Prime Mathematics 3

Odd and even numbers

Do you remember how to find the given
number is an odd or an even number?

Sir, I have studied in class 2 but I have
forgotten. So, could you repeat once again?

To find the given number is an odd or an even, we
have to observe the digit in ones place. If the digit
in ones place is 0, 2, 4, 6 or 8, then the number is an
even number. If the digit in ones place is 1, 3, 5, 7 or

9 then the number is an odd number.

Natural and Whole Numbers.
a. Natural Numbers.

Number like 1,2,3,4,5, ... etc are used to count the number of things or object. Such
numbers are called counting numbers. The counting numbers are also called natural
number. Guess which is the least natural number and the greatest natural number.

b. Whole Numbers.

How many 2 years old students are there in your
class ?

There are no 2 years old students in my class.

It means there are 0 number of 2 years
students.

0,1,2,3,.. etc. are called whole number.

Oh, whole number are also natural number
including 0 (zero)
0 is the smallest whole number.
The set of whole number is denoted by W = {0,1,2,3,4...}

46 Prime Mathematics Book − 3

Exercise - 2.12

A) Find whether the given numbers are even or odd.

Ones digit Type Ones digit Type

1,23,456 6 Even 7,64,902

2,45,769 8,09,408

4,56,710 9,45,675

6,97,841 3,49,609

B. Answer the following questions :

1. What is the smallest natural number ? ............................
2. What is the smallest whole number ? ............................
3. What is the smallest natural odd number ? ............................
4. What is the smallest natural even number ? ............................
5. What is the even number between 3 and 5 ? ............................
6. What is the odd number between 20 and 22 ? ............................

C. List the even number between 25 and 35.

D. List the odd number between 14 and 22.

Prime Mathematics Book − 3 47

Rounding off to nearest 10 and 100

Shiba had Rs. 125 in the morning. He spent Rs. 35. Suman asked him how
much money he had?
He answered, "About Rs. 100". Here he applied a mathematical process
called rounding off. We round off a number to the nearest 10 or 100 or
1000 etc.

Far from 10 Near to 20

10 11 12 13 14 15 16 17 18 19 20 21 22

18 is in between two tens i.e. 10 and 20. But 18 is farther from 10 than
20. So, while rounding 18 to nearest ten, we round off as 20.

Let’s round off 24. Far from 30

Near to 20

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

24 is in between two tens and they are 20 and 30. 24 is nearer to 20 than
30. So, while rounding off 24 to nearest ten, we round off it as 20.

Round off 55 to nearest ten.

48 50 52 54 55 56 58 60 62

55 is exactly in between 50 and 60. So we round off 55 as 60. Similarly,
45 is round off as 50.

Exercise - 2.13

A. Round off the following numbers to the nearest ten.

76 67 26
44 94 73
55 11 82

48 Prime Mathematics Book − 3

B. Represent the following numbers in a number line
and round off to nearest 10.

43 40

40 41 42 43 44 45 46 47 48 49 50

67

60 61 62 63 64 65 66 67 68 69 70

88

80 81 82 83 84 85 86 87 88 89 90

35

30 31 32 33 34 35 36 37 38 39 40

14

10 11 12 13 14 15 16 17 18 19 20

77
70 71 72 73 74 75 76 77 78 79 80

94
90 91 92 93 94 95 96 97 98 99 100

59
50 52 54 56 58 60

45
40 42 44 46 48 50

27 20 22 24 26 28 30
Prime Mathematics Book − 3 49

Let’s represent 140 in a number line and
try to round off to the nearest 100.

100 110 120 130 140 150 160 170 180 190 200

140 is in between 100 and 200. It is nearer to 100 than 200. So, it is
rounded off as 100.

Let’s round off 270.

200 210 220 230 240 250 260 270 280 290 300

270 is in between 200 and 300. It is nearest to 300 than 200.
So it is round off as 300.

Let’s try to round
off 350.

300 310 320 330 340 350 360 370 380 390 400

350 is exactly in between 300 and 400. So 350 is round off as 400.

Exercise - 2.14

A. Round off to nearest 100.
130 100 680
260 710
390 820
450 940
570 285

50 Prime Mathematics Book − 3

B. Represent the given numbers in a number line and
round off to nearest 100.

140 100 110 120 130 140 150 160 170 180 190 200 100

270

200 210 220 230 240 250 260 270 280 290 300

380

300 310 320 330 340 350 360 370 380 390 400

460

400 410 420 430 440 450 460 470 480 490 500

550

500 510 520 530 540 550 560 570 580 590 600

610

600 610 620 630 640 650 660 670 680 690 700

780

700 710 720 730 740 750 760 770 780 790 800

890

800 810 820 830 840 850 860 870 880 890 900

Roman numerals

Do you remember the symbols
used in Roman numeral system?

Yes, sir there are seven symbols used in Roman
numeral system. They are I, V, X, L, C, D and M.

Could you tell what those Yes, sir !
symbols stand for? They stand for

Prime Mathematics Book − 3 51

Roman Numeral Hindu Arabic Roman Numeral Hindu Arabic
I 1 C 100
V 5 D 500
X 10 M 1000
L 50

Let’s write the numbers I 1
from 1 to 10 in Roman II 2
III 3
Numeral System.

It shows that we can put I together three times.

Could you represent 4 in Roman Numeral System?
Yes, sir. It is IIII.

That’s wrong. We can’t write I for four times. 4 is
written as IV. Here, smaller symbol I comes before

greater symbol V. So 1 is subtracted from 5.
∴ 4 = 5 – 1 = IV

But, to represent 6, we write VI
Here, the smaller symbol I comes after the greater symbol V so, we add
them.
∴ 6 = 5 + 1 = VI
Similarly, 7 = 5 + 1 + 1 = VII

8 = 5 + 1 + 1 + 1 = VIII
But 9 is written as IX because I can’t be repeated for four times.
Now, 10 = X
For 10, we can’t write V V. It means V can’t be repeated for two times.
From the examples given above it is clear that
I comes before and after V and X only.

