Math 2

Now, H T O H T O H T O
5 6 8
+ 2 5 6 1 11
7 11 14
5 6 8 5 6 8
+ 2 5 6 + 2 5 6

7 12 4 8 2 4

Now, do you Yes, I understand. I can do
understand Dolma? such type of problems now.

Ok, let’s add 437 Thank you my sister.
and 286.

Very good H T O 7 ones + 6 ones = 13 ones
Dolma! 13 ones = 1 ten + 3 ones
1 1 1 ten + 3 tens + 8 tens = 12 tens
12 tens = 1 hundred + 2 tens
4 3 7
+ 2 8 6
6 11 13
6 12 3
7 2 3

See, feel and do.

1. Perform the following additions as shown in the example below:

11 2 7 5 5 3 5 4 7 6
+ 4 6 8 + 2 9 6 + 3 5 7
2 7 4
+ 3 5 9

5 12 13

6 33

3 9 5 3 6 8 4 6 3 7 2 3
+ 4 0 9 + 1 4 3 + 2 5 7 + 1 9 6

2 5 9 2 6 5 6 9 7 2 5 3
+ 6 8 7 + 4 6 8 + 1 3 8 + 3 7 9

Mathematics 2 Approved by CDC 101

2. Perform the following additions as shown in the example below:

11 2 5 6 3 3 9 6 2 6
3 4 3 2 4 8 1 7 2
3 6 2 + 2 3 2 + 1 2 1 + 1 3 5
2 5 4
+ 1 3 6
6 14 12

7 52

5 3 4 3 4 7 1 4 9 2 4 8
2 8 5 1 5 6 3 3 2 3 6 9
+ 1 1 4 + 2 4 9 + 4 6 4 + 2 5 7

3. Do the following sums as given in the example: 1

a) Ramu’s father spent Rs. 528 to buy books 5 2 8
and Rs. 247 to buy a school bag for Ramu. + 2 4 7
How much did he spend altogether? He spent
Rs. 775 altogether. 7 6 15
7 75
b) There are 238 boys and 226 girls in a school. +

How many students are there altogether in +

the school? There are students in the +

school.

c) Puran pays Rs. 525 for a pair of shoes and

Rs. 238 for a T-shirt. How much does he pay

altogether to buy these two items?

He pays to buy the things.

d) There are 278 pages in a maths book and 157

pages in an English book. How many pages

are there altogether in these two books?

There are pages altogether.

102 Approved by CDC Mathematics 2

4. Study the price list of the given items in a shop. Perform the
following questions as given in the example.

Items Price
Iron Rs. 375
Rice cooker Rs. 625
Plate Rs. 275
Thermos flask Rs. 485
Pressure cooker Rs. 578

Puran Tharu buys a rice cooker H T O
and a plate. How much money does
he pay for these items? 11

He pays Rs. 900 for both items. 6 2 5
+ 2 7 5

8 9 10

9 00

a) Pemba Sherpa wants to buy an Iron and a
thermos flask. How much money does he
pay for these two items?

He pays for these items.

b) Mohan Shrestha buys a plate and a
pressure cooker. How much money does
he pay for these items?

He pays for these items.

c) Rajendra buys an iron and a pressure
cooker. How much money does he pay for
these two items.

He pays for these items.

Mathematics 2 Approved by CDC 103

5.2 Subtraction

See, feel and learn. Yes, I know
teacher, there are
I give you 4 pencils only 12 pencils
out of 16 pencils from the left in the table.
table. How many pencils will

be there in the table?

–=

16 –4 = 12

I give you 5 apples Yes, I know
out of 20 apples from the teacher, there are
table. How many apples will
only 15 apples
be there in the table? left in the table.

–=

20 –5 = 15

104 Approved by CDC Mathematics 2

See, feel and do.

Subtract the following:

4 5 2 5 3 6 5 7 6 3
- 2 3 - 1 4 - 3 2 - 3 2 - 4 3

2 2 5 8 9 4 7 2
- 3 2 - 6 0 - 3 0
8 5 6 6
- 2 3 -3 4 8 8 7 8
- 3 4 - 5 4
8 5 6 6 5 8
- 2 3 -3 4 - 3 2

Subtraction of three digits numbers:

Hundred Tens Ones Hundred Tens Ones Hundred Tens Ones

–=

3 47 2 13 1 34

Symbolic subtraction

Hundred Tens Ones

347 – 213 = 134 3 47
Horizontal subtraction
–2 13

1 34

Vertical subtraction

Mathematics 2 Approved by CDC 105

1. Perform the following as given in the example.

4 7 5 = 4 hundreds + 7 tens + 5 ones
+ 2 ones
– 2 4 2 = - 2 hundreds + 4 tens + 3 ones
2 3 3 = 2 hundreds + 3 tens

