Math 4

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


Excel in
vedanta



MATHEMATICS








Book 4
Book 4






Author
Hukum Pd. Dahal







Editor

Tara Bahadur Magar












vedanta

Vedanta Publication (P) Ltd.

]
jbfGt klAns;g k|f= ln=
]
Vanasthali, Kathmandu, Nepal
+977-01-4982404, 01-4962082
[email protected]

www.vedantapublication.com.np

Excel in
vedanta

Mathematics



Book 4
Book 4










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.)















Published by:

Vedanta Publication (P) Ltd.
jbfGt 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.


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 5 - 25
1.1 Counting and writing numbers - Looking back, 1.2 Number, numeral and
digit, 1.3 Hindu - Arabic number system, 1.4 Place and Place value and Face value,
1.5 Expanded form of numbers, 1.6 Order of numbers, 1.7 6-digit numerals,
1.8 7-digit numerals, 1.9 8 and 9-digit numerals, 1.10 International place
value system, 1.11 Use of commas, 1.12 The greatest and the least numbers,
1.13 The greatest and the least numbers formed by given digits, 1.14 Rounding off
numbers - Estimation, 1.15 Roman number system, 1.16 Conversion of Roman
numerals to Hindu-Arabic numerals, 1.17 Conversion of Hindu-Arabic numerals
to Roman numerals
2 Whole Numbers 26 - 29
2.1 Natural numbers - The counting numbers, 2.2 Whole numbers, 2.3 Odd and
even numbers, 2.4 Prime and Composite numbers
3 Fundamental Operations 30 - 66
3.1 Addition and Subtraction - Looking back , 3.2 Relation between addition
and subtraction, 3.3 Multiplication - Looking back, 3.4 Multiplier, multiplicand
and product, 3.5 Row and column multiplication, 3.6 Multiplication facts,
3.7. Multiplication of 10, 100, 200, 3000, ... and so on, 3.8 Multiplication of
bigger numbers, 3.9 Division - Looking back, 3.10 Dividend, divisor, quotient
and remainder, 3.11 Division as repeated subtraction, 3.12 Relation between
multiplication and division, 3.13 Division by row and column, 3.14 Dividing tens,
hundreds, thousands, ... by 10, 20, 300, 4000, ..., 3.15 Division facts, 3.16 Division
of bigger numbers, 3.17 Simpli ication - A single answer of a mixed operation,
3.18 Order of operations
4 Factors and Multiples 67 - 75
4.1 Divisibility Test, 4.2 Factors and multiples, 4.3 Prime Factors, 4.4 Process of
inding prime factors, 4.5 Highest Common Factor (H. C. F.), 4.6 Process of inding
multiples of a given number, 4.7 Lowest Common Multiple (L. C. M.)
5 Fraction 76 - 100
5.1 Fraction - Looking back, 5.2 Equivalent fractions, 5.3 Process of inding
a fraction equivalent to the given fraction, 5.4 Test of equivalent fractions,
5.5 Reducing fractions to their lowest terms, 5.6 Like and unlike fractions,
5.7 Comparison of like fractions, 5.8 Conversion of unlike fractions into like
fractions, 5.9 Comparison of unlike fractions, 5.10 Proper and improper
fractions, 5.11 Mixed numbers, 5.12 Process of changing improper fraction to
mixed number, 5.13 Process of changing mixed number to improper fraction,
5.14 Addition and subtraction of like fractions, 5.15 Addition and subtraction of
unlike fractions, 5.16 Multiplication of fractions, 5.17 To ind the value of fraction
of a number in a collection
6 Decimal and Percent 101 - 122
6.1 Tenths and hundredths - Looking back, 6.2 Thousandths, 6.3 Mixed
number and decimal, 6.4 Place and place value of decimal numbers,
6.5 Comparison of decimal numbers, 6.6 Conversion of a decimal number into
a fraction, 6.7 Conversion of a fraction into a decimal number, 6.8 Addition
and subtraction of decimal numbers, 6.9 Multiplication of decimal numbers,
6.10 Use of decimals, 6.11 Percent - How many out of 100?, 6.12 Conversion of
fraction into percent, 6.13 Conversion of percent into fraction, 6.14 To ind the
value of the given percent of a quantity

