Vedanta mathematics _Book - 4

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 are
Was your guessing close to the actual number?

(b) Guess, how many students are there?
Now, count the number of students.
The actual number of students are
Was your guessing 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

5 vedanta Excel in Mathematics - Book 4

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's depth is about
ten thousand nine hundred ninety-four metres.

(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 are there 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 her/his 4 digit numerals as quickly
as possible.


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

(a) A 2-digit numeral
(b) A 3-digit numeral
(c) A 4-digit numeral

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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)
HTO

(c)
HTO

(d)
HTO

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
names.

(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

7 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 67 8 9
Devanagari digits
Devanagari number names ) ! @ # $ % ^& * (
;'Go Ps b'O{ tLg rf/ kfrF 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.

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. 2 hundreds = 2 × 100 = 200
1 ten = 1 × 10 = 10
In this number, 2 is at hundreds place
1 is at tens place and 3 is at ones 3 ones
place. The place value of 2 is 200, the =3×1=3
place value of 1 is 10 and the place
value of 3 is 3. 200 blocks 10 blocks 3 blocks

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Number System

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 #)))_

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 =

= 4 × 10 + 5 × 1

4 × 10 5 × 1

236 = = 2 × 100 + 3 × 10 + 6 × 1

2 × 100 3 × 10 6 × 1

3104 = 1 × 100 = 3 × 1000 + 1 × 100 + 4 × 1

3 × 1000 9 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 kZ| gx?sf] pQ/ hlt;Sbf] rfF8f] egf+} / n]vf}+ x} t .
-s_ krf;L ;V+ ofgfdsf] cu+ ]|hL ;+Vofgfd / ;V+ of slt xG' 5 <

-v_ &%^$ nfO{ c+uh]| L ;V+ ofdf nv] .

-u_ 9328 nfO{ gk] fnL ;+Vofgfddf n]v .

-3_ 8140 nfO{ gk] fnL ;V+ ofdf n]v .

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

-r_ %@(# df % sg' :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.

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

11 vedanta Excel in Mathematics - Book 4

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 6-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) 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 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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1.7 7-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 8 and 9-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.


13 vedanta Excel in Mathematics - Book 4

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
Tens Ones 1 One
Hundreds
Thousands Tens 10 Two
Ten-thousands
Lakhs Hundreds 100 Three
Ten-lakhs
Crores Thousands 1000 Four
Ten-crores
Ten-thousands 10000 Five

Hundred-thousands 100000 Six

Millions 1000000 Seven

Ten-millions 10000000 Eight

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 and 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
70000 70, 000 International systems are the same.

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
15327 system System

804930

6831400

32495600

517382490

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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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Number System

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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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 d) 460032180

5. Rewrite these numerals using commas in Nepali as well as in International
system. The 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
f) 90 lakh 1 crore = 10000000
d) 40 lakh e) 50 lakh = 10 million!
c) 3 crore
8. Let's find how many millions in 10 million = 10000000
= 1 crore!
a) 1 crore b) 2 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 one hundred
eighty-one square kilometres.

19 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 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 to 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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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

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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
is always to the upper
c) The price of a mobile is Rs 15,850. The
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.

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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.

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.

23 vedanta Excel in Mathematics - Book 4

Number System

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

vedanta Excel in Mathematics - Book 4 24

Number System

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 to 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.

?

25 vedanta Excel in Mathematics - Book 4

Whole Numbers Whole Numbers

Unit

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) also. 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,
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?

vedanta Excel in Mathematics - Book 4 26

Whole Numbers

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

a) Does 1 pencil make a pair? make two pairs and one
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.

2.4 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?

27 vedanta Excel in Mathematics - Book 4

Whole Numbers

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

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

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

vedanta Excel in Mathematics - Book 4 28

Whole Numbers

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

?

29 vedanta Excel in Mathematics - Book 4

Fundamental Operations Fundamental Operations

Unit

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 =
(v) 80 – 50 = (vi) 90 – 20 =
(iv) 60 – 40 = (ii) 45 – 30 = (iii) 58 – 20 =
d) (i) 27 – 10 = (v) 86 – 50 = (vi) 99 – 60 =

(iv) 64 – 40 =

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

vedanta Excel in Mathematics - Book 4 30

Fundamental Operations

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 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 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) + ( – ) =

31 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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 – =

vedanta Excel in Mathematics - Book 4 32

Fundamental Operations

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

8+ = 18 – 25 = 75
–
+
– 20 =
+5 =

==

13 + 32 =

Quiz Time!

6. a) The sum of two numbers is 12 and the difference 10 + 2 and 10 – 2, no!

is 2. The numbers are and 9 + 3 and 9 – 3, no!
8 + 4 and 8 – 4, no!

b) The difference of two number is 5 and their 7 + 5 and 7 – 5, yes!

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
b) What should be subtracted from 20 to get 15? is less than Rs 50
9. 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?