52 Prime Mathematics Book − 3

Can you represent 40 in Roman
Numeral System?
Yes, sir! it is XL.

Could you explain it?

The smaller symbol comes before the greater
symbol. So, XL means 50 – 10 = 40.

Exercise - 2.15

A.Write the Roman Numeral for the given numbers.

4 25 60

8 15 55

19 24 59

30 35 80

35 42 99

20 48 95

B.Write the numerals for the given Roman numeral.

VII XXX LXXV

XIV XXXIV LXXXIV

XII XXVIII XV

XX XIX LXVX

XXV XXIX C

XXVIII XXXIX XLV

IX LXII LXXXIX

Prime Mathematics Book − 3 53

Hindu Arabic Devanagari Numerals. Nepali words

1 Devanagari Ps
2 bO' {
3 ! tLg
4 @ rf/
5 # kfr“
6 $ 5
7 % ;ft
8 ^ cf7
9 & gf}
10 * bz
11 ( P3f/
12 !) afx|
13 !! t]x|
14 !@ rfw}
15 !# kGw|
16 !$ ;fx] |
17 !% ;q
18 !^ c7f/
19 !& pGgfO;
20 !* aL;
21 !( PSsfO;
22 @) afO;
23 @! tO] ;
24 @@ rfa} L;
25 @# kRrL;
@$
@%

54 Prime Mathematics Book − 3

Hindu Arabic Devanagari Nepali words
26
27 @^ 5AaL;
28 @& ;QfO;
29 @* c77\ fO;
30 @( pgGtL;
31 #) tL;
32 #! PstL;
33 #@ aQL;
34 ## t]QL;
35 #$ rf+l} t;
36 #%
37 #^ kl+} t;
38 #& 5QL;
39 #* ;t+} L;
40 #( c7t\ L;
41 $) pgGrfnL;
42 $! rfnL;
43 $@ PsrfnL;
44 $# aofnL;
45 $$ lqrfnL;
46 $% rjfnL;
47 $^ k+}tfnL;
48 $& 5ofnL;
49 $* ;tr\ fnL;
50 $( c7\rfnL;
%) pgGkrf;
krf;

Prime Mathematics Book − 3 55

Hindu Arabic Devanagari Nepali words
51
52 %! PsfpGg
53 %@ afpGg
54 %# lqkGg
55 %$ rf}jGg
56 %% krkGg
57 %^ 5kGg
58 %& ;GtfpGg
59 %* cG7fpGg
60 %( pgG;f7L
61 ^) ;f7L
62 ^! Ps;L
63 ^@ a;} L
64 ^# lq;¶L
65 ^$ rf;} ¶L
66 ^% k};+ ¶L
67 ^^ 5;} ¶L
68 ^& ;t;¶L
69 ^* c7;¶L
70 ^( pgG;Q/L
71 &) ;Q/L
72 &! PsxQ/
73 &@ axQ/
&# lqxQ/
74
75 &$ rfx} Q/
&% krxQ/

56 Prime Mathematics Book − 3

Hindu Arabic Devanagari Nepali words
76
77 &^ 5oxQ/
78 && ;txQ/
79 &* c7xQ/
80 &( pgf;L
81 *) c:;L
82 *! Psf;L
83 *@ aof;L
84 *# lqof;L
85 *$ rf/} f;L
86 *% krf;L
87 *^ 5of;L
88 *& ;tf;L
89 ** c7f;L
90 *( pgfGgAa]
91 ()
92 (! gAa]
93 (@ PsfgAa]
94 (# aofgAa]
95 ($ lqofgAa]
96 (% rf}/fgAa]
97 (^ kGrfgAa]
98 (& 5ofgAa]
99 (* ;GtfgAa]
100 (( cG7fgAa]
!)) pgfgzo
Ps ;o

Prime Mathematics Book − 3 57

Exercise - 2.15

x]/, k9 / l;s .

xhf/ ;o bz Ps = %))% xhf/ ;o bz Ps = #%#&
%) )% # %# &
tLg xhf/ kfrF ;o ;Ft} L;
kfrF xhf/ kfrF . Ps
%
s_ :yfgdfg tflnsf e/L cIf/df nv] . @_ $^@%
!
xhf/ ;o
xhf/ ;o bz Ps $^ bz
@
@ @) !
bO' { xhf/ bO' { ;o Ps

#_ !)!)% ==============================================================

b;xhf/ xhf/ ;o bz Ps $_ %#&%@
! ) ! )%
b;xhf/ xhf/ ;o bz Ps
% # & %@

================================================================== =========================================================

%_ *@^%(

b;xhf/ xhf/ ;o bz Ps
* @ ^ %(

=========================================================

B. ;+Vofdf n]v .

!= k};7\7L xhf/ rf/ ;o aQL;

@= PsfpGg xhf/ kfFr;o kfrF

#= kt} L; xhf/ 5kGg

58 Prime Mathematics Book − 3

$= c7f;L xhf/ Ps ;o rf}/fgAa]
%= lqxTt/ xhf/ 5 ;o

C. tnsf ;+VofnfO{ cIf/df n]v .

!= %%%)
@= *#$@!
#= ^*($
$= &)!)%
%= (((((

Unit Revision Test

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

a) 4,259 b) 54,908 c) 8,15,210 d) 7,05,213

B.Write in numerals.

a) Five thousand and one hundred.
b) Ninety eight thousand four hundred and ten.
c) One lakh twenty three thousand five hundred and ninety

two.
d) Three lakh forty five thousand two hundred and nineteen.