= 200 + 30 + 3

= 233

Steps:

• First subtract the digits of ones. 5 – 2 = 3
• Then subtract the digits of tens. 7 – 4 = 3
• Subtract the digits of hundreds. 4 – 2 = 2
• Finally it is written as : 233

5 6 4 = hundreds + tens + ones
– 3 4 1 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

7 5 8 = hundreds + tens + ones
– 4 2 3 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

9 6 8 = hundreds + tens + ones
– 4 3 6 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

9 6 8 = hundreds + tens + ones
– 4 3 6 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

106 Approved by CDC Mathematics 2

5 6 4 = hundreds + tens + ones
– 3 4 1 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

7 5 8 = hundreds + tens + ones
– 4 2 3 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

5 6 4 = hundreds + tens + ones
– 3 4 1 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

7 5 8 = hundreds + tens + ones
– 4 2 3 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

9 6 8 = hundreds + tens + ones
– 4 3 6 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

9 6 8 = hundreds + tens + ones
– 4 3 6 = - hundreds + tens + ones
= hundreds + tens + ones
= + +
=

Mathematics 2 Approved by CDC 107

2. Perform the following subtractions:

HTO 5 8 7 HTO 6 5 9
587 - 3 2 5 659 - 4 3 6
–3 2 5 –4 3 6
262 2 6 2 223 223

HTO 8 2 9 HTO 7 5 4
829 - 5 0 3 754 - 2 3 1
–5 0 3 –2 3 1

HTO 6 8 7 HTO 9 3 7
687 - 3 2 5 937 - 7 1 5
–3 2 5 –7 1 5

HTO 6 8 7 HTO 9 3 7
687 - 3 2 5 937 - 7 1 5
–3 2 5 –7 1 5

HTO 6 8 7 HTO 9 3 7
687 - 3 2 5 937 - 7 1 5
–3 2 5 –7 1 5

HTO 6 8 7 HTO 9 3 7
687 - 3 2 5 937 - 7 1 5
–3 2 5 –7 1 5

108 Approved by CDC Mathematics 2

Relation between addition and subtraction

See, feel and learn.

Lakhan, how many books I have 8 books
do you have? Please, bring teacher and
here in the table with my 12
altogether becomes
books. 20 books in the table.

12 +8 = 20

After school you have to take
your books from the table.

Okey sir, I have taken
and your 12 books
are left in the table.

20 –8 = 12 16
+9 16 +7

–7 –9

7 + 9 = 16 9 + 7 = 16

16 – 7 = 9 16 – 9 = 7

Mathematics 2 Approved by CDC 109

3. Perform the following task:

32 + 6 = 38 38 – 6 = 32 38 – 32 = 6
45 + 4 = 49 – 4 = 49 – 45 =
62 + 7 = 69 – 7 = 69 – 62 =

2 3 6 5 4 3 2 6 4 7 6 4 7
+ 4 2 - 2 3 + 2 1 5 - 2 1 5 - 4 3 2

4. Do the following sums as given in the example: 2 9
– 1 2
There are 29 apples in a basket. 12 of them are
rotten. Find the number of good apples in the 1 7
basket?
The number of good apples are 17 .

There are 35 students in class two. 14 of them are 3 5
– 1 4
girl. What is the number of boy students?
1 7
The number of boys are .

Adrash had Rs. 75. He bought a packet of one

dozen pencils for Rs. 52. How money is left with

him?

He has left .

A person bought a book and a geometric box 4 7 5
- 2 4 5
for Rs. 475. If the price of the book is Rs. 245,

what is the price of the geometric box?

The price of the geometric box is .

110 Approved by CDC Mathematics 2

A boy had 348 marbles in his collection. He lost 3 4 8
- 2 3 5
235 of them. How many marble are with him?

He has marble with him.

Aftapha had Rs. 345. He bought a T-shirt for

Rs. 230. How much moeny does he have? ­_

He has left .

Anima bought a school bag and books for Rs. 6 2 5
- 4 1 0
625. If the price of the books is Rs. 410, what

is the price of the school bag?

The price of the school bag is .

Subtraction of two digit number
with borrowing

Study and learn.

Siru, can you subtract Yes mam!
27 from 42? I can subtract it.

Ok, let’s start. 4 2
- 2 7
No, It is incorrect. Can
you subtract 7 ones 2 5
from 2 ones? It is 25

No, we can not subtract
7 ones from 2 ones.

