many lakhs are there in 2 million?

h) How many millions are there in 30 lakh?

i) How many millions are there in 1 crore?

j) What is the least number of 8-digit?

Section B

3. Let's write these numerals in place value tables of Nepali system. Then,
write the number names.

a) 125610 b) 2718309 c) 41736082

vedanta Excel in Mathematics - Book 4 20 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

4. Let's write these numerals in place value tables of International system.
Then, write the number names.

a) 157320 b) 3271068 c) 21049355

5. Rewrite these numerals using commas in Nepali as well as in International
system. Then, write the number names in both systems.

a) 7560 b) 26908 c) 125043
d) 3804100 e) 50609050

6. Let's write the place names, place value and face value of the red coloured

digits in Nepali as well as in International system. 1 million = 1000000
a) 257410 b) 4689032 c) 13720548 = 10 lakh!

7. Let's find how many millions in 1 crore = 10000000
= 10 million!
a) 10 lakh b) 20 lakh c) 30 lakh
f) 90 lakh 10 million = 10000000
d) 40 lakh e) 50 lakh = 1 crore!

8. Let's find how many millions in

a) 1 crore b) 2 crore c) 3 crore

d) 5 crore e) 8 crore

9. Let's find how many lakhs in

a) 1 million b) 6 million c) 7 million
c) 70 million
10. Let's find how many crores in

a) 10 million b) 40 million

11. Let's write the numerals of the number names. Then, rewrite the number
names in International system.

a) The population of a town is three lakh forty-seven thousand.
b) The cost of a car is twenty-five lakh eighty thousand five hundred

rupees.

c) The population of Nepal is about two crore ninety-one lakh ninety-
two thousand four hundred eighty.

12. Let's write the numerals for the number names. Then, rewrite the number
names in Nepali system.

a) The area of Nepal is one hundred forty-seven thousand five hundred

sixteen square kilometres.

21Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

b) Nepal Government decided to provide a grant of four million seven
hundred fifty thousand three hundred rupees to the flood and
landslide victims.

c) The cost of constructing a road is about ninety-nine million five
hundred eighty thousand rupees.

13. Let's write the greatest and the least numbers formed by the given
digits.

a) 3-digit numbers formed by 7, 0 4
b) 4-digit numbers formed by 6, 2, 5, 8
c) 5-digit numbers formed by 3, 0, 1, 9 6
d) 6-digit numbers formed by 2, 7, 4, 0, 8, 5

Its your time -Project work!

14. a) Write one numeral for each of 6-digit, 7-digit, and 8-digit in a chart
paper.

(i) Rewrite them using commas in Nepali and International systems.
(ii) Write their number names in Nepali and International systems.
(iii) Show them in place value table in Nepali and International systems.
b) Make 10 flash-cards of equal size by cutting a chart paper.

(i) Write 0 to 9 in each flash-card 0 1 2 3 4 5 6 7 8 9

(ii) Play with the greatest and the least numbers of 2-digit, 3-digit...
8-digit by arranging the different flash-cards.

c) Visit the available website such as www.google.com in your school
computer or your own computer or your family member's mobile.

(i) Search and write the present population of Nepal in Nepali and
International systems.

(ii) Can you search the population of your district? If so, write the
present population of your district.

1.13 Rounding off numbers - Estimation
Let's investigate the rules for rounding off numbers to the nearest tens.

a) Round off 3 to the nearest tens.

3 is close to 0. 0 1 2 3 4 5 6 7 8 9 10

So, rounding off 3 to the nearest ten in 0.

vedanta Excel in Mathematics - Book 4 22 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

b) Now round off 26 to the nearest tens.

26 is close to 30. 20 21 22 23 24 25 26 27 28 29 30

So, rounding off 26 to the nearest tens is 30.

c) Round off 142 to the nearest tens.

142 is close to 140.

140 141 142 143 144 145 146 147 148 149 150

So, rounding off 142 to the nearest tens is 140.

d) Round off 278 to the nearest hundreds.

278 is closer to

300 than 200. So, 200 210 220 230 240 250 260 270 280 290 300

rounding off 278 to 278

the nearest hundreds is 300.

Now, can you tell the general rules for rounding off a number to the nearest
tens and hundreds? Discuss with your friends.

Exercise - 1.3

Section A - Classwork

1. Let's use number lines and round off the numbers to the nearest tens.

a) Rounding off 4 is

0 1 2 3 4 5 6 7 8 9 10

b) Rounding off 7 is
c) Rounding off 53 is
50 51 52 53 54 55 56 57 58 59 60

d) Rounding off 135 is 130 131 132 133 134 135 136 137 138 139 140

2. Let's use number lines and round off the numbers to the nearest hundreds.

a) Rounding off 140 is 100 110 120 130 140 150 160 170 180 190 200

b) Rounding off 260 is 200 210 220 230 240 250 260 270 280 290 300

23Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

c) Rounding off 385 is 300 310 320 330 340 350 360 370 380 390 400

d) Rounding off 450 is

400 410 420 430 440 450 460 470 480 490 500

Section B

3. Let's focus on the digit at ones place. Then round off the figures to the

nearest tens.

a) There are 36 students in a class. I got the rule!