7 Unitary Method, Buying, Selling and Billing 123 - 131
7.1 Unitary Method - unit number, unit value, more number, more value,
7.2 Rate of cost, 7.3 Buying and selling, 7.4 Pro it and loss, 7.5 Billing
8 Time and Money 132 - 147
8.1 Telling time - Looking back, 8.2 24 - hour clock system, 8.3 The calendar -
Days, weeks, months and year, 8.4 Conversion of units of time, 8.5 Addition
and subtraction of time, 8.6 Money, 8.7 Conversion between rupees and paisa,
8.8 Addition and subtraction of money
9 Algebra 148 - 172
9.1 Letters and numbers - Looking back, 9.2 Constant and variable, 9.3 Operation
on constant and variable, 9.4 Algebraic term and expression, 9.5 Coef icient
and base of algebraic term , 9.6 Evaluation of terms or expressions, 9.7 Like
and unlike terms, 9.8 Addition and subtraction of like terms, 9.9 Addition and
subtraction of unlike terms, 9.10 Addition and subtraction of expressions,
9.11 Open mathematical sentence, 9.12 Equation, 9.13 Solving equation,
9.14 Process of solving equation, 9.15 Use of equation
10 Measurement 173 - 198
10.1 Measurement of length - Looking back, 10.2 Standard units of length,
10.3 Conversion of units of length, 10.4 Addition and subtraction of lengths,
10.5 Map and distance, 10.6 Measurement of weight, 10.7 Conversion of units
of weight, 10.8 Addition and subtraction of weights, 10.9 Measurement of
capacity, 10.10 Conversion of units of capacity, 10.11 Addition and subtraction
of capacities
11 Perimeter, Area and Volume 199 - 210
11.1 Perimeter - The distance all the round, 11.2 Perimeter of rectangle and
square, 11.3 Area - Space covered by a surface, 11.4 Area of rectangle and
square, 11.5 Volume - space occupied by an object, 11.6 Volume of cube,
11.7 Volume of cuboid
12 Geometry 211 - 230
12.1 Point, line and line segment - Looking back, 12.2 Measuring the length
of line segments, 12.3 Angle - Looking back, 12.4 Measurement of angles,
12.5 Construction of angles, 12.6 Types of angles by their sizes, 12.7 Plane
igures (or shapes), 12.8 Triangle, 12.9 Types of triangles by sides, 12.10 Types
of triangles by angles, 12.11 Quadrilaterals, 12.12 Circle, 12.13 Solid igures (or
shapes)
13 Statistics 231 - 240
13.1 Bar graph - Looking back, 13.2 Measurement of temperature,
13.3 Ordered pairs
14 Set 241 - 245
14.1 Set - A collection of objects - Looking back, 14.2 Set - A well-de ined
collection, 14.3 Methods of writing sets
Answers 246- 257
Evaluation Model 258- 260

Unit Number System
1





1.1 Counting and writing numbers - Looking back

Classwork - Exercise
1. At first, let's estimate the number. Then count and find the actual
number.


(a) Guess, how many fruits are there on the tree?
Now, count the number of fruits on the tree.
The actual number of fruits is

Was your guess close to the actual number?


(b) Guess, how many students are there?

Now, count the number of students.
The actual number of students is

Was your guess close to the actual number?

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

(a) Rs

rupees.

(b) Rs
rupees.

(c) Rs

rupees.



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










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



(a) Calculator:

(b) Watch:

(c) Mobile:


(d) Headphone:

(e) Sound box:
4. Let's read these interesting facts. Rewrite the number names in
numerals.


(a) The highest peak of the world 'Sagarmatha' is eight thousand eight

hundred forty-eight 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 per hour.
5. Let's tell and write how many digits there are in these numerals.