Mathematics 2 Approved by CDC 111

Ok, you know that 1 ten means 10 ones.
So, you should borrow 1 ten from 4 tens to 2 ones.
Then there will be 10 ones and 2 ones equal to 12 ones.

Now, I can subtract 7 ones from 12 ones.
12 ones - 7 ones = 5 ones.

Good. Now how many
tens are left in 4 tens?

T O There are 3 tens left in 4 tens.
1 ten 2 tens can be subtracted from 3 tens.
3 12 = 10 ones

4 2
- 2 7

1 5

See, feel and do.

1. Perform the following additions as given in the example:
Subtract 38 from 54.

TO 1 ten = 10 ones

4 14

5 4 = 5 tens + 4 ones = 4 tens + 14 ones
- 3 8 = 3 tens + 8 ones = - 3 tens + 8 ones

16 = 1 ten + 6 ones
= 10 + 6 = 16

TO 1 ten = 10 ones

4 2= tens + ones = tens + ones
-1 7 = tens + ones =- tens + ones

= ten + ones
= +=

112 Approved by CDC Mathematics 2

T O 1 ten = 10 ones

4 2= tens + ones = tens + ones
-1 7 = tens + ones =- tens + ones
=
= ten + ones
+=
=
TO 1 ten = 10 ones =-
=
4 2= tens + ones = tens + ones
-1 7 = tens + ones tens + ones
=
=- ten + ones
= +=
=
TO 1 ten = 10 ones
=
7 5= tens + ones =- tens + ones
-4 9 = tens + ones = tens + ones
=
ten + ones
+=

TO 1 ten = 10 ones

6 4= tens + ones tens + ones
-2 7 = tens + ones tens + ones

ten + ones
+=

2. Perform the following substraction as given in the example.

1 15 47 – 9 4 7 98 – 9 9 8
= - 9 = - 9
25 – 7 2 5
= 18 - 7
1 8

Mathematics 2 Approved by CDC 113

54 – 5 5 4 63 – 7 6 3 33 – 6 3 3
= - 5 = - 7 = - 6

3. Do the following substraction as given in the example:

T O T O T O T O

3 12 3 1 2 2 4 3
- 1 5 - 1 8 - 2 7
4 2
- 1 8

2 4

T O T O T O T O

6 2 7 4 8 3 9 2
- 2 8 - 3 6 - 5 8 - 4 9

T O T O T O T O

6 7 8 4 6 1 5 4
- 3 9 - 2 7 - 4 5 - 2 7

4. Do the following sums as in given example:

There are 42 eggs in a basket. 28 of them 3 12
are broken. How many good eggs are left in
the basket? 4 1 2 (+10)
There are 14 good eggs left. – 2 8

1 4

Mohan had Rs. 55. He bought a pen for Rs. 38.

How much money is left with him? 5 5
– 3 8
He has left.

114 Approved by CDC Mathematics 2

There are 32 students in a class. 18 of

them were absent yesterday. How many 3 2
– 1 8
students were present yesterday?

There are students were present.

Mohan had 72 sweets. He distributed 45

sweets out of them among his friends. How 7 2
– 4 5
many sweets are left with him?

He has left sweets now.

A shopkeeper bought 65 mathematics

books of class two in his shop. He sold 6 5
– 4 8
48 books out of them. How many books

are left in his shop?

There are books left in his shop.

5. Do the following sums as in given example:

1 5 8 1 6 6 1 4 9 1 6 8
- 1 3 - 2 4 - 3 6 - 4 1
1 4 5
3 2 4 4 3 5 5 2 7
2 7 6 - 2 4 - 3 2 - 1 5
- 2 4

5 6 7 3 3 3 4 3 5 3 6 8
- 1 3 - 2 1 - 2 5 - 5 2

8 9 7 9 8 6 3 4 5 5 6 7
- 3 2 7 - 2 8 6 - 1 4 2 - 1 6 1

Mathematics 2 Approved by CDC 115

Subtraction of three digits numbers with
borrowing to ones place

Study and learn.

Let me subtract 253 from 481

H T O Step 1 : Look at the ones place.
Step 2 : The number 1 in ones place is smaller than 3.
7 11
So, borrow 1 ten from the tens place and add
4 8 1 1(+ 10)
it to the ones place number (10 + 1 = 11).
- 2 5 3
Step 3 : Subtract, 11 – 3 = 8, subtract 1 ten from 8
2 2 8
tens, then subtract 5 tens from 7 tens,

7 – 5 = 2.