The number in round figure is Rounding off 1, 2, 3 and 4 at ones
place is always to the lower tens!!

b) The cost of a book is Rs 225.

The cost in round figure is Rounding off 5, 6, 7, 8 and 9 at
ones place is always to the upper
c) The distance between Kathmandu
and Butwal is 262 km. tens!!

The distance in round figure is

d) The population of a village is 4,614.
The population in round figure is

4. Let's focus on the digit at tens place. Then, round off the figures to the

nearest hundreds.

a) The distance between Kathmandu The rule is very simple!

and Pathari is 491 km. The distance in Rounding off 1, 2 3 and 4 at
round figure is tens place is always to the

lower hundreds!!

b) There are 715 students in a school. The And rounding off 5, 6,
number in round figure is 7, 8 and 9 at tens place

c) The price of a mobile is Rs 15,850. The is always to the upper
price in round figure is hundreds!!

d) The capacity of an oil Tanker is 19,925
litres. The capacity in round figure is

5. At first, let's round off these numbers to the nearest tens. Then again
round off to the nearest hundreds.

a) Round off 218 to the nearest tens then to the nearest hundreds.

b) Round off 572 to the nearest tens then to the nearest hundreds.

c) Round off 1,655 to the nearest tens then to the nearest hundreds.

d) Round off 34,845 to the nearest tens then to the nearest hundreds.

vedanta Excel in Mathematics - Book 4 24 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

1.14 Roman number system

Roman numerals originated, as the name might suggest, in
ancient Rome. They used only seven basic symbols to write
any number. The seven symbols are I, V, X, L, C, D and M.

Let's know the values of these symbols in Hindu-Arabic
System.

Roman Numbers IVX L C D M
Hindu-Arabic Numbers 1 5 10 50 100 500 1000

There are no special symbols for 2, 3, 4, 6, 7, 8 and 9 in Roman number
system. There is no symbol for zero (0) and there is no way to calculate
fractions in this system.

Exercise - 1.4
Section A - Classwork
Let's say and write the answers as quickly as possible.
1. a) The seven basic symbols in Roman numerals are

b) The Roman numeral for the value of 50 is

c) The Roman numeral for the value of 100 is

d) The Roman numeral for the value of 500 is

e) The Roman numeral for the value of 1000 is

2. a) The Hindu-Arabic value of the Roman numeral V is

a) The Hindu-Arabic value of the Roman numeral X is

b) The Hindu-Arabic value of the Roman numeral XI is

c) The Hindu-Arabic value of the Roman numeral XII is

d) The Hindu-Arabic value of the Roman numeral L is

e) The Hindu-Arabic value of the Roman numeral C is

25Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

1.15 Natural numbers - The counting numbers

Let's have some discussions on these questions.
a) How do you count the number of fingers of your hands?

b) How do you count the number of students of your class?

c) How do you count your pocket money?
We count the number of objects by one (1), two (2), three (3), four (4), five

(5), ... Therefore, 1, 2, 3, 4, 5, ... are the counting numbers. These counting
numbers are the natural numbers.

1.16 Whole numbers

Again, let's have some discussions on these questions.

a) You had a sweet and you gave it to your sister. How many sweets were
left with you?

b) How much is left when 5 is subtracted from 5?

c) How many oceans are there in Nepal?

The answer of each of these questions is 'None'

In counting, none means zero (0). So, zero also counts the number of

objects. However, it counts 'there is no any number of objects'.

In this way, counting numbers include zero (0) as well. The natural numbers
including zero are the whole numbers. 0, 1, 2, 3, 4, 5, ... are the whole

numbers. Classwork - Exercise

1. Let's say and write the answer as quickly as possible.

a) Natural number less than 6 are

b) Whole numbers less than 6 are

c) Is 0 a natural number? Greatest whole number?
d) Is 100 a whole number? 10, 100, 1000, ... lakh,
e) What is the least natural number? crore, ten-crore, ...
f) What is the least whole number? I cannot count. It is
infinite!

g) What is the greatest whole number?

h) Are all natural numbers whole numbers?

i) Are all whole numbers natural numbers?

vedanta Excel in Mathematics - Book 4 26 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Number System

1.17 Odd and even numbers In 5 pencils, four pencils
Let's have some discussions on these questions. make two pairs and one
a) Does 1 pencil make a pair? pencil is left unpaired. So,
b) Do 2 pencils make a pair?
5 is an odd number!!

c) Do 3 pencils make a pair?
d) Do 4 pencils make two pairs?