(a) 70 is a digit numeral. (b) 306 is a digit numeral.

(c) 5080 is a digit numeral. (d) 73014 is a digit numeral.
6. Let's listen to your teacher! Write 4 digit numerals from your teacher
as quickly as possible.





7. It's your time! Let's write any numerals, and then rewrite number names.


(a) A 2-digit numeral

(b) A 3-digit numeral

(c) A 4-digit numeral


vedanta Excel in Mathematics - Book 4 6 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Number System


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

(a)
H T O 101
1 0 1 One hundred one




(b)
H T O





(c)
H T O





(d)

H T O




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



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

Number System




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.

Devanagari number system is also similar to the Hindu-Arabic number
system. But it has a bit different digits.

Hindu-Arabic digits 0 1 2 3 4 5 6 7 8 9
Devanagari digits ) ! @ # $ % ^ & * (
Devanagari number names z"Go Ps b'O{ tLg rf/ kfFr 5 ;ft cf7 gf}+

1.4 Place, Place value, and Face value

Let's take a number 27.
2 tens = 2 × 10 = 20
In this number, 2 is at tens place and 7 is at
7 ones = 7 × 1 = 7
ones place. The place value of 2 is 20 and the
place value of 7 is 7.
20 blocks 7 blocks
2 7
Ones place = 7 × 1 = 7 -Pssf] :yfgdf & Ö &_
Tens place = 2 × 10 = 20 -bzsf] :yfgdf @ Ö @)_

Let's take another number 213.
2 hundreds = 2 × 100 = 200
In this number, 2 is at hundreds place; 1 ten = 1 × 10 = 10
1 is at tens place; and 3 is at ones
3 ones
place. The place value of 2 is 200; the
place value of 1 is 10; and the place = 3 × 1 = 3

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

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

Number System


2 1 3
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.


3 4 0 5
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 #)))_

1 6 0 7 2
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 =

= 4 × 10 + 5 × 1
4 × 10 5 × 1



236 =

= 2 × 100 + 3 × 10 + 6 × 1
2 × 100 3 × 10 6 × 1




3104 =


= 3 × 1000 + 1 × 100 + 4 × 1
3 × 1000 1 × 100 4 × 1
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Number System


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


Exercise - 1.1

Section A - Classwork

1. Let's tell 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] rfF8f] egf}+ / n]vf}+ x} t .

-s_ krf;L ;+Vofgfdsf] c+u|]hL ;+Vofgfd / ;+Vof slt x'G5 <
-v_ &%^$ nfO{ c+u|]hL ;+Vofdf n]v .

-u_ 9328 nfO{ g]kfnL ;+Vofgfddf n]v .

-3_ 8140 nfO{ g]kfnL ;+Vofdf n]v .

-ª_ ^#%* df ;osf] :yfgdf s'g c+s 5 / To;sf] :yfgdfg slt x'G5 <

-r_ %@(# df % s'g :yfgdf 5 / o;sf] :yfgdfg slt x'G5 <

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Number System


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

(a) (b)







(c) (d)






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

T O H T 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
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Number System

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.
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

1.6 Six-digit numerals

Classwork - Exercise

1. Let's tell 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) How many digits are there in 90000 (Ninety thousand)?
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 hundred thousand = 1 lakh ⇒ 100000

Two hundred thousand = 2 lakh ⇒ 200000 and so on.
100000, 200000, 300000, ... 900000 are 6-digit numerals.


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Number System

1.7 Seven-digit numerals

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

1.8 Eight and Nine-digit numerals


Classwork - Exercise

1. Let's tell 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 tell and write the missing crores.

a) 1 crore, 2 crore, , , 5 crore

b) 6 crore, , , 9 crore, then

Of course, after 9 crore (90000000), it comes 10 crore (100000000).

100000000 = ten crore is a 9-digit numeral.

Now, 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
4 7 9 1 0 3 8 thirty-eight.