Prime Mathematics Book − 3 59

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

a) 4512 4501 b) 59,008 49,008

c) 6,45,123 8,45,123 d) 9,63,459 9,73,459

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

a) 1,298 b) 54,019 c) 6,95,198 d) 9,84,756

E. Form the greatest number and smallest number of
the given digits:

a) 5,3,0,1 b) 9,1,8,6 c) 7,3,4,2 d) 8,4,2,7

F. Use comma in Hindu Arabic System.

a) 4571 b) 64982 c) 794610 d) 859217

E. Find whether the given numbers are even or odd.

a) 4598 b) 64,127 c) 9,48,200 d) 8,45,239

F. Round off the following numbers to the nearest 10.

a) 35 b) 52 c) 69 d) 87

G. Round off the following numbers to the nearest 100.

a) 250 b) 360 c) 480 d) 520

* tnsf ;+VofnfO{ cIf/df n]v . @_ !)#)% ==================================
!_ @%^#$ ===================================

#_ !%)* ====================================

* tnsf ;V+ ofnfO{ cs+ df n]v
!_ Ps xhf/ rf/ ;o afx| ==================== @_ ;ft xhf/ gf} ;o aof;L
=================
#_ 5;} 7\7L xhf/ kfFr ;o kt} L; ===========================

60 Prime Mathematics Book − 3

Unit Estimated periods − 12

3

ADDITION

Objectives

At the end of this unit, the students will be able to:
• find the sum of maximum 4 addends of 4 digit numbers without and with carrying.
• find the sum of 5 digit and 6 digit numbers without and with carrying.
• make the simple word problems on addition and solve them.

Teaching Materials
• Abacus, place value chart etc.

Activities

It is better to:
• let the students do the addition without and with carrying from the discussion by

using the abacus and place value chart.
• ask the students write the word problems on addition in mathematical form and solve

them.
• ask the students make their own simple word problems on addition with carrying and

solve them.
• involve the students to demonstrate the activities related to this lesson suggested in

the curriculum prescribed by CDC.

Review
Exercise - 3.1

Addition up to 3 digit numbers without carrying

A) Do the following task:

25 30 43 2 65 4
+6 3 +5 0 +2 5 4 +3 2 5

23 20 43 2 12 3
41 53 12 3 24 1
+3 4 +1 4 +3 0 4 +3 1 4

41 7 60 5 63 53 2
23 0 24 1 31 4 46
+1 5 2 + 52 +5 0 1
+1

31 52 1 32 4 40 2
23 20 3 11 1 13 1
14 11 2 20 3 24 0
+2 1 +1 4 3 +1 4 1 +1 2 3

B) Fill in the boxes as shown below:

8 + 2 + 5 = 15 54 + 10 + 20 =

5+5 +2= 342 + 123 + 204 =

30 + 40 + 20 = 625 + 171 + 203

62 Prime Mathematics Book − 3

Review
Addition up to 3 digit numbers with carrying

Hari, how many tens Yes, I know, there are 2
and ones are in 24? tens and 4 ones in 24,

Very good Hari. Madam

Let’s add ones and Remember
make the groups of 1 ten = 10 ones

tens and ones!

5 ones + 7 ones = 12 ones = 1 ten + 2 ones

8 ones + 9 ones = ones = ten + ones

12 ones + 17 ones = ones = tens + ones

Exercise - 3.2

A) Perform the following task as shown below:

1 28 87 56
+3 7 +9 5 +4 7
76
+1 5

91

32 28 17 17
45 37 25 25
+1 6 +1 9 34 34
+1 6 +1 6

Prime Mathematics Book − 3 63

Review

Mina, how many hundreds, tens Sir, let me think
and ones are there in 325? 325 = 300 + 20 + 5

Very good, Mina! Oh! Sir, there are 3
hundreds, 2 tens and 5 ones.

Let’s add tens and Remember
make the groups of 1 ten = 10 ones
hundreds and tens! 1 hundred = 10 tens

Exercise - 3.3

Perform the following as shown below:

6 tens + 7 tens = 13 tens = 11 hundred + 3 tens

8 tens + 9 tens = tens = hundred + tens

13 tens + 15 tens = tens = hundred + tens

Do the following as shown below:

11 5 68 6 22 2 43
3 67 +3 5 4 +1 9 7 +3 8 9
+4 5 4
8 21

2 65 2 67 2 46 6 32
3 43 3 48 1 32 1 45
+1 5 7 +1 5 4 2 54 2 56
+1 3 5 +3 4 7

Note to the teacher:
Please ask the students to make such types of addition problems
and add them.

64 Prime Mathematics Book − 3

Addition by using abacus without and with carrying

Study and learn:

Th H T O Th H T O Th H T O

24 4 3 + 33 53 = 579 6 Th H T O
2 44 3
3
+3 3 5
5 79 6

Exercise - 3.4

A. Do the following as shown above.

Th H T O Th H T O Th H T O Th H T O

Th H T O + = +
Th H T O Th H T O Th H T O

+= +

Th H T O Th H T O Th H T O Th H T O

+= +

Prime Mathematics Book − 3 65

Th H T O Th H T O Th H T O Th H T O

+= +

TTh Th H T O TTh Th H T O TTh Th H T O Th H T O

+= +

Addition of 4 digit numbers without carrying

Ramu, can you add Sir, let me think.
4 digit numbers?

Yes, Ramu, can you Let me try.
add 3562 and 3214?

Good!

Th H TO Oh! I got the idea. Sir, it is
35 62 the same method as addition
+3 2 14 of 3 digit numbers, isn’t it?
67 76

66 Prime Mathematics Book − 3

Exercise - 3.5

Perform the following task:

Th H T O Th H T O Th H T O Th H T O
52 6 3 43 5 2 27 4 3 3 62 8
+2 4 3 4 +1 5 4 3 +3 0 4 6 +4 2 6 1

Th H T O Th H T O Th H T O Th H T O
23 4 1 62 1 2 1 23 2 2 22 2
32 1 5 10 3 4 2 52 1 3
+1 3 2 3 +2 3 0 1 3 14 2 33 2
+1 0 0 1 3 22 1
+1 0 1

Addition of 4 digit numbers with carrying

Can you add 2453
and 3218?

Let me try. I think it is also
same as in addition of 3
digit numbers, isn’t it?