In this way, 1, 3, 5, 7, ... are unpaired numbers. So, they are odd numbers.
2, 4, 6, 8, ... are paired numbers. So, they are even numbers.

Again, let's divide some of these natural numbers by 2.

2 ÷ 2 = 1 quotient and no remainder 2 is an even number.
3 ÷ 2 = 1 quotient and 1 remainder 3 is an odd number.
4 ÷ 2 = 2 quotient and no remainder 4 is an even number.
5 ÷ 2 = 2 quotient and 1 remainder 5 is an odd number.
10 ÷ 2 = 5 quotient and no remainder 10 is an even number.
17 ÷ 2 = 8 quotient and 1 remainder 17 is an odd number.

Can you investigate the idea to identify the given natural number is an odd
or an even number? Discuss with your friends.

Now, let's take some bigger numbers and see the digits at ones place of
these numbers.

71 1 is an odd number. So, 71 is an odd number.
256 6 is an even number. So, 256 is an even number.
629 9 is an odd number. So, 629 is an odd number.
540 If the digit at ones place is 0, the number is always even.

1.18 Prime and Composite numbers 2 ÷ 1 = 2 and 2 ÷ 2 = 1
Let's have some discussions on these questions.

a) Which numbers can divide 2 exactly,
or, without a remainder?

b) Which numbers can divide 3 exactly? 3 ÷ 1 = 3 and 3 ÷ 3 = 1
c) Which numbers can divide 5 exactly? 5 ÷ 1 = 5 and 5 ÷ 5 = 1
d) Which numbers can divide 7 exactly? 7 ÷ 1 = 7 and 7 ÷ 7 = 1
27Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Number System

In this way, 2, 3, 5, 7, ... are exactly divisible (without remainder) by 1 or by
the number itself. So, 2, 3, 5, 7, ... are prime numbers.

11, 13, 17, 19, 23, ... are also the prime numbers.

Again, let's discuss on these questions.
a) Which numbers can divide 4 exactly? 4 ÷ 1 = 4, 4 ÷ 4 = 1, 4 ÷ 2 = 2

9 ÷ 1 = 9, 9 ÷ 9 = 1, 9 ÷ 3 = 3
b) Which numbers can divide 9 exactly?

Thus, 4 and 9 are exactly divisible not only by 1 and by themselves. 4
is divisible by 2 and 9 is divisible by 3 also. So, 4 and 9 are composite
numbers.

6, 8, 10, 12, 14, 15, ... are also the composite numbers.

1 is neither a prime number nor a composite number.

Exercise - 1.5
Section A - Classwork
1. Let's say and write the answers as quickly as possible.

a) Natural numbers less than 10 are

b) Whole numbers less than 10 are

c) The least and the greatest natural numbers are and

d) The least and the greatest whole numbers are and

e) Are all natural numbers whole numbers?

f) Are all whole numbers natural numbers?

g) Is the sum of 5 and 4 a natural number?

h) Is the difference of 5 and 5 a natural number?

i) Is the difference of 5 and 5 a whole number?

2. a) Odd numbers between 10 and 20 are

b) Even number between 20 and 30 are

c) Prime numbers less than 20 are

d) Composite numbers less than 20 are

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Number System

Section B
3. Let's copy and complete the pattern of odd numbers.

a) 141, 143, , , , 151. I investigated the rule!
b) 265, , , , , 275. The next odd number to

143 is 143 + 2 = 145!!

c) 589, , , 595, , 599.

4. Let's copy and complete the pattern of even numbers.

a) 300, 302, , , , 310. I also investigated!
b) 404, , , , , 414. The next even number to
c) 796, , , , , 806.
302 is 302 + 2 = 304

It's your time - Project work!

5. a) Write the natural numbers upto 100. List the odd, even, prime, and

composite numbers separately.

b) Let's take any three pairs of odd numbers and 3 + 5 = 8 (even)
1 + 9 = 10 (even)

perform addition and multiplication between 3 × 5 = 15 (odd)
each pair. Discuss about the results with your 7 × 9 = 63 (odd)

friends and investigate the facts. 2 + 4 = 6 (even)

c) Let's take any three pairs of even numbers and 8 + 6 = 14 (even)
perform addition and multiplication between 4 × 6 = 24 (even)
8 × 2 = 16 (even)

each pair. Discuss about the results with your

friends and investigate the facts.

d) Let's take any three pairs of odd and even 2 + 3 = 5 (odd)
numbers. Perform addition and multiplication 4 + 7 = 11 (odd)
between each pair. Discuss about the results 5 × 6 = 30 (even)
with your friends and investigate the facts. 9 × 2 = 18 (even)

6. Let's draw the following number of circles in a chart paper. Colour each pair
of circles and identify odd and even numbers.

a) 7 circles b) 10 circles c) 15 circles d) 18 circles

?

29Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

Unit Fundamental Operations - I
(Addition and Subtraction)
2

2.1 Addition and Subtraction - Looking back

Classwork - Exercise
Let's count the number of cubes in the following blocks.

A block of cubes. A block of cubes. A block of cubes.

1. Let's count the blocks of hundreds, tens and the unit cubes. Add them
and find the sums.

a) + =

27 + 18 = 45

b) + =

+=

c) + =

+= =

d) +

+=

e) + =

+ = Approved by Curriculum Development CentreSanothimi, Bhaktapur
30
vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

Let's investigate the rule of addition and subtraction with 10, 20, 30, ...
10 + 20 = 30 20 + 30 = 50 40 + 50 = 90

10 + 14 = 24 20 + 23 = 43 28 + 40 = 68

30 – 10 = 20 47 – 20 = 27 75 – 40 = 35

2. Let's apply the above tricks. Then, say and write the answer as quickly
as possible. It is your mental maths!

a) (i) 10 + 30 = (ii) 20 + 40 = (iii) 30 + 50 =

(iv) 10 + 16 = (v) 20 + 18 = (vi) 14 + 30 =

(vii) 27 + 30 = (viii) 40 + 25 = (ix) 36 + 50 =

b) (i) 30 – 20 = (ii) 40 – 10 = (iii) 90 – 30 =

(iv) 27 – 10 = (v) 45 – 30 = (vi) 58 – 20 =

(vii) 64 – 40 = (viii) 86 – 50 = (ix) 99 – 60 =

Let's investigate some tricks to add or subtract the numbers faster.

4 + 8 + 6 = 10 + 8 = 18 5 + 7 + 13 = 20 + 5 = 25

12 + 16 = (10 + 10) + (2 + 6) = 28 34 + 33 = (30 + 30) + (4 + 3) = 67

24 – 13 = (24 – 10) – 3 = 11 47 – 25 = (47 – 20) – 5 = 22
26 – 12 = (20 – 10) + (6 – 2) = 14 38 – 15 = (30 – 10) + (8 – 5) = 23

3. Let's apply the above tricks. Then, say and write the answer as quickly
as possible. It is your mental maths!

a) 1 + 9 + 7 = b) 8 + 6 + 2 = c) 15 + 4 + 5 =

d) 14 + 12 = e) 25 + 33 = f) 32 + 34 =

g) 25 – 13 = h) 36 – 14 = i) 44 – 21 =

31Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

4. Let's write the missing numbers and then add as quickly as possible.

a) 2 + 7 + 8 = 10 + 7 = b) 6 + 14 + 9 = + 9 =

c) 5 + 3 + 27 = 5 + = d) 45 + 8 + 5 = + 8 =

e) 4 + 17 + 6 + 3 = 10 + =

f) 7 + 25 + 13 + 5 = 20 + = +=

g) 12 + 14 = (10 + 10) + ( 2 + 4) =

h) 15 + 12 = ( + ) + (5 + 2) = +=

i) 23 + 25 = (20 + ) + (3 + 5) = +=

5. Let's write the missing numbers and then subtract as quickly as
possible.

a) 27 – 14 = (27 – 10) – 4 = –=

b) 36 – 13 = (36 – ) – 3 = –=

c) 28 – 12 = (20 – 10) + (8 – ) = –=

d) 38 – 23 = (38 – 20) – 3 = –=

2.2 Relation between addition and subtraction

Let's investigate, how addition and subtraction work together.

Classwork - Exercise

1. Let's say and write the answer as quickly as possible.

a) 4 + 3 = Then 7 – 4 = and 7 – 3 =

b) 4 + 5 = Then 9 – 4 = and 9 – 5 =

c) 2 + 8 = Then 10 – 2 = and 10 – 8 =

d) 7 + 6 = Then – 7 = 6 and 13 – = 7

e) 8 + 7 = Then 15 – = 7 and – 7 = 8

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Fundamental Operations - I

2. It's your time!
Let's write your numbers in the blanks. Then, complete the sums.

a) + = Then – = and – =

b) + = Then – = and – =

c) + = Then – = and – =

Puzzle Time!

3. Let's fill in the missing numbers to complete the sums.

8 + 12 = 20 24 + = – 9 = 21

+ + ++ + +– ––

10 + 5 = 15 + 4= – =5

= = == = == ==

+ 17 = 35 40 + = 54 22 – =

4. Let's fill in the blanks of each crossword puzzle to make the addition
and subtraction equations true.

8+ = 18 – 25 = 75
+ –

+5 = – 20 =

==

13 + 32 =

Quiz Time (Mental Maths)!