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Number System


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.


d) 703906517
T-C C T-L L T-th Th H T O Seventy crore thirty-nine lakh six
7 0 3 9 0 6 5 1 7 thousand five hundred seventeen.

1.9 International place value system

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

Nepali place International place Place values Number of digits
names names

Ones Ones 1 One
Tens Tens 10 Two
Hundreds Hundreds 100 Three
Thousands Thousands 1000 Four

Ten-thousands Ten-thousands 10000 Five
Lakhs Hundred-thousands 100000 Six
Ten-lakhs Millions 1000000 Seven
Crores Ten-millions 10000000 Eight

Ten-crores Hundred-millions 100000000 Nine

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. Tell and write the answers as quickly as
possible.



a) How many hundred-thousands are there in 1 lakh?

b) How many ten-lakhs are there in 2 million?

c) How many ten-millions are there in 2 crore


d) How many ten-crores are there in hundred-millions?


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Number System

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.

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
International systems are the same.
70000 70, 000


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


700000 700,000 In International system, each group of 3-digits greater
than hundreds place is separated by commas

Use of commas in Nepali system Use of commas in International system

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

3,25,00,000 32,500,000

Three crore twenty-five lakh Thirty-two million five hundred 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

517382490


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Approved 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
The least 9-digit number The greatest 9-digit number

2. Let's tell 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.

d) 999999999 is the number of digits.

1.12 The greatest and the least numbers formed by given digits


Classwork - Exercise

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


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

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

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

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

h) 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.

2. 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?
3. 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 tell 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
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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 tell 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 d) 154409150

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4. Let's write these numerals in place value tables of International system.
Then, write the number names.
a) 157320 b) 3271068 c) 21049355 d) 460032180

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 f) 430085027

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.

a) 257410 b) 4689032 c) 13720548 d) 301847900
7. Let's find how many millions in 1 million = 1000000
= 10 lakh!
a) 10 lakh b) 20 lakh c) 30 lakh
1 crore = 10000000
d) 40 lakh e) 50 lakh f) 90 lakh = 10 million!

8. Let's find how many millions in 10 million = 10000000
= 1 crore!
a) 1 crore b) 2 crore c) 3 crore
d) 5 crore e) 8 crore f) 10 crore

9. Let's find how many lakhs in

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

a) 10 million b) 40 million c) 70 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 three crore two lakhs sixty thousand.

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.
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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 one hundred twenty 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
14. Its your time -Project work!


a) Write one numeral for each of 6-digit, 8-digit, and 9-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...
9-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.


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b) Now round off 26 to the nearest tens.
20 21 22 23 24 25 26 27 28 29 30
26 is close to 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
50 51 52 53 54 55 56 57 58 59 60
c) Rounding off 53 is

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

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


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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!
Rounding off 1, 2, 3 and 4 at ones
The number in round figure is 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 tens!!
and Butwal is 262 km.
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.
The rule is very simple!
a) The distance between Kathmandu
Rounding off 1, 2 3 and 4 at
and Pathari is 491 km. The distance in tens place is always to the
round figure is 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
is always to the upper
c) The price of a mobile is Rs 15,850. The
hundreds!!
price in round figure is

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.

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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 I V X 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.
1.15 Conversion of Roman numerals to Hindu-Arabic numerals


Let's read these rules and examples. Then, learn to convert Roman
numerals into Hindu-Arabic numerals.
Rule 1

We can repeat the symbols I, X, C and M only upto three times. The
repetition of these symbols means addition. The symbols V, L and D are
never be repeated in a number.
Examples

a) II = 1 + 1 = 2 b) XXX = 10 + 10 + 10 = 30

c) LXXV = 50 + 10 + 10 + 5 = 75 d) DCCX = 500 + 100 + 100 + 10 = 710
Rule 2

If a smaller symbol comes before a larger one, the net value is the difference
of values of the symbols.
Examples