Prime Mathematics Book − 3 67

1 • First we add the digit of ones place.
Th H T O 3 ones + 8 ones = 11 ones = 1 ten + 1 one
2 45 3 We write 1 in ones place and carry 1 ten to tens
+3 2 1 8 column.
5 67 1
• Now, we add the digit of tens place.
1 ten (carry over) + 5 tens + 1 ten = 7 tens
7 tens are less than 10 tens. So, there is no carry
over.

• Then we add the digit of hundred place.
4 hundreds + 2 hundreds = 6 hundreds
6 hundreds are also less than 10 hundreds. So, there
is no carry over.

• Finally we add the digit of thousands place.
2 thousands + 3 thousands = 5 thousands.

Let’s try another sum. Ok! sir
Add: 3 7 8 9 and 2
3 4 2.

Th H T O • Addition of ones
111 9 + 2 = 11 = 1 ten + 1 one
3 78 9
+2 3 4 2 • Addition of tens
6 13 1 1 (carry over) + 8 + 4 = 13 tens = 1 hundred + 3 tens

• Addition of hundreds
1 (carry over) + 7 + 3 = 11 hundred = 1 thousand + 1 hundred

• Addition of thousands
1 (carry over) + 3 + 2 = 6 thousands.

Exercise - 3.6

A. Perform the following task as shown below:

Th H T O Th H T O Th H T O Th H T O

1 2 35 6 3 24 8 1 35 4
5 34 7 +4 2 3 8 +2 4 1 7 +2 1 3 9
+3 2 3 6
8 58 3

68 Prime Mathematics Book − 3

Th H T O Th H T O Th H T O Th H T O

2 34 5 4 24 5 2 57 8 4 35 9
+3 4 8 6 +3 6 6 7 +3 2 5 7 +3 2 6 4

Th H T O Th H T O Th H T O Th H T O

5 36 7 4 84 5 2 57 8 4 35 9
+2 8 5 4 +3 6 6 7 +3 6 5 7 +3 2 6 4

B. Perform the following task as shown below:

Th H T O Th H T O Th H T O Th H T O
1
4 73 2 2 35 8 5 24 3
2 43 5 1 05 7 1 00 4 1 15 6
1 32 4 +2 1 0 6 +2 1 3 5 +2 3 6 5
+3 1 0 6
6 86 5

Th H T O Th H T O Th H T O Th H T O

1 23 4 3 23 6 4 27 3 3 26 5
4 56 7 1 35 4 1 34 5 5 64 3
+2 1 5 3 +2 1 4 7 +2 1 8 4 + 52 6

Prime Mathematics Book − 3 69

Th H T O Th H T O Th H T O Th H T O

2 45 8 4 23 7 2 13 2 6 78 9
3 64 9 1 76 5 1 45 6 56 8
+2 5 6 3 +2 3 4 9 2 10 4 27
+ 30 2
+5

Addition of more than 4 digit numbers
without carrying

Remember the concept of T Th Th H TO
addition of 4 digit numbers by using 25 3 42
1 35
the place value chart. +4 2 4 77
67

Add: 25342 and 42135.

Exercise - 3.7

A. Do the following task as shown below:

T Th Th H TO T Th Th H T O T Th Th H TO
43 2 65 3 4 2 56 56 2 57
4 12 3 21
+5 2 6 77 +5 3 4 2 3 +1 2
95

L T Th Th H T O L T Th Th H T O L T Th Th H T O
2 3 4 562 3 5 6 372 4 2 7 513
+4 5 2 3 1 6 +5 2 3 5 1 7 +2 4 0 2 6 4

70 Prime Mathematics Book − 3

Addition of more than 4 digit numbers with
carry over

Lila, can you add 36986 Yes, I can because I know
and 24537? the process of addition of 4

Good! Lila, you have good digit numbers.

idea. So, Let’s do it.

T Th Th H T O • First add ones
6 + 7 = 13 ones = 1 ten + 3 ones
31 16 19 81 6 Write 3 in ones place and carry over 1 ten to
+2 4 5 3 7 tens place.

6 1 5 23 • Then add the tens.
1 ten (carry over) + 8 tens + 3 tens = 12 tens
= 1 hundred + 2 tens
Write 2 in tens place and carry over 1
hundred to hundreds place.

• Similarly we add hundreds, thousands and
ten thousands.

Exercise - 3.8

A. Do the following task:

T Th Th H T O T Th Th H T O T Th Th H T O

4 5 3 87 2 4 5 68 5 3 6 57
+2 6 8 6 5 +1 8 2 9 6 +2 3 5 2 6

T Th Th H T O L T Th Th H T O L T Th Th H T O

2 7 3 85 3 6 7 542 4 7 2 685
+4 5 7 6 9 +2 6 5 7 8 9 +2 5 9 5 3 8

Prime Mathematics Book − 3 71

T Th Th H T O L T Th Th H T O T Th Th H T O

3 5 2 74 24 5 367 8 8 8 88
3 8 25 32 4 673 8 8 88
+2 3 5 254 8 88
+ 6 43
+ 88

Word problems on addition

Study and learn the following example.

There are 2432 students in school 'A' and 3254 students in school 'B'.

How many students are there altogether in both schools?

Students in school 'A' = 2432

Students in school 'B' = + 3254

5686

∴ There are altogether 5686 students in both schools.

Exercise - 3.3

A. Do the following problems:

a) Ram had Rs. 2346. Shyam gives him Rs. 1433.
How much money does he have now?

∴ Ram has Rs. now. +

72 Prime Mathematics Book − 3

b) A box contains 1265 marbles and another box

contains 2324 marbles. How many marbles are

there altogether? +

∴ There are altogether marbles.

c) There are 4320 apples in one box and 2457 apples

in another box. How many apples are there

altogether? +

∴ There are altogether apples.

d) A Farmer sold 1324 kg of potatoes in Baishakh,

2142 kg in Jestha and 2231kg in Asar. How many

kgs of potatoes did he sell in three months? +

∴ He sold kg potatoes in three months.

e) Mohan gave Rs. 50125 donation to orphan house,

Rs. 25600 to Bir Hospital and Rs. 32260 to a

Bridha Ashram. How much money did he donate +

altogether?