5. a) The sum of two numbers is 12 and the difference 10 + 2 and 10 – 2, no!
9 + 3 and 9 – 3, no!
is 2. The numbers are and 8 + 4 and 8 – 4, no!
7 + 5 and 7 – 5, yes!

b) The difference of two number is 5 and their

sum is 25. The numbers are and

33Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

6. a) When a number is added to 6, the sum is 14. The number is

b) When a number is added to 12, the sum is 17. The number is
c) When a number is subtracted from 18, the difference is 8.
The number is
d) The difference of 9 and a number is 7. The number is

7. a) What should be added to 5 to get 13? Interesting Rs 10
b) What should be subtracted from 20 to get 15? is less than Rs 50
8. a) By how much is Rs 10 less than Rs 50? by 50 – 10 = Rs 40
b) By how much is 35 kg more than 25 kg?

2.3 Adding and regrouping! + =
Let's add and regroup into the higher places.
9. a) 6 ones + 9 ones = 15 ones = 1 ten and 5 ones

b) 4 ones + 7 ones = =

c) 8 ones + 5 ones = =
d) 9 ones + 9 ones = =

10. a) 5 tens + 7 tens = tens = hundred and tens

b) 8 tens + 6 tens = =

c) 9 tens + 8 tens = =

11. a) 8 hundreds + 4 hundreds = h = thousands and hundreds

b) 7 hundreds + 6 hundreds = =

c) 5 hundreds + 9 hundreds = =

Exercise - 2.1

Section A - Classwork
1. Let's say and write the missing numbers as quickly as possible.

a) 8 + = 15 b) + 6 = 18 c) 14 + = 21

d) + 40 = 60 e) 30 + = 80 f) + 45 = 90

vedanta Excel in Mathematics - Book 4 34 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Fundamental Operations - I

g) 16 – = 7 h) – 5 = 13 i) 28 – = 8

j) – 10 = 40 k) 70 – = 30 l) – 40 = 50

2. Each hexagon is made by adding up the numbers in the two hexagons
below it. Let's say and write the missing numbers.

a) b)

17 10 27 8
6 11 7 13

9

3. The sum of the numbers in each row, column, and diagonal is the same.
Let's complete these magic squares.

a) b) c)
99 11

6 10 8

3 10 5 5 7

Sum is 18 Sum is 24 Sum is 30

4. a) The numbers in the circles have been added in pairs 10
and the sum of each pair is in the square between the 15 17
circles. Complete these puzzles. 5 12 7

4 14 15

20 24

8 7 43

b) Let's add as shown and complete the addition puzzles.

+6 + 10 + 15
16 5
4 10
14 17
11 12 8 15
35 vedanta Excel in Mathematics - Book 4
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fundamental Operations - I

5. a) 60 girls and 45 boys how many children altogether?
b) 150 men and 125 women how many people altogether?
c) Among 350 students, 150 are girls. Number of boys are
d) The total cost of a book and a pen is Rs 260 and the cost of the pen is

Rs 100. The cost of the book is
6. a) By how much is Rs 500 more than Rs 350?
b) By how much is Rs 450 less than Rs 750?
c) How many rupees are needed to add with Rs 725 to make it

Rs 1000?
d) How many rupees do you need to spend from Rs 500 to remain Rs 175

with you?
7. Let's jump forward on the number line and add or subtract as shown.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

7+8=

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

+=

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

9+5=

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

–=

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

16 – 7 =

vedanta Excel in Mathematics - Book 4 36 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Fundamental Operations - I

Section B
8. Let's rewrite these problems and solve them in your exercise book.

a) Rs 480 b) 645 kg c) 586 boys d) 2350 women

+ Rs 360 + 575 kg + 465 girls + 1995 men

Rs kg students people

e) Rs 920 f) 1032 l g) 1780 students h) 5143 people
– Rs 455 – 656 l – 794 boys – 2855 women
Rs l girls men

i) selling price = Rs 1350 j) buying price = Rs 2410
buying price = – Rs 1065 selling price = – Rs 1875
profit = Rs loss = Rs

9. Let's subtract and check your answer by addition in your exercise

book.

a) 320 b) 407 c) 712

– 145 + 145 – 178 + 178 – 325 + 325

d) 1580 e) 5005 f) 8250 + 4563
– 699 + 699 – 2125 + 2125 – 4563

Let's read these problems carefully. Rewrite the solutions and solve
them in your exercise book.

10. a) There are 485 girls and 456 boys in a school. Find the total number

of students in the school. It's easy!
Solution When, I add the numbers of
girls and boys, I can find the
Number of girls = total number of students!

Number of boys =

Total number of students = +

Hence, the total number of students in the school is

37Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

b) There are 941 students in a school. Among them 456 are boys. Find the
number of girls.