Step 4 : Subtract hundred place digits

4 – 2 = 2.

See, feel and do.

Perform the following subtractions:

H T O H T O H T O H T O
6 7 4
5 12 3 5 3 4 6 5 - 4 5 9
- 3 6 - 1 2 8
5 6 2 H T O
- 3 7 8 8 2
- 2 4 6
3 2 5

H T O H T O H T O

5 9 6 7 6 4 8 5 3
- 2 7 9 - 4 3 8 - 5 3 7

H T O H T O H T O H T O

2 7 1 3 5 4 4 5 2 6 2 1
- 2 4 - 3 6 - 1 3 6 - 1 7

116 Approved by CDC Mathematics 2

Subtraction of three digits numbers with
borrowing to tens place

Study and learn.

Let me subtract 462 from 625

H T O Step 1 : Look at the ones place. 5 is greater than 2.
So, we don’t need to borrow from tens place.
5 12 Simply we subtract 2 from 5.

6 1 2 5 Step 2 : Look at the tens place. 2 is smaller than 6.
- 4 6 2 So, we borrow 1 hundred from the hundred
place and add it to the tens place. We know
1 6 3 that 1 hundred = 10 tens. So, 10 tens + 2
tens = 12 tens.

And deduct 1 hundred in the hundred place.
Step 3 : Then subtract 5 – 2 = 3, 12 – 6 = 6 and

5 – 4 = 1.

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

HT O 1 hundred = 10 tens

6 12 6 = 7 H+ 2 T+ 6 O = 6 H + 12 T + 6O
4 = 4 H+ 5 T+ 4 O= – 4 H+ 5 T+ 4O
7 12 2 2O
–4 5 = 2 H+ 7 T+ 2= 272
= 200 + 70 +
27

H T O 1 hundred = 10 tens

8 2 7 = H+ T+ O= H+ T+ O
– 4 6 5 = H+ T+ O= – H+ T+ O
= H+ T+ O
= ++ =

Mathematics 2 Approved by CDC 117

H T O 1 hundred = 10 tens

6 3 8 = H+ T+ O= H+ T+ O
– 2 7 5 = H+ T+ O= – H+ T+ O
= H+ T+ O
= ++ =

H T O 1 hundred = 10 tens

5 4 6 = H+ T+ O= H+ T+ O
– 2 8 2 = H+ T+ O= – H+ T+ O
= H+ T+ O
= ++ =

H T O 1 hundred = 10 tens

8 3 9 = H+ T+ O= H+ T+ O
– 5 8 7 = H+ T+ O= – H+ T+ O
= H+ T+ O
= ++ =

2. Perform the following subtractions as given in the example.

H T O H T O H T O H T O

4 14 6 3 7 4 2 5 6 4 9
- 2 8 5 - 1 5 2 - 3 7 5
5 4 6
- 2 9 4

2 5 2

H T O H T O H T O H T O

8 3 5 7 5 6 6 2 7 9 4 3
- 6 7 3 - 2 8 4 - 3 6 4 - 6 8 3

H T O H T O H T O H T O
6 7 2
- 2 9 1 9 2 4 8 6 7 7 3 1
- 6 7 3 - 3 9 5 - 5 5 1
118
Approved by CDC Mathematics 2

Subtraction of three digit numbers with borrowing
to both places (tens and ones)

Study and learn.

Let me subtract 347 from 524

H T O Step 1 : Look at ones place.

11 (+10) Step 2 : The number 4 in ones place is smaller than
4 1 14 7. So, we borrow 1 ten from the tens place

1H 1T

5 2 4 (+10) and add it to the ones place number (10 + 4
- 3 4 7 = 14). Deduct 1 ten in the tens place (2 – 1
= 1).
1 7 7 Step 3 : Now the number of tens place is 1 which is

smaller than the number 4 of tens place. So, we borrow 1 hundred

from the hundred place and add it to the tens place number (10 +

1 = 11 tens). Deduct 1 hundred in the hundreds place (5 – 1 = 4).

Step 4 : Then subtract 14 – 7 = 7, 11 – 4 = 7 and 4 – 3 = 1

Step 5 : The answer is 177.