∴ He donated Rs. altogether.

Prime Mathematics Book − 3 73

B. Study and learn the following example:

The cost of a radio is Rs. 2975 and the cost of a television is Rs. 5675. What

is the total cost of both items?

The cost of a radio = 111

2975

The cost of a television = +5675

8650
∴ The total cost of both items is Rs. 8650.

B. Solve the following problems:

a) The cost of a bicycle is Rs. 4276 and the cost of a 4 27 6
+1 64 5
telephone set is Rs. 1645. What is the total cost of

both items?

∴ The total cost of both items is Rs. .

b) The price of a shirt is Rs. 1375 and the price of a

jacket is Rs. 2948. What is the total price of both 1 37 5
+2 94 8
items?

∴ The total price of both items is Rs. .

c) There are 5342 men and 4697 women in a village. 5 34 2
+4 69 7
How many people are there altogether?

∴ There are people altogether.

74 Prime Mathematics Book − 3

d) A man earns Rs. 3750 from house rent, Rs. 4375 from
farming and Rs. 5275 from business in a month. How

much money does he earn altogether?

∴ He earns Rs. altogether.

e) A truck carried 1285 kg of mangoes on Sunday, 2435kg
on Monday and 2527kg on Tuesday. How many kgs of

mangoes are carried by the truck altogether?

∴ It carried kgs of mangoes.

f) A fruit seller bought 2587kg apples, 1735kg mangoes

and 643kg guavas. How many kgs of fruits did he buy?

∴ He bought kgs of fruits.

Unit Revision Test

A) Perform the following task:

2756 63572 820456 2346
+3142 +24326 +167321 3121
+1412

Prime Mathematics Book − 3 75

4356 2468 53728 364582
+2874 +4354 +37693 +274879

4632 5784 37485 13785
589 4376 42637 24365
3283 +56574
+2374 +4765 3684
+573

B) Perform the following task:

a) 2 3 + 1 5 9 + 2 345 = b) 251 + 6254 + 252=
c) 4 0 3 + 2 3 5 1 + 76 = d) 965 + 2458 + 365=

C) Solve the following problems:

a) The cost of a computer is Rs. 15785 and the cost of a volt guard is

Rs. 1865. What is the total cost of the both items?

The total cost is Rs. .

b) The monthly expenditure of a family is Rs. 8500 on food, Rs. 2375 on

education of children, Rs. 865 on fuel and Rs. 3600 on house rent. Find

the total expenditure of the family in a month.

The total expenditure is Rs. .

76 Prime Mathematics Book − 3

Unit Estimated periods − 12

4

SUBTRACTION

Objectives

As the end of this unit, the students will be able to:
• Subtract the number of 4 digits with borrowing in at most three places.
• Subtract the number of 5 digits and 6 digits also with borrowing in at most three places.
• Illustrate the word problems in mathematical form and solve it.

Teaching Materials
• Abacus, place value chart etc.

Activities

It is better to:
• let the students do the subtraction without and with borrowing by using place value

chart.
• ask the students to write the word problems on subtraction in mathematical form

and solve them.
• ask the students to make their own simple word problems on subtraction with

borrowing and solve them.
• involve the students to demonstrate the activities to this lesson suggested in the

curriculum prescribed by CDC.

Substraction (Revision)
Subtraction upto 3 digit numbers without borrowing

Exercise - 4.1

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

TO TO TO H TO

46 57 69 354

−2 5 −3 4 −2 7 −2 4 3

21

H TO H TO H TO H TO
573 756 643 875
−3 4 1 −4 3 4 −3 2 1 −4 5 2

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

76 − 34 = 42 35 − 24 = 567 − 52 =

89 − 56 = 67 − 34 = 734 − 222 =

54 − 23 = 257 − 124 = 654 − 431 =

60 − 40 = 435 − 214 = 965 − 425 =

Subtraction upto 3 digit numbers with borrowing

Mohan, can you subtract Yes, sir! Let me try.
246 from 362?

Good Mohan! 6 can’t be subtracted from 2.
So, 2 borrows 1 ten from 6 tens.
H TO 1 ten + 2 ones = 12 ones

362 12 ones − 6 ones = 6 ones

−2 4 6 6 tens has left 5 tens.
1 1 6 Then we subtract 4 tens from 5 tens.

78 Prime Mathematics Book − 3

Exercise - 4.2

A. Perform the following task as shown above in the example:

T O T O T O T O
5 2 6 4 8 1 9 4
−2 7 −3 6 −4 5 −5 9

H TO H TO H TO H TO
462 574 363 435
−2 3 5 −2 4 7 −1 4 8 −2 7 2

Subtraction of 4 digit numbers without borrowing

Meena, do you know the Oh! I think I have an idea. Yes,
process of subtraction of 4 sir! The process is same as the

digit numbers? process of subtraction of 3
digit numbers, isn’t it?
Can you subtract 3245 from 5469?

Yes, good.

Th H T O Of course sir ! First we arrange
5469 the given numbers according
to their place value. Then
−3 2 4 5 subtract one by one.
2224

Exercise - 4.3

A. Perform the following problems:

Th H T O Th H T O Th H T O
5638 4786 7958

−2 4 1 6 −2 4 5 3 −3 6 4 6

Th H T O Th H T O Th H T O
6835 5436 4375

−4 5 1 3 −2 4 1 5 −2 0 5 4

Prime Mathematics Book − 3 79

Th H T O Th H T O Th H T O
4835 2748 5739

−3 6 1 3 −1 5 2 8 −4 5 2 4

Subtraction of 4 digit numbers with borrowing

Jeena, can you subtract Yes, sir! Let me try.
2347 from 4572?

Yes, Jeena I think it is same as the
you can try. subtraction of 3 digit
number, isn’t it Sir ?