Solution

Total number of students =

Number of boys =

Number of girls = –

Hence, the number of girls in the school are

c) There are 25,460 men, 24,390 women, and 10,700 children in a village.

Find the total population of the village.

Solution = I got it!
Population of men = When, I add the numbers of men,
Population of women women and children, I can find the
total population!

Population of children =

Total population =

Hence, the population of the village is

d) The total population of a village is 60,550. Among them 25,460 are
men, 24,390 are women and the rest are children. Find the population
of the children.

Solution

Population of men = Total population =
Population of women = +
Population of men and women = –

Population of men and women = Population of children =

e) A fruit seller bought 548 kg of fruits. She bought 165 kg of avocados,
180 kg of oranges, and the rest is apples. How many kilograms of apples
did she buy?

11. a) A shopkeeper bought a mobile for Rs 6,230. He sold it for
Rs 7,155. How much profit did he make?

Solution It's easy!
Selling price of the mobile = When, I subtract buying price from
selling price, I can find profit!!

Buying price of the mobile =
Profit =

vedanta Excel in Mathematics - Book 4 38 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Fundamental Operations - I

b) Mr. Shrestha bought a bicycle for Rs 9,450. He sold it for Rs 10,300.
How much profit did he make?

12. a) There are 178 more girls than boys in a school. There are 456 boys in
the school.

(i) Find the number of girls in the school.

(ii) Find the total number of students in the school.

b) There are 178 more girls than boys in a school. There are 634 girls in
the school.

(i) Find the number of boys in the school.

(ii) Find the total number of students in the school.

c) Mrs. Subba paid Rs 1,250 more for a jacket than a trouser. She paid
Rs 1,785 for the trouser.

(i) Find the cost of the jacket.

(ii) Find the total cost of these two items.
Shopping Time!
13. Let's read the price tags of these items. Then answer the following

questions.

Rs 1675 Rs 2325 – Rs 2740 Rs 1185

Rs 1350

a) Find the total cost of a sweater and a jacket.

b) Find the total cost of a pair of shoes and a jean.

c) Find the total cost of a sweater, jacket and a set of school dresses.

d) By how much is the jacket more expensive than the sweater?

e) By how much is the jean cheaper than shoes?

f) You give Rs 1,500 to the shopkeeper to buy the sport shoes. How much
changes does the shopkeeper return to you?

39Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fundamental Operations - I

g) You paid only Rs 1,480 to buy a sweater. How much discount did you get on
this item?

h) Sunayana paid only Rs 2,575 to buy her school dresses. How much discount
did she get on this item?

i) If the shopkeeper gives you a discount of Rs 150 on the jean, how much do
you needed to pay for it?

j) If the shopkeeper gives a discount of Rs 275 on the jacket, how much does a
customer pay for it?

It's your time - Project Work!

14. Let's make groups of 5 students each and do a survey to find the number
of girls and boys in your school in primary level (grade 1 to 5). Write the
numbers in the table and answer the given questions.

Grades Number of girls Number of boys Total Numbers
1
2
3
4
5

Total

a) Find the total number of students in each class.
b) Find the total number of girls in the primary level.
c) Find the total number of boys in the primary level.
d) Find the total number of students in the primary level.
e) Which number is greater in each class girls or boys and by how many?
f) Which numbers is greater in the primary level girls or boys and by how

many?

15. Let's visit the available website (such as www.google.com) in your school
computer of in your computer or in your family member's mobile.

a) Search the live population of Nepal. Write the male population and
female population in numerals.

b) Rewrite the male and female population in words.

c) Find today's total population of Nepal.

?

vedanta Excel in Mathematics - Book 4 40 Approved by Curriculum Development CentreSanothimi, Bhaktapur

Unit Fundamental Operations - I

3 Fundamental Operations - II
(Multiplication and Division)

3.1 Multiplication - Looking back

Classwork - Exercise
1. Let's count how many times the groups of dots are. Then, multiply. Say

and write the total number of dots.

a) 5 times 2 dots = 5 × 2 =

b) times dots = × =

c) times dots = × =

d) times dots = × =

2. Let's draw as many dots in each box as to match the sums.

a) 3 × 2 = and 2 × 3 = =

b) 2 × 4 = and 4 × 2 = =

c) 4 × 3 = and 3 × 4 = =

Did you understand how are the meaning of 3 × 2 and 2 × 3 not same?

3. Let's have fun of addition and multiplication! Tell and write the correct
numbers in the blanks.

a) + + + + + 2 is added 6 times =6×2

b) + + + + is added times = ×

c) + + + is added times = ×

d) + + is added times = ×

Did you understand the relation between multiplication and addition?

Multiplication is the repeated addition.

41Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

FuFnudnadmamenetnatlaOl Opepreartaitoinosns- I- II

4. Let's write the correct numbers in the blank spaces.

a) 4 twos are = 4 × 2 = and 2 fours are = 2 × 4 =
=
b) 3 fours are = × = and 4 threes are = × =
c) 5 sixes are = × = and 6 fives are = × =
=
d) 7 eights are = × = and 8 sevens are = ×

e) 9 tens are = × = and 10 nines are = ×

5. Let's complete the multiplication tables of 2 to 10.

× 1 2 3 4 5 6 7 8 9 10

224

3 15

4 16 24

5 15 35

6 12 48

77 49

8 16 48

9 27 45

10 40

3.2 Multiplier, multiplicand, and product
Let's multiply 6 by 7 7 × 6 = 42
Here, 7 is the multiplier, 6 is the multiplicand, and 42 is the product.

Classwork - Exercise

1. Let's say and write the answer as quickly as possible.

a) In 4 × 6 = , multiplier is , multiplicand is , product is

b) In 6 × 8 = , multiplier is , multiplicand is , product is

c) In 9 × 7 = , multiplier is , multiplicand is , product is
42 Approved by Curriculum Development CentreSanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 4

FFuunnddaammeennttaallOOppeerraattioionnss--II

2. Let's say and write the multipliers and multiplicands as quickly as
possible.

a) 1 × 6 b) × c) ×

6×1 6 2×3 × 8 × × 10 ×

3×2 × ×

3. It's your time!
Let's write your multiplier and multiplicand to get the given product.

a) × = 12 b) × = 16 c) × = 18

d) × = 20 e) × = 24 f) × = 36

g) × = 40 h) × = 48 i) × = 50

3.3 Row and column multiplication

Let's investigate the idea about row and column multiplication from the
illustration given below.

C1 C2 C3 4 columns of 3 children
3 rows of 4 children
R1 R1, R2, R3, R4 are rows
4 rows of 3 children

R2 4 × 3 = 12 children

R3 C1, C2, C3 are columns

3 columns of 4 children
R4 3 × 4 = 12 children
4 × 3 = 12 children
or 3 × 4 = 12 children

Classwork - Exercise

Let's say and write the answers as quickly as possible.

1. a) Number of rows = b) Number of rows =

Number of columns = Number of columns =
43
vedanta Excel in Mathematics - Book 4



Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

FuFnudnadmamenetnatlaOl Opepreartaitoinosns- I- II c) How many children?

2. a) How many chairs? b) How many eggs?

× = chairs × = eggs × = children

3.4 Multiplication facts

Classwork - Exercise
1. Let's say and write the products as quickly as possible.

a) 5 × 1 = , 7 × 1 = , 10 × 1 = , 12 × 1 =

Fact I: The product of any number and 1 is the number itself.

b) 3 × 0 = , 6 × 0 = , 9 × 0 = , 14 × 0 =

Fact II: The product of any number and 0 (zero) is always 0.

c) 4 × 5 = 5 × 4 , 7 × 10 = 10 × 7 = , 9 × 6 = 6 × 9

Fact III: The product remains the same even if the order of multiplier and
multiplicand is interchanged.

3.5 Multiplication of 10, 100, 200, 3000, ... and so on
Let's investigate the idea of multiplication of the numbers ending with 0 (zeros).

5 times 10 is 50. 3 times 30 is 90.
5 × 10 = 50 3 × 30 = 90

2 times 100 is 200. 2 times 200 is 400.
2 × 200 = 400
2 × 100 = 200
40 × 100 = 4000

Similarly,

4 × 10 = 40, 40 × 10 = 400,

6 × 20 = 120, 60 × 20 = 1200, 60 × 200 = 12000

vedanta Excel in Mathematics - Book 4 44 Approved by Curriculum Development CentreSanothimi, Bhaktapur

FFuunnddaammeennttaallOOppeerraattioionnss--II

Classwork - Exercise

1. Let's say and write the products as quickly as possible.

a) 3 × 10 = 3 0 30 × 10 = 300 30 × 100 = 3000

b) 5 × 20 = 50 × 20 = 50 × 200 =

c) 5 × 30 = 50 × 30 = 50 × 300 =

d) 6 × 30 = 60 × 30 = 60 × 300 =
2. a) 2 × 10 = 2 × 100 = 2 × 1000 =
b) 4 × 20 = 4 × 200 = 4 × 2000 =
c) 6 × 40 = 6 × 400 = 6 × 4000 =
d) 8 × 60 = 8 × 600 = 8 × 6000 =

3.6 Multiplication of bigger numbers
Let's investigate the idea of multiplication of bigger numbers from these

illustrations.

Example 1. Multiply 32 by 4.