a) IV = 5 – 1 = 4 b) IX = 10 – 1 = 9

c) XL = 50 – 10 = 40 d) XC = 100 – 10 = 90

e) CD = 500 – 100 = 400 f) CM = 1000 – 100 = 900
Rule 3


If a smaller symbol comes after a larger one, the net values is the addition
of the values of the symbols.
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Examples

a) VI = 5 + 1 = 6 b) XVIII = 10 + 5 + 3 = 18

c) LXVII = 50 + 10 + 5 + 2 = 67 d) CCLV = 100 + 100 + 50 + 5 = 255

1.16 Conversion of Hindu-Arabic numerals to Roman numerals

Let's recall the Roman symbols upto 10. In the case of Hindu-Arabic
numerals greater than 10, write them in the expanded forms and convert
them into Roman numerals.

Examples

a) 19 = 10 + 9 = XIX b) 28 = 20 + 8 = XXVIII

c) 39 = 30 + 9 = XXXIX d) 40 = 50 – 10 = XL

e) 49 = 40 + 9 = XLIX f) 86 = 50 + 30 + 6 = LXXXVI

g) 90 = 100 – 10 = XC h) 93 = 90 + 3 = XCIII

i) 389 = 300 + 80 + 9 = CCCLXXXIX

j) 765 = 500 + 200 + 50 + 10 + 5 = DCCLXV

k) 999 = 900 + 90 + 9 = CMXCIX

l) 2145 = 2000 + 100 + 40 + 5 = MMCXLV



Exercise - 1.4

Section A - Classwork


Let's tell 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




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


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


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


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


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

Section B

3. Let's convert these Roman numerals into Hindu-Arabic numerals.

a) XIX b) XXVII c) XXXIX d) XLIV

e) XLIX f) LXXVIII g) XCIX h) CCXLVI

i) CDXXIX j) DCCCLXV k) CMXCIV l) MMCCXC

4. Let's convert these Hindu-Arabic numerals into Roman numerals.

a) 18 b) 29 c) 38 d) 45 e) 67

f) 89 g) 96 h) 240 i) 392 j) 454


k) 599 l) 643 m) 975 n) 1504 o) 2390
It's your time - Project work!


5. Let's visit the available website such as www.google.com or
www.youtube.com in your school computer or in your computer or in
your family member's mobile.


a) Search and collect the important information about the history of the
Roman numerals.

b) Search and collect the meaning of the symbols of Roman numerals.

c) Search and collect the use of Roman numerals in the modern time.



?




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Whole Numbers Whole Numbers

Unit Whole Numbers
2




2.1 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.
2.2 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 tell 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,
crore, ten-crore, ...
e) What is the least natural number?
I cannot count. It is
f) What is the least whole number? infinite!

g) What is the greatest whole number?

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h) Are all natural numbers whole numbers?

i) Are all whole numbers natural numbers?

2.3 Odd and even numbers


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

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.
2.4 Prime and Composite numbers


Let's have some discussions on these questions.

a) Which numbers can divide 2 exactly,
2 ÷ 1 = 2 and 2 ÷ 2 = 1
or, without a remainder?
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3 ÷ 1 = 3 and 3 ÷ 3 = 1
b) Which numbers can divide 3 exactly?
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
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.
4 ÷ 1 = 4, 4 ÷ 4 = 1, 4 ÷ 2 = 2
a) Which numbers can divide 4 exactly?
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 - 2.1
Section A - Classwork

1. Let's tell 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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Section B

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


a) 141, 143, , , , 151. I investigated the rule!
The next odd number to
b) 265, , , , , 275. 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!
The next even number to
b) 404, , , , , 414.
302 is 302 + 2 = 304
c) 796, , , , , 806.
It's your time - Project work!

5. a) Write the natural numbers upto 100. List the odd, even, prime, and
composite numbers separately.
3 + 5 = 8 (even)
b) Let's take any three pairs of odd numbers and 1 + 9 = 10 (even)
3 × 5 = 15 (odd)
perform addition and multiplication between
7 × 9 = 63 (odd)
each pair. Discuss about the results with your
friends and investigate the facts. 2 + 4 = 6 (even)
8 + 6 = 14 (even)
c) Let's take any three pairs of even numbers and 4 × 6 = 24 (even)
perform addition and multiplication between 8 × 2 = 16 (even)
each pair. Discuss about the results with your
friends and investigate the facts.