6 12 Steps:
• 7 can’t be subtracted from 2. So, 2 can
Th H T O
4572 borrow 1 ten from 7 tens.
∴ 1 ten + 2 ones = 12 ones
−2 3 4 7 12 ones − 7 ones = 5 ones
2225 • 7 tens has left 6 tens
• 6 tens − 4 tens = 2 tens
• 5 hundreds − 3 hundreds = 2 hundreds
• 4 thousands − 2 thousands = 2 thousands.

Exercise - 4.4

A. Perform the following task as shown in the above example:

Th H T O Th H T O Th H T O Th H T O
3573 4654 5435 4830

−1 3 4 5 −2 3 4 7 −2 3 2 8 −2 5 1 7

Th H T O Th H T O Th H T O Th H T O
6245 7560 4692 7560

−4 2 1 7 −5 3 4 8 −3 5 7 4 −2 3 4 9

80 Prime Mathematics Book − 3

Jeena, can you subtract Yes, sir! I can.
3469 from 8652? Let me
try.

Step:
• First we subtract the digit of ones place. But 9
14 can’t be subtracted from 2. So, 2 borrows 1 ten
5 4 12 from 5 tens.
∴ 1 ten + 2 ones = 12 ones
Th H T O 12 ones − 9 ones = 3 ones
8652
• Now, 5 tens has left 4 tens. But 6 tens can’t be
−3 4 6 9 subtraced from 4 tens. So, 4 borrows 1 hundred
5183

from 6 hundred.

1 hundred + 4 tens = 10 tens + 4 tens = 14 tens

14 tens − 6 tens = 8 tens.

• Then, 6 hundreds has left 5 hundreds.

4 hundreds is subtracted from 5 hundreds

5 hundred − 4 hundred = 1 hundred.

• 8 thousands − 3 thousands = 5 thousands.

Exercise - 4.5

A. Perform the following problems:

Th H T O Th H T O Th H T O Th H T O
342 6 254 3 584 0 654 3

−1 2 4 8 −1 3 8 7 −2 5 6 4 −3 2 6 5

Th H T O Th H T O Th H T O Th H T O
572 6 437 4 692 5 590 3

−2 4 5 9 −2 1 9 6 −4 7 6 9 −2 4 6 8

Prime Mathematics Book − 3 81

Adarsh, can you subtract
5243 from 7042?

9 13 Yes, sir! I can do it.
Let me try.
6 10 3 12

Th H T O
7042

−5 2 4 3
1799

Steps:
• 2 ones is less than 3 ones. So, 2 borrows 1 ten from 4 tens.

∴ 1 ten + 2 ones = 12 ones
12 ones − 3 ones = 9 ones
• 4 tens has left 3 tens. 4 tens can’t be subtracted from 3 tens. So,
3 borrows 1 hundred i.e. 10 tens from digit of hundred place. But
the digit of hundred place is 0.
• 0 borrows 1 thousand i.e. 10 hundreds from 7 thousands.
• 0 has 10 hundred and 7 thousand has left 6 thousand.
• Then, repeated the above same process.

Exercise - 4.6

A. Perform the following problems:

Th H T O Th H T O Th H T O Th H T O
342 5 485 7 648 7 764 7

−1 6 4 7 −2 9 6 8 −4 4 9 8 −4 7 6 3

Th H T O Th H T O Th H T O Th H T O
540 3 354 0 536 1 407 0

−2 5 7 6 −1 7 6 2 −3 4 7 4 −2 9 8 4

82 Prime Mathematics Book − 3

Subtraction of more than 4 digit numbers without borrowing

How to subtract large
numbers, Madan?
Don’t worry, Anima. We can
subtract the large numbers as
the same process as 4 digit numbers. So,
Ok Madan ! first we should arrange the numbers in

their place value
columns.
TTh Th H T O
5 6 324

−3 4 2 0 3 Let’s try one
2 2 121 example.

Exercise - 4.7

A. Perform the following task:

43245 52673 46734 47892
−21032 −21451 −35714 −5432

352648 467384 573747
−140325 −245174 −263543

73254 843673 953744
−32140 −621542 −521463

B. Do the following task as shown below:

53246–20124= 3 3 1 2 2 643542–421421=
76521–53210= 437653–215421=
36976–15435= 574327–253224=

Prime Mathematics Book − 3 83

Subtraction of more than 4 digit numbers with borrowing

Rita, Can you subtract 43265 Sir, It is a large number.
from 62172 ? So, I can’t do it.

Ok! Rita don’t worry. I Now, I understand
explain it. and can do it.

First we subtract ones from ones, TTh Th H T O

11
then tens from tens, hundreds from 5 1TTh211Th111 6 1T 1 2
hundreds and so on by borrowing
from the higher place number of 6 72
− 4 3 2 6 5
the left column if necessary. 1 8 90 7

Exercise - 4.8

A. Perform the following task:

25324 43253 423546 53482
−1 3 1 7 6 −3 1 0 6 8 −2 4 1 6 5 4 −2 6 7 5 4

67024 63542 586430 43006
−3 4 4 5 7 −2 6 3 6 5 −2 8 7 2 4 8 −1 2 4 6 9

Word problems on subtraction without and with borrowing

Study and learn:
There were 5432 fishes in a pond. A fisherman caught 3258 fishes in his
net. How many fishes are left in the pond?
Total fishes = 5 4 3 2
Caught fishes = −3 2 5 8

= 2174
∴ 2174 fishes are left in the pond.

84 Prime Mathematics Book − 3

Exercise - 4.9

A. Do the following problems:

1) There were 4743 apples in a box. 3421 of them were

rotten. How many apples were good? −
∴ apples were good.

2) Safir earns Rs. 15750 from his salary. He spends

Rs. 11550. How much money does he save? −

∴ He saves Rs. .

3) The sum of two numbers is 96787. If one of the number

is 56575, what is the other number? −

∴ The other number is .

4) There are 3452 students in a school. 1774 of them are

boys. How many of them are girls? −

∴ The girl students are .

5) Ram had Rs. 95000. He bought a motor bike for

Rs. 78525. How much money is left with him? −

∴ He has Rs. with him.

6) Aadarsh earns Rs. 17250 in a month. If he spends

Rs. 12775 for his family, how much money does he save −

in a month?

∴ He saves Rs. in a month.

Prime Mathematics Book − 3 85

Simplification of addition and subtraction

Mohan, you have 12 pencils. I give you 15 pencils
more. From which, you gave 14 pencils to your
friends. How many pencils will be left with you now?

12 + 15 – 14 I think I have to add
= 27 – 14 first and then subtract,
= 13
shouldn't I ?

Yes, very good.

Exercise - 4.9

Simplify A: b) 7 + 3 - 5 c) 7 + 3 - 5
a) 6 + 4 – 3

= 10 - 3 = =

=7 = =

d) 6 - 2 – 3 e) 7 - 8 + 5 f) 8 - 9 + 7
= = =
= = =

Simplify B:

a) 17 + 12 – 15 b) 29 + 14 – 12 c) 35 – 27 + 18 d) 15 – 8 + 6
= − 15
= = − 12 = − 27 = − 8

= ==

a) 18 – 12 + 37 – 32 b) 16 – 14 + 43 – 12
=−
= 18 + 37 − 12 + 32
= 55 − 44 =−
= 11
=
86 Prime Mathematics Book − 3

c) 24 – 13 + 37 – 22 d) 21 – 15 + 38 – 29
=− =−

=− =−

= =

Simplification of addition and subtraction by machines
Exercise - 4.10

Simplify the following by machine as shown in the example:

12 15 8

7 +8 −5 10 9
24 +2 −4

27 3

4 5

8 3
+9 −5 +10 −8

4 7

20 15

30 +5 −10 12
40 +8 −13

10

Prime Mathematics Book − 3 87

Unit Revision Test

A. Do the following task :

37 457 6357 52157 743259
−25 −235 −4243 −32024 −341248

42 327 4235 6432 43248
−27 −219 −2146 −2857 −24856

B. Solve the following problems:

a) Safir had Rs. 4235. He spent Rs. 2487 to buy a watch.

How much money does he have now? −

Now he had left Rs. .

b) There are 5435 mangoes in a basket. 2546 of them −
are rotten. How many of them are good mangoes?
∴ mangoes are good.

C. Simplify:

a) 19 + 12 – 8 b) 35 − 14 + 21 c) 46 − 28 + 53 − 45
=
==
=
== =
== f) 25 + 30 – 10 − 18
=
d) 21 + 32 – 25 e) 24 – 13 + 19
= = =
=
= =
=
=

88 Prime Mathematics Book − 3

Unit Estimated periods − 12

5

MULTIPLICATION

Objectives

At the end of this unit, the students will be able to:
• read and write the multiplication table of 2 to 12.
• write the problems of multiplication in mathematical form.
• multiply the numbers of two digits or three digits by one, two and three digit number

with or without carrying.
• solve the word problems on multiplication.

Teaching Materials
• multiplication tables, pencils, blocks, place value chart, etc.

Activities

It is better to
• ask the students to prepare and write the multiplication table from 2 to 12 by the

concept of repeated addition step counting method.
• drill the problems on multiplication with the help of multiplication table with the

discussion of multiplication method.
• ask the students to discuss the simple word problems on multiplication among

themselves and write the problems in mathematical sentence by using multiplication
symbol and find the product also.
• ask the students to write the word problems on multiplication and tell them to discuss
the problems are right or not.
• ask the students to demonstrate the activities related to these lessons suggested in the
curriculum prescribed by CDC.

Review of multiplication Recall the facts of multiplication which

you learnt in class 2.

3 + 3 + 3 + 3 = 12

There are 4 groups of 3 pens = 12 4
4 × 3 = 12 ×3
From the above example, it concludes that the 12
multiplication is repeated addition. Multiply quickly

Exercise - 5.1 3×2 =
5×3 =
A. Fill in the boxes as shown as below: 4×7 =
7×5 =
2+2+2+2+2 = 10 3+3+3+3+3 = 3×8 =
6×4 =
5 × 2 = 10 5× = 4×9 =
2×7 =
4+4+4+4 = 6+6+6+6+6+6 = 8×5 =
×4= 6× = 9×6 =
10 × 4 =
8+8+8 = 0+0+0+0+0 = 6×7 =
3× = 5× = 5×9 =
9×3 =
Recall the product and factors. 3×7 =
2×9 =
We know that, 10 × 7 =
7 × 3 = 21

In fact, 21 is called the product of 7
and 3.
7 and 3 are called the factors of 21.

Exercise - 5.2

B.Write the product and factors in the boxes:

In 5 × 4, Product = 20 , Factors = 5 and 4

In 4 × 9, Product = , Factors = and

In 9 × 6, product = , factors = and

In 7 × 5, product = , factors = and

In 8 × 0, product = , factors = and

90 Prime Mathematics Book − 3

Multiplication Table

I want to recall and write the multiplication table
from 1 to 10 by step counting method.