3 2 30 + 2 ×4= =
×4 × 4
128 120 + 8

3 tens + 2 ones 10 tens = 1 hundred + 2 tens + 8 ones 100 + 20 + 8



Example 2. Multiply 256 by 7.

256 200 + 50 + 6 34
×7 × 7
42 1400 + 350 + 42 256
350 = 1792 ×7
+1400 1792
1792

45Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

FuFnudnadmamenetnatlaOl pOepreartaiotinosn-sI- II

Example 3. Multiply 3475 by 25. Example 4. Multiply 4897 by 364.

3475 4897

× 2 5 20 + 5 × 3 6 4 300 + 60 + 4

17375 5 × 3475 19588 4 × 4897

+69500 20 × 3475 293820 60 × 4897

86875 +1469100 300 × 4897

1782508

Exercise - 3.1
Section A - Classwork

1. Let's say and write the multiplier and multiplicand. Then, find the
product.

a) b) c)

×= ×= ×=

2. Let's draw as many dots as to match the given sums. Then, say and
write the product as quickly as possible.

a) 5 × 3 = = dots

b) 3 × 5 = = dots

c) 4 × 6 = = dots

d) 6 × 4 = = dots

3. Let's multiply row by column (or column by row) and find the total
number of shapes.

a) b) c)

× = circles × = triangles × = squares
46
vedanta Excel in Mathematics - Book 4 Approved by Curriculum Development CentreSanothimi, Bhaktapur

FFuunnddaammeennttaallOOppeerraattiioonnss--III

4. Let's say and write the product as quickly as possible.

a) 4 × 600 = b) 30 × 70 = c) 200 × 80 =

d) 5 × 3000 = e) 500 × 90 = f) 100 × 100 =

5. Let's say and write how many rupees?

a) 50 numbers of Rs 5 notes = × Rs 5 = Rs

b) 100 numbers of Rs 10 notes = × =

c) 70 numbers of Rs 20 notes = × =

d) 10 numbers of Rs 50 notes = × =

e) 100 numbers of Rs 100 notes = × =

6. Let's say and write the answer as quickly as possible.

a) Cost of 1 pencil = Rs 7, cost of 8 pencils = 8 × Rs 7 = Rs

b) Cost of 1 kg of rice = Rs 80, cost of 10 kg of rice = × =

c) 1 meter (m) = 100 centimetres (cm), 5 m = × =

d) 1 km = 1000 m, 6 km = × =

e) 1 kg = 1000 gm, 9 kg = × =

f) 1 l = 1000 ml, 7 l = × =

g) 1 hour = 60 minutes, 3 hours = × =

h) 1 minute = 60 seconds, 4 minutes = × =

7. Let's jump forward as many steps and as many times as to match the

sums. Then, find the products.
a)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

6 times 3 = 6 × 3 =
b)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

times =×=

47Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

FuFnudnadmamenetnatlaOl Opepreartaitoinosns- I- II

c)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

times =×=

Section B
Let's rewrite these sums and calculate the products.

8. a) 8 × 20 b) 80 × 20 c) 70 × 30 d) 70 × 300 e) 600 × 40

f) 110 × 10 g) 110 × 200 h) 120 × 50 i) 150 × 30 j) 240 × 20

9. a) 24 × 8 b) 46 × 7 c) 85 × 9 d) 18 × 12

e) 36 × 25 f) 54 × 37 g) 92 × 44 h) 116 × 15

i) 225 × 27 j) 408 × 32 k) 560 × 56 l) 2375 × 236

Let's read these problems carefully and solve them.

10. a) The cost of 1 kg of apples is Rs 125. Find the cost of 10 kg of apples.
b) The cost of 1 l of petrol is Rs 108. Find the cost of 15 l of petrol.
c) The cost of a gas cylinder is Rs 1425. Find the cost of 4 gas cylinders.

11. a) There are 30 eggs in a crate of eggs. Find the number of eggs in 10 crates.
b) 1 dozen of pencils is equal to 12 pencils. How many pencils are there in

12 dozens of pencils?

c) A box has 20 packets of table tennis balls and each packet contains a
dozen of balls. How many balls are there in the box?

d) There are 32 students in grade IV. Each of them donated Rs 150 to the
flood and landslide victim people. How much was the total of donation
amount.

e) The monthly salary of Mrs. Tamang is Rs 16,250. Calculate her salary in
1 year.

12. a) 1 quintal of weight is equal to 100 kg. How many kilograms (kg) are
there in 50 quintals of weight?

b) 1 metric ton of weight is equal to 1000 kg. How many kilograms are
there in 7 metric tons of weight?

c) A bottle can hold 630 millilitres (ml) of liquid. How much liquid do
18 such bottles hold?

vedanta Excel in Mathematics - Book 4 48 Approved by Curriculum Development CentreSanothimi, Bhaktapur