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



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
?

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Unit Fundamental Operations
3





3.1 Addition and Subtraction - Looking back


Classwork - Exercise

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

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


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

(iv) 50 + 20 = (v) 60 +30 = (vi) 70 + 20 =

b) (i) 10 + 16 = (ii) 20 + 18 = (iii) 14 + 30 =

(iv) 27 + 30 = (v) 40 + 25 = (vi) 36 + 50 =

c) (i) 30 – 20 = (ii) 40 – 10 = (iii) 70 – 30 =

(iv) 60 – 40 = (v) 80 – 50 = (vi) 90 – 20 =

d) (i) 27 – 10 = (ii) 45 – 30 = (iii) 58 – 20 =


(iv) 64 – 40 = (v) 86 – 50 = (vi) 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

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


a) 1 + 9 + 7 = b) 8 + 6 + 2 = c) 9 + 3 + 7 =

d) 15 + 4 + 5 = e) 14 + 6 + 7 = f) 3 + 12 + 8 =


g) 14 + 2 = h) 25 + 3 = i) 32 + 34 =

j) 25 – 13 = k) 36 – 14 = l) 44 – 21 =

m) 53 – 22 = n) 67 – 35 = o) 78 – 55 =

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


a) 2 + 7 + 8 = + 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) + + 4) =

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

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


j) 33 + 32 = (30 + 30) + ( + ) =
4. Let's write the missing numbers and then subtract as quickly as
possible.



a) 27 – 14 = (27 – 10) – =

b) 36 – 13 = (36 – ) – 3 =

c) 45 – 21 = (45 – ) – 1 =


d) 28 – 12 = (20 – 10) + (8 – ) =

e) 27 – 15 = (20 – ) + (7 – 5) =

f) 39 – 26 = (30 – 20) + ( – ) =
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3.2 Relation between addition and subtraction

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

1. Let's tell 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
2. Let's listen to your teacher and perform the following operations.

a) + = Then – = and – =


b) + = Then – = and – =


c) + = Then – = and – =

3. 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!

4. 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 – =

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5. 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!


6. 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

7. 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

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

b) By how much is 35 kg more than 25 kg?
Adding and regrouping!

Let's add and regroup into the higher places.


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

b) 8 tens + 6 tens = =

c) 9 tens + 8 tens = =

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

b) 7 hundreds + 6 hundreds = =


c) 5 hundreds + 9 hundreds = =

Exercise - 3.1

Section A - Classwork
1. Let's tell 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

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 tell and write the missing numbers.

a) b)


27

17 10 13
6 11 7 9 8

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

a) b) c)
9 9 11


6 10 8

3 10 5 5 7

Sum is 18 Sum is 24 Sum is 30
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10
4. a) The numbers in the circles have been added in pairs
15 17
and the sum of each pair is in the square between the
circles. Complete these puzzles. 5 12 7

4 14 15


20 24


8 7 4 3



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


+ 6 + 10 + 15


4 10 16 5

11 12 8 15 14 17


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 =
35
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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 =

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) b) c)
320 407 712
– 145 + 145 – 178 + 178 – 325 + 325


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


Number of girls =
Number of boys = +

Total number of students =

Hence, the total number of students in the school is


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


Population of men =
Population of women =

Population of children =

Total population =

Hence, the population of the village is



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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

Selling price of the mobile =
Buying price of the mobile =

Profit =
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.
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Shopping Time!

13. Let's read the price tags of these items. Then answer the following
questions.










Rs 1675
Rs 2325 Rs 1350 Rs 2740 Rs 1185

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?
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 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.
15. 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.
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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?
3.3 Multiplication - Looking back

Classwork - Exercise

1. Let's count how many times the groups of dots are. Then, multiply. Tell
and write the total number of dots.
5 times 2 5 × 2
a) dots = =


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 the difference between 3 × 2 and 2 × 3?
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3. Let's have fun of addition and multiplication! Tell and write the correct
numbers in the blanks.