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 = =

33 vedanta Excel in Mathematics - Book 4

Fundamental Operations

11. a) 5 tens + 7 tens = tens = hundred and tens
hundreds
b) 8 tens + 6 tens = = thousands and
=
c) 9 tens + 8 tens = = =

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

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)

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

vedanta Excel in Mathematics - Book 4 34

Fundamental Operations

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

4 14 15

20 24

8 7 43

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 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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) 320 b) 407 c) 712

– 145 + 145 – 178 + 178 – 325 + 325

vedanta Excel in Mathematics - Book 4 36

Fundamental Operations

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

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

37 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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/he bought 165 kg of avocados,
180 kg of oranges and the rest is apples. How many kilograms of apples
did the fruit seller buy?

11. a) A shopkeeper bought a mobile for Rs 6,230. She/he sold it for
Rs 7,155. How much profit did she/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 th–an 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.

vedanta Excel in Mathematics - Book 4 38

Fundamental Operations

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 5/5 students 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.

39 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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.

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 the difference between 3 × 2 and 2 × 3?

vedanta Excel in Mathematics - Book 4 40

Fundamental Operations

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

a) + + + + + 2 is added 6 times. ++ =6×2=
b) + + + + +++ times ×=
is added +=

+++

c) + + + is added times =
d) + + +++ =× =
times
is added =×
+++

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

224

3 15

4 16 24

5 15 35

6 12 48

77 49

8 16 48

9 27 45

10 40

41 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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.

a) In 4 × 6 = 2 4, multiplier is 4 , multiplicand is 6 , product is 24

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) 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

vedanta Excel in Mathematics - Book 4 42

Fundamental Operations

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 3 rows of 5 children

5 rows of 3 children
R2 5 × 3 = 15 children

R3

R4 C1, C2, C3 are columns 5 × 3 = 15 children
3 columns of 5 children

R5 3 × 5 = 15 children 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 =
c) How many children?




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

× = 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.

43 vedanta Excel in Mathematics - Book 4

Fundamental Operations

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

40 × 100 = 4000
Similarly,

4 × 10 = 40, 40 × 10 = 400,

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 =

vedanta Excel in Mathematics - Book 4 44

Fundamental Operations

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 34
×7 × 7
42 1400 + 350 + 42 256
350 = 1792 ×7
+1400 1792

1792

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 - 3.2
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 forwards 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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14. a) In a school assembly, students are arranged in 16 rows with 25 students
in each row. How many students are there in the assembly?

b) In a hall, chairs are arranged in 15 columns with 18 chairs in each
column. How many chairs are there in the hall?

It's your time - Project work!

15. a) A 8-10 year old child needs to drink roughly 1500 ml of water each day.
Estimate, how many millilitres of water do you drink in 1 day and in 1
week?

b) How many grams (or kilograms) of vegetables do your family (or your
hostel) consume in 1 day? Discuss with your family members (or with
hostel incharge) and estimate the quantities of vegetables consumed
in 30 days.

C) How many grams (or kilograms) of rice do your family (or your hostel)
consume in 1 day? Discuss with your family members (or hostel
incharge) and estimate the quantities of rice consumed in 30 days.

16. a) Let's draw as many circles as the number of rows equally in each row
in a chart paper. Then find the number of circles by multiplication.

b) Let's draw as many circles as the number of columns equally in
each column in a chart paper. Then find the number of circles by
multiplication.

3.9 Division - Looking back

Let's investigate a few interesting ideas about division from these
illustrations.

When 6 pencils are shared between 2 children, how many pencils will each
share?

6 ÷ 2 = 3 Each will share 3 pencils.
How many twos are there in 6?
6 ÷ 2 = 3 There are 3 twos in 6.

Classwork - Exercise

1. Let's tell and write the correct numbers in the blank spaces.

a) If 3 children share 6 pencils, how many does each get?

Each gets ÷ = pencils.

How many twos are there in 6? ÷=
49
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b) If 2 boys share 8 apples, how many does each get?

Each gets ÷ = apples.

How many fours are there in 8?

÷ =

c) If 4 girls share 12 guavas, how many does each get?

Each gets ÷ = guavas.

How many threes are there in 12?

÷ =

2. Let's circle and group the marbles. Then complete the division.

a) 9 divided into 3 groups b) 10 divided into 2 groups



÷ = ÷=
d) 16 divided into 4 groups
c) 15 divided into 5 groups

÷ = ÷=

3.10 Dividend, divisor, quotient and remainder

Classwork - Exercise

Let's tell and write the answer in the blank spaces.