X 1 2 3 4 5 6 7 8 9 10
11 4 8
2 6 12
33 15 27
48 24
5 15 50
6
7 14 42
88 56
9 36 90
10 20 70

Multiply two digit and three digit numbers by one digit number
without carrying

Study and learn
Multiply 43 by 2

4 3 Steps :
× 2 First multiply the ones digit by 2, 2 × 3 = 6
8 6 Then multiply the tens digit by 2, 2 × 4 = 8

Exercise - 5.3

A. Perform the following task:
23 34 20 41 60 45 53
×2 ×2 ×4 ×5 ×3 ×1 ×2

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

43 × 2 = 86 23 × 3 = 43 × 3 =
44 × 2 = 12 × 4 = 82 × 3 =
40 × 3 = 52 × 2 = 33 × 3 =

Prime Mathematics Book − 3 91

A. Study and learn:

Multiply 2 3 3 by 3
Steps :
233 • First multiply the digit of ones, 3 × 3 = 9
×3 • Then multiply the digit of tens, 3 × 3 = 9

699 • Finally multiply the digit of hundred, 3 × 2 = 6

Exercise - 5.4

B. Find the product of :

314 243 312 401 212
×2 ×2 ×3 ×3 ×4

423 503 610 423 720
×3 ×2 ×5 ×2 ×4

C. Find the product as shown:

213×2= 426 502×3= 304×2=
712×4=
2 3 4×2 = 423×3=

Multiplication of two digits numbers by one digit numbers with
carrying
Jadu lal, can you
multiply 46 by 2? Yes, sir ! I can multiply it.
I know the multiplication
table for 2.
Ok! Jadu lal.
Show your work

Steps:
• First multiply the digit of ones, 2 × 6 = 12 ones
T O 12 ones = 1 ten + 2 ones.

1 Write 2 in the column of ones place and carry over 1
46 ten to the tens place.

× 2 • Then multiply the digit of tens. 2 × 4 = 8 tens
92 8 tens + 1 ten = 9 tens.

Now, write 9 in tens place.

92 Prime Mathematics Book − 3

Exercise - 5.5

A. Perform the following task:

TO TO TO T O TO

35 39 46 35 38
×2 ×2 ×3 ×7 ×4

TO TO TO TO TO

47 65 76 39 47
×3 ×5 ×7 ×6 ×5

TO TO TO TO TO

63 73 84 24 33
×6 ×7 ×6 ×8 ×9

Multiplication of three digit numbers by one digit number with
carrying

Kritika! Can you multiply 3 6 4 by 3 ? Let’s try, sir!

Ok! carry Steps:
First multiply 4 ones by 3.
on • 3 × 4 ones = 12 ones = 1 ten + 2 ones
Write 2 in ones place and carry 1 ten to tens place.
HTO • Then multiply 6 tens by 3.
• 3 × 6 tens = 18 tens
11 18 tens + 1 ten (carry) = 19 tens
19 tens = 1 hundred + 9 tens.
364 Write 9 in tens place and carry 1 hundred to hundreds
×3 place.
Finally multiply 3 hundreds by 3.
1092 3 × 3 hundreds = 9 hundreds
9 hundreds + 1 hundred (carry) = 10 hundreds.
Write 10 hundreds in hundreds place.

Prime Mathematics Book − 3 93

Exercise - 5.6

A. Perform the following task:

247 164 253 343 354
×2 ×3 ×4 ×5 ×6

436 325 378 468 246
×3 ×5 ×4 ×2 ×7

B. Perform the following problems in your exercise book :

1. 48 × 3 2. 39 × 2 3. 74 × 4 4. 54 × 6

5. 72 × 8 6. 324 × 5 7. 352 × 7 8. 426 × 9

C. Learn the multiplication table of 11 and 12.

1 time 11 = 11 = 1 × 11 = 11 1 time 12 = 12 = 1 × 12 = 12

2 times 11 = 22 = 2 × 11 = 22 2 times 12 = 24 = 2 × 12 = 24

3 times 11 = 33 = 3 × 11 = 33 3 times 12 = 36 = 3 × 12 = 36

4 times 11 = 44 = 4 × 11 = 44 4 times 12 = 48 = 4 × 12 = 48

5 times 11 = 55 = 5 × 11 = 55 5 times 12 = 60 = 5 × 12 = 60

6 times 11 = 66 = 6 × 11 = 66 6 times 12 = 72 = 6 × 12 = 72

7 times 11 = 77 = 7 × 11 = 77 7 times 12 = 84 = 7 × 12 = 84

8 times 11 = 88 = 8 × 11 = 88 8 times 12 = 96 = 8 × 12 = 96

9 times 11 = 99 = 9 × 11 = 99 9 times 12 = 108 = 9 × 12 = 108

10 times 11 = 110 = 10 × 11 = 110 10 times 12 = 120 = 10 × 12 = 120

94 Prime Mathematics Book − 3

Multiplication of the numbers by 10, 100 and 1000

Let’s multiply the numbers Let’s try some more
by 10, 100 and 1000. problems.

First, we just multiply the numbers
without zeros, then write as many
zeros as the numbers have, to the right side.

3 × 10 = 3 tens = 30 4 × 10 = 40
5 × 100 = 5 hundreds = 500 32 × 100 = 3200
7 × 1000 = 7 thousands = 7000 23 × 200 = 4600
12 × 400 = 4800
From the examples, we remember the following points:
1. When a number is multiplied by 10, 20, 30, 40, 50, 60, 70, 80 and 90
we multiply the numbers by 1, 2, 3, 4, 5, 6, 7, 8 and 9 and put one
zero to the end of the product.
2. When a number is multiplied by 100, 200, 300, 400, 500, 600, 700, 800
and 900, we multiply the numbers by 1, 2, 3, 4, 5, 6, 7, 8 and 9 and
put two zeroes to the end of the product.
3. When a number is multiplied by 1000, 2000, 3000, 4000, 5000, 6000,
7000, 8000 and 9000, we multiply the given numbers by 1, 2, 3, 4, 5,
6, 7, 8 and 9 and put three zeroes to the end of the product.

Exercise - 5.7

A. Complete the following boxes:

2 × 10 = ....... 7 × 2000 = ....... 8 × 60 = .......

3 × 100 = ....... 52 × 600 = ....... 42 × 400 = .......

5 × 1000 = ....... 5 × 40 = ....... 12 × 3000 = .......

26 × 30 = .............. 23 × 200 = .............. 9 × 50 = ..............
4 × 20 = ....... 8 × 5000 = ....... 71 × 200 = .......
5 × 300 = 75 × 3000 = 125 × 100 =

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

20 40 50 30 400 700 5000
×30 ×60 ×70 ×80 ×70 ×50 ×30
600

Prime Mathematics Book − 3 95