1. Perform the following as given in the example:

11
4 1 131H = 10T
H T O 1T = 10 H T O 1H = 10T 1T = 10
5 2 3 6 3 4
- 2 4 6 = 5 H+ 2 T+ 3 O - 2 5 8 = H+ T+ O
=– H± T± O
=– 2 H ± 4 T ± 6 O

2 7 7 2 H+ 7 T+ 7 O H+ T+ O

= 200 + 70 + 7 = ++

= 277 =

H T O = 1H = 10T 1T = 10 O H T O = 1H = 10T 1T = 10 O
7 2 5 =– O 8 5 6 =– O
- 4 5 8 H+ T+ - 3 6 9 H+ T+
H± T± H± T±

H+ T+ O H+ T+ O

= ++ = ++

==

Mathematics 2 Approved by CDC 119

H T O = 1H = 10T 1T = 10 O H T O = 1H = 10T 1T = 10 O
7 4 5 =– O 8 5 2 =– O
- 4 8 7 H+ T+ - 5 8 7 H+ T+
H± T± H± T±

H+ T+ O H+ T+ O

= ++ = ++

==

2. Subtract the following:

H T O H T O H T O H T O

3 11 (+10) (+10) 5 3 5 6 4 3 7 3 2
1 13 - 2 4 6 - 3 6 8 - 4 5 6

4 1 2 1 3 H T O H T O

- 2 5 6

1 6 7

H T O H T O

5 1 3 4 2 4 8 3 5 7 2 4
- 2 6 5 - 1 4 5 - 4 7 8 - 3 5 6

H T O H T O H T O H T O

6 3 5 8 4 3 5 2 3 7 5 2
- 3 8 7 - 5 7 5 - 2 4 7 - 3 8 4

H T O H T O H T O H T O

6 3 5 8 4 3 5 2 3 7 5 2
- 3 8 7 - 5 7 5 - 2 4 7 - 3 8 4

120 Approved by CDC Mathematics 2

Word problems on subtraction of three digit
numbers with borrowing

3. Do the following sums as given in the example:

a) A man earns Rs. 435 and spends Rs. 258 12
in a day. How much money does he save in 3 2 15
a day?
4 3 5 (+10)
He saves Rs. 177 in a day.
- 2 5 8

1 7 7

b) Gita has Rs. 475. She gives Rs. 238 to her 4 7 5
- 2 3 8
sister Rita. How much money does she have

now?

She has left now.

c) There are 527 students in a school. 265 of 5 2 7
- 2 6 5
them are boys. How many of them are girls?

There are girls.

d) There were 545 books in a library. 258 of

them were Nepali books. The rest of them

were English books. How many English books

were there?

There were English books.

e) Ram had Rs. 650 in his purse. When he went

for shopping, he spent Rs. 456. How much

money does he have now?

He has left.

Mathematics 2 Approved by CDC 121

5.3 Multiplication

See, feel and learn.

1 +1 = 2 1 is repeatedly added 2 times.
We write, 1 + 1 = 2
(i.e. 1 × 2 = 2)

Oh, I understand multiplication is repeated
addition of same number.

2 is repeatedly added 2 times.
We write 2 + 2 = 4

Symbol of multiplication.
2×2=4

+=

2 is repeatedly added 3 times.
We write, 2 + 2 + 2 = 6
(i.e. 2 × 3 = 6)

122 Approved by CDC Mathematics 2

What is the meaning of

2 + 2 + 2 + 2, Ram? It means, 2 is repeated

4 times. It is repeated

addition.

Ram, the repeated addition is

called multiplication.

So, can you write it multiplication

form? Yes, I can write it.

2 + 2 + 2 + 2 = 4 times 2

Good, you know that. = 4 × 2

Complete the boxes below.

1 + 1 + 1 =3
1× 3 = 3

+ = 123
× =

Mathematics 2 Approved by CDC

++=
×=

+ +=
×=

2×1= 2 2
2×2= ×1
2×3=
2
2
×2

2
×3

124 Approved by CDC Mathematics 2

Mathematics 2 2×4= 2
2×5= ×4
2×6=
2×7= 2
2×8= ×5
2×9=
2 × 10 = 2
×6
Approved by CDC
2
×7

2
×8

2
×9

2
× 10

125

Observe the number line and complete :

Jumping by 2.

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

Jumping by 3.

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

Jumping by 4.

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

Jumping by 5.

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

Observe the table and colour the numbers starting from 2 and every
second number. [Multiplication table of 2]

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

126 Approved by CDC Mathematics 2

Starting from 3 and every third number. [Multiplication of 3] 10
123456789 20
11 12 13 14 15 16 17 18 19 30
21 22 23 24 25 26 27 28 29 40
31 32 33 34 35 36 37 38 39 50
41 42 43 44 45 46 47 48 49 60
51 52 53 54 55 56 57 58 59 70
61 62 63 64 65 66 67 68 69 80
71 72 73 74 75 76 77 78 79 90
81 82 83 84 85 86 87 88 89 100
91 92 93 94 95 96 97 98 99

Starting from 4 and every fourth number. [Multiplication of 4]
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Mathematics 2 Approved by CDC 127

Starting from 5 and every fifth number. [Multiplication of 5] 10
123456789 20
11 12 13 14 15 16 17 18 19 30
21 22 23 24 25 26 27 28 29 40
31 32 33 34 35 36 37 38 39 50
41 42 43 44 45 46 47 48 49 60
51 52 53 54 55 56 57 58 59 70
61 62 63 64 65 66 67 68 69 80
71 72 73 74 75 76 77 78 79 90
81 82 83 84 85 86 87 88 89 100
91 92 93 94 95 96 97 98 99

Multiplication Table 1 to 5

1×1 =1 2×1 =2 3×1 =3 4×1 =4 5×1 =5
1 × 2 = 2 2 × 2 = 4 3 × 2 = 6 4 × 2 = 8 5 × 2 = 10
1 × 3 = 3 2 × 3 = 6 3 × 3 = 9 4 × 3 = 12 5 × 3 = 15
1 × 4 = 4 2 × 4 = 8 3 × 4 = 12 4 × 4 = 16 5 × 4 = 20
1 × 5 = 5 2 × 5 = 10 3 × 5 = 15 4 × 5 = 20 5 × 5 = 25
1 × 6 = 6 2 × 6 = 12 3 × 6 = 18 4 × 6 = 24 5 × 6 = 30
1 × 7 = 7 2 × 7 = 14 3 × 7 = 21 4 × 7 = 28 5 × 7 = 35
1 × 8 = 8 2 × 8 = 16 3 × 8 = 24 4 × 8 = 32 5 × 8 = 40
1 × 9 = 9 2 × 9 = 18 3 × 9 = 27 4 × 9 = 36 5 × 9 = 45
1 × 10 = 10 2 × 10 = 20 3 × 10 = 30 4 × 10 = 40 5 × 10 = 50

128 Approved by CDC Mathematics 2

Multiplication Table of 6

See, feel and do.

1. Count and write: (Mulipliction is the repeated addition.)

6= 6
1 group of 6 = 6
1 time 6 = 1 × 6 = 6
6 one is 6

6+6=
2 groups of 6 =
2 times 6 = 2 × 6 =

6 twos are

6+6+6=
3 groups of 6 =
3 times 6 = 3 × 6 =

6 threes are

6+6+6+6=
4 groups of 6 =
4 times 6 = 4 × 6 =

6 fours are

Mathematics 2 Approved by CDC 6+6+6+6+6=
5 groups of 6 =

5 times 6 = 5 × 6 =
6 fives are

129

6+6+6+6+6+6=
6 groups of 6 =

6 times 6 = 6 × 6 =
6 sixs are

6+6+6+6+6+6+6=
7 groups of 6 =

7 times 6 = 7 × 6 =
6 sevens are

6+6+6+6+6+6+6+6=
8 groups of 6 =

8 times 6 = 8 × 6 =
6 eights are

6+6+6+6+6+6+6+6+6=
9 groups of 6 =

9 times 6 = 9 × 6 =
6 nines are

6+6+6+6+6+6+6+6+6+6=
10 groups of 6 =

10 time 6 = 10 × 6 =
6 tens are

130 Approved by CDC Mathematics 2

2. Write the multiples of 6 that come after the following numbers:

6 12
18 24
30
48
12 18
42

3. Fill in the boxes as shown in the example below:

3 × 6 = 18 5×6= 2×6=
7×6= 1×6= 4×6=
6×6= 9×6= 8×6=

4. Colour every sixth boxes in the given table below starting at 6
to find the multiples of 6.

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
Now write all the coloured numbers in the boxes given below.

6 12

Mathematics 2 Approved by CDC 131

Multiplication Table of 7

See, feel and do. 7= 6
1 group of 7 = 6
1. Count and write: 1 time 7 = 1 × 7 = 6

7 one is 6

7+7=
2 groups of 7 =
2 times 7 = 2 × 7 =

7 twos are

7+7+7=
3 groups of 7 =
3 times 7 = 3 × 7 =

7 threes are

7+7+7+7=
4 groups of 7 =
4 times 7 = 4 × 7 =

7 fours are

7+7+7+7+7=
5 groups of 7 =

5 times 7 = 5 × 7 =
7 fives are

132 Approved by CDC Mathematics 2

7+7+7+7+7+7=
6 groups of 7 =

6 times 7 = 6 × 7 =
7 sixs are

7+7+7+7+7+7+7=
7 groups of 7 =

7 times 7 = 7 × 7 =
7 sevens are

7+7+7+7+7+7+7+7=
8 groups of 7 =

8 times 7 = 8 × 7 =
7 eights are

7+7+7+7+7+7+7+7+7=
9 groups of 7 =

9 times 7 = 9 × 7 =
7 nines are

7+7+7+7+7+7+7+7+7+7=
10 groups of 7 =

10 time 7 = 10 × 7 =
7 tens are

Mathematics 2 Approved by CDC 133

2. Colour every seventh boxes in the given table below starting at
7 to find the multiples of 7.

1 2 3 4 5 6 7 8 9 10
11 1 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Now write all the coloured numbers in the boxes given below.

7 14

3. Write the multiples of 7 that come after the following:

7 14 42

21 35 56

4. Fill in the boxes as shown.

2 × 7 = 14 4 × 7 = 10 × 7 =
8 × 7 = 9 × 7 = 6×7 =
3 × 7 = 5 × 7 = 7×7 =

134 Approved by CDC Mathematics 2

5. Match the following: B

A 4×7
10 × 7
7 5×7
7 + 7 + 7 3×7
7 + 7 + 7 + 7 + 7 + 7 + 7 7×7
7 + 7 8×7
7+7+7+7 1×7
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 6×7
7 + 7 + 7 + 7 + 7 + 7 2×7
7 + 7 + 7 + 7 + 7 + 7 + 7 + 7
7 + 7 + 7 + 7 + 7

Multiplication Table of 8

6. Colour every eighth boxes in the given number table to find the
multiples of 8 starting from 8.

1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100

Mathematics 2 Approved by CDC 135

7. Perform the following multiplication:

3×0 = 5×0 = 2×0 =
7×0 = 0×9 = 4×0 =
1×0 = 6×0 = 0 × 10 =

Multiplication of a single digit by 0 and 10

X 0 10 When two numbers are
1 0 10 multiplied, the result is called
2 0 20
3 0 30 the product.The numbers
4 0 40 are called the factors of the
5 0 50
product.

6 0 60 Let’s multiply 4 by 6.
7 0 70 4 × 6 = 24
8 0 80 24 is the product of 4 and 6.
9 0 90 4 and 6 are the factors of 24.

See, feel and learn.

Multiplication table of 6 to 10.

6×1=6 7×1=7 8×1=8 9×1=9 10 × 1 = 10
6 × 2 = 12 7 × 2 = 14 8 × 2 = 16 9 × 2 = 18 10 × 2 = 20
6 × 3 = 18 7 × 3 = 21 8 × 3 = 24 9 × 3 = 27 10 × 3 = 30
6 × 4 = 24 7 × 4 = 28 8 × 4 = 32 9 × 4 = 36 10 × 4 = 40
6 × 5 = 30 7 × 5 = 35 8 × 5 = 40 9 × 5 = 45 10 × 5 = 50
6 × 6 = 36 7 × 6 = 42 8 × 6 = 48 9 × 6 = 54 10 × 6 = 60
6 × 7 = 42 7 × 7 = 49 8 × 7 = 56 9 × 7 = 63 10 × 7 = 70
6 × 8 = 48 7 × 8 = 56 8 × 8 = 64 9 × 8 = 72 10 × 8 = 80
6 × 9 = 54 7 × 9 = 63 8 × 9 = 72 9 × 9 = 81 10 × 9 = 90
6 × 10 = 60 7 × 10 = 70 8 × 10 = 80 9 × 10 = 90 10 × 10 = 100

136 Approved by CDC Mathematics 2

Complete the following multiplication table:

X 1 2 3 4 5 6 7 8 9 10

1 1 4 7 10

22 6 12 18

36 15 24 30

44 12 28

5 10 30 45

66 24 48 60

7 14 35 63

88 32 64

9 27 54 90

10 20 50 80

Multiplication of two digit number by
a single digit number

Study and learn:

To multiply 23 by 2. First multiply the digit of
ones place 2 × 3 = 6
23
×2 Then multiply the digit of
46 tens place 2 × 2 = 4
The product is 46

Mathematics 2 Approved by CDC 137

See, feel and do.

1. Perform the following multiplication:

TO TO TO TO TO
24 32 21 43 12
×2 ×3 ×4 ×2 ×3

TO TO TO TO TO
34 22 33 31 23
×2 ×4 ×3 ×3 ×3

Let’s multiply 34 by 2

34 = 3 tens + 4 ones

× 2 ×2
68 6 tens + 8 ones

2. Perform the following task:

43 = tens + ones 23 = tens + ones
ones ones
× 2 × × 3 ×
tens + tens +

21 = tens + ones 32 = tens + ones
× 4 ones ones
× × 3 ×
tens + tens +
138
Approved by CDC Mathematics 2

31 = tens + ones 20 = tens + ones
× 3 ones × 4 ones
× ×
tens + tens +
14 = 42 =
× 2 tens + ones × 2 tens + ones
ones ones
× ×
tens + tens +

Multiplication of three digit number by a
single digit number:

Study and learn. O 1 × 3 = 3
T 2 × 3 = 6
To multiply 321 by 3. H 3 × 3 = 9

321
×3

963

To multiply 234 by 2.

234 = 2 hundreds + 3 tens + 4 ones

× 2 ×2
468
4 hundreds + 6 tens + 8 ones

Mathematics 2 Approved by CDC 139

See, feel and learn.

1. Perform the following multiplication:

H T O H T O H T O H T O
2 3 4 3 1 2 2 0 2 3 1 2
× 2 × 2 × 3 × 3

H T O H T O H T O H T O
2 1 0 1 1 1 2 2 1 1 1 0
× 4 × 5 × 4 × 6

2. Perform the following task:

132 = hundreds + tens + ones
ones
× 3 ×
= hundreds + tens +

122 = H + T + O 212 = H+ T+ O

× 3 × × 4 ×
= H+ T+ O
H + T + O =

423 = H + T + O 443 = H+ T+ O

× 2 × × 2 ×
= H+ T+ O
H + T + O =

323 = H + T + O 232 = H+ T+ O
× 3
= × × 3 ×
H+ T+ O
140 H + T + O =

Approved by CDC Mathematics 2

Multiplication of two digit number by one digit
number by carrying over:

Study and learn.

Maya, can you multiply The product of 24
24 by 4? by 4 is 816.

Ok, show 24 Yes, Ma'am
your work. ×4 Maya
8 16
No, it’s wrong,
look at the following method.

1 16

2 4 = 2 tens + 4 ones
× 4 × 4
9 6 8 tens + 16 ones
= 8 tens + 1 ten + 6 ones
= 9 tens + 6 ones
= 90 + 6
= 96

Process:
* First multiply the digit of ones by 4.
4 × 4 = 16 = 1 ten + 6 ones

* 1 ten carry over the digit of tens place.

* Multiply the digit of tens by 4.
4×2=8
8 tens + 1 ten = 9 tens

Mathematics 2 Approved by CDC 141

See, feel and do.

Perform the following task as shown above in the example.

2 6 = tens + ones 2 9 = tens + ones

× 2 × ones × 3 × ones
ones ones
= tens + ones = tens + ones

= tens + = tens +

= tens + = tens +

= + = +

= =

4 7 = tens + ones 3 4 = tens + ones

× 4 × ones × 6 × ones
ones ones
= tens + ones = tens + ones

= tens + = tens +

= tens + = tens +

= + = +

= =

6 4 = tens + ones 3 6 = tens + ones

× 5 × ones × 4 × ones
ones ones
= tens + ones = tens + ones

= tens + = tens +

= tens + = tens +

= + = +

= =

142 Approved by CDC Mathematics 2

Multiplication by carrying over in
short cut method

Study and learn.

Maya, can you multiply Let've, try Ma'am. Of courses
26 by 3 in short cut Ma'am
method? 1

Ok, do 26
your work. ×3
78

Steps:
* First multiply the digit of ones.
3 × 6 = 18 = 1 ten + 8 ones.
* Write 8 ones in column of ones place and 1 ten

carry in the column of tens place.
* Multiply the digit of tens.
3 × 2 = 6 tens
Then add 6 tens + 1 ten = 7 tens

Oh, I understand now. Ok, multiply 46
Let me try one more by 6.

problem. Good, you now can
perfectly multiply two
3 digit number by one digit

46 by carrying over.
×6
276

Mathematics 2 Approved by CDC Mam

143

1. Multiply 38 54 74 63 66
×7 ×6 ×4 ×6 ×5
36 45
×4 ×6

74 39 43 99 45 55 64
×8 ×6 ×5 ×3 ×6 ×7 ×5

2. Multiplication of three digit number by one digit number by
carrying over:

To multiply 158 by 4. Remember:

2 3 1 ten = 10 ones

158 = 1 H+ 5 T+ 8 O 1 hundred = 10 tens

×4 × 4 O