1. a) 18 ÷ 3 = 6 dividend is 18 divisor is 3 quotient is 6

b) 36 ÷ 4 = dividend is divisor is quotient is

c) 56 ÷ 7 = dividend is divisor is quotient is

d) 70 ÷ 10 = dividend is divisor is quotient is

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2. a) 9 ÷ 2 = 4 quotient and 1 is remainder

b) 7 ÷ 2 = quotient and is remainder

c) 10 ÷ 3 = quotient and is remainder

d) 11 ÷ 3 = quotient and is remainder

e) 18 ÷ 4 = quotient and is remainder

f) 23 ÷ 5 = quotient and is remainder

3.11 Division as repeated subtraction

Let's investigate the relation between division and subtraction from the
following illustrations.

1. How many times 2 is subtracted from 6 to get 0?

6 – 2 = 4 4–2=2 2–2=0
1 time
2 times 3 times So, 6 ÷ 2 = 3

2. How many times 3 is subtracted from 12 to get 0?

12 – 3 = 9 9 – 3 = 6 6–3=3 3 – 3 = 0
4 times
1 time 2 times 3 times So, 12 ÷ 3 = 4

Did you investigate the fact of division and subtraction?
Division is a process of repeated subtraction.

Classwork - Exercise

1. Let's write the correct number in the blank spaces.

a) How many times 2 is subtracted from 8 to get 0?

8 – 2 = , 6 – 2 = , 4 – 2 = , 2 – 2 = So, 8 ÷ 2 =

b) How many times 3 is subtracted from 9 to get 0?

9 – 3 = , 6 – 3 = , 3 – 3 = So, 9 ÷ 3 =

c) How many times 4 is subtracted from 16 to get 0?

16 – 4 = , 12 – 4 = , 8 – 4 = , 4 – 4 = So, 16 ÷ 4 =

d) How many times 6 is subtracted from 12 to get 0?

12 – 6 = , 6 – 6 = So, 12 ÷ 6 =

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3.12 Relation between multiplication and division

Classwork - Exercise

Let's investigate the relation between multiplication and division from
the given example. Then tell and write the correct numbers in the blank
spaces.

1. a) It is 4 × 3 = 12 It also means 12 ÷ 4 = 3

4 times 3 dots 12 dots are divided into 4 groups.

b) × = and ÷ =

c) × = and ÷ =

d) × = and ÷ =

2. a) 5 × 3 = 15, So, 15 ÷ 5 = 3 and 15 ÷ 3 = 5

b) 2 × 4 = , So, 8 ÷ 2 = and 8 ÷ 4 =

c) 4 × 7 = , So, 28 ÷ 4 = and 28 ÷ 7 =

d) 8 × 6 = , So, ÷ 8 = 6 and ÷6 =8

e) 9 × 10 = , So, ÷ 9 = 10 and ÷ 10 = 9

3. It's your time! Let's write your numbers. Then have a fun of
multiplication and division.

a) × = So, ÷ = and ÷ =

b) × = So, ÷ = and ÷ =

c) × = So, ÷ = and ÷ =

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Quiz time!

4. Let's tell and write the numbers as quickly as possible.
a) The product of two numbers is 14 and one of them is 2.

The other number is ÷ =

b) The product of two numbers is 18 and one of them is 6.

The other number is ÷ =

c) The quotient of 30 divided by a number is 5.

The number is ÷ =

d) The quotient of 56 divided by a number is 8.

The number is ÷ =

e) Dividend is 13, divisor is 2, quotient = remainder =

f) Dividend is 27, divisor is 5, quotient = remainder =

Puzzle Time!

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

× 4 = 20 90 ÷ =9 ÷ 4=

× × ×÷ ÷ ÷× ××

×= ÷= ÷ =3

= == = == = ==
÷ 8 =9
15 × = 60 15 ÷ =3

6. Let's recall the multiplication tables of 1, 2, 3, .... 10. Tell and write the
answers as quickly as possible.

a) 24 ÷ 4 = b) 30 ÷ 5 = 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15,
c) 42 ÷ 7 = d) 54 ÷ 6 = 5 × 4 = 20, 5 × 5 = 25, 5 × 6 = 30
So, 30 ÷ 5 = 6

e) 72 ÷ 9 = f) 80 ÷ 8 =

g) 45 ÷ 5 = h) 56 ÷ 7 =

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3.13 Division by row and column
Let's investigate the fact that how dividing into rows is different from dividing

into columns.

Dividing into rows Dividing into column
6 ÷ 2 = 3 in each row 6 ÷ 3 = 2 in each column

Classwork - Exercise

1. Let's complete these rows and columns division.

a) b) c)

÷ = ÷ = ÷ =

d) e) f)

÷ = ÷ = ÷=

2. Let's draw dotted lines and divide into rows or in columns. Then find
the quotient.

a) b) c)

12 ÷ 3 = 10 ÷ 5 = 24 ÷ 4 =

3.14 Dividing tens, hundreds, thousands,... by 10, 20, 300, 4000, ...

Let's investigate the rule of division with these numbers and become
faster than a calculator!

1. Divide 60 by 20. Equal number of zeros from
60 ÷ 20 = 6 ÷ 2 = 3 60 and 20 are cancelled.
Then 6 ÷ 2 = 3!

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