2 is added 6 times.
a)
+
+
+
+
+
+ + + + + = 6 × 2 =
is added times
b)
+
+
+
+
+ + + + = × =
is added times
c)
+
+
+
+ + + = × =
d) is added times
+
+
+ + + = × =
Did you understand the relation between multiplication and addition?
Multiplication is the repeated addition.
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
2 2 4
3 15

4 16 24
5 15 35
6 12 48
7 7 49

8 16 48
9 27 45
10 40

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3.4 Multiplier, multiplicand, and product

Let's multiply 6 and 7 7 × 6 = 42

Here, 7 is the multiplier, 6 is the multiplicand, and 42 is the product.


Classwork - Exercise


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

24 4 6 , product is 24
a) In 4 × 6 = , multiplier is , multiplicand is


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



c) In 9 × 7 = , multiplier is , multiplicand is , product is


d) In 3 × 2 = 6, 6 is , 2 is , 3 is



e) In 10 × 5 = 50, 5 is , 10 is , 50 is

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


a) b) c)
1 × 6 × ×
6 8 10
6 × 1 2 × 3 × × × ×

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


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3.5 Row and column multiplication
Let's investigate the idea about row and column multiplication from the

illustration given below.
C1 C2 C3
5 columns of 3 children
R1 R1, R2, R3, R4, R5 are rows
5 rows of 3 children
R2
5 × 3 = 15 children

R3 3 rows of 5 children
C1, C2, C3 are columns
R4
3 columns of 5 children 5 × 3 = 15 children
3 × 5 = 15 children
R5 or 3 × 5 = 15 children

Classwork - Exercise

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


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

Number of columns = Number of columns =




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














× = chairs × = eggs × = children
3.6 Multiplication facts

Classwork - Exercise

1. Let's tell 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.

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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.
3.7. 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 × 100 = 200 2 × 200 = 400

Similarly,


4 × 10 = 40, 40 × 10 = 400, 40 × 100 = 4000



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


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


a) 3 × 10 = 30 × 10 = 30 × 100 =


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 =
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3.8 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 3 4
× 7
× 7 2 5 6
42
1400 + 350 + 42 × 7
350
= 1792 1792
+1400
1792
Example 3. Multiply 3475 by 25. Example 4. Multiply 4897 by 364.


3 4 7 5 4 8 9 7
× 2 5 20 + 5 × 3 6 4 300 + 60 + 4
17375 5 × 3475 19588 4 × 4897
+69500 20 × 3475 293820 60 × 4897
1469100
86875 + 300 × 4897
1782508
Exercise - 3.2
Section A - Classwork

1. Let's tell 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 tell and
write the product as quickly as possible.


a) 5 × 3 = = dots

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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

4. Let's tell 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 tell 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 tell and write the answer as quickly as possible.

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

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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 = × =
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.

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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?

d) A packet of 500 ml of milk gives 17 g of protein. If you drink 18 packets
of milk in a month, how much protein do you get?

e) We get roughly 72 calories from 1 boiled egg. How much calories do we
get from 30 boiled eggs?
f) A water tanker full of water carries 7,500 litres of water in one trip.
How much water does it carry in 20 trips?

g) The distance between your home and your school is 8 km. How many
kilometres do you travel in 15 days?
h) The distance between place A and place B is 32 km. A bus carries
passengers from A to B and B to A 7/7 times everyday. How many
kilometres does the bus travel in a day?

i) A bus can travel 55 km in 1 hour. How many kilometres does it travel in
24 hours?

13. a) There are 7 days in one week. How many days are there in 52 weeks?
b) There are 12 months in one year. How many months are there in
12 years?

c) There are 365 days in one year. How many days are there in 15 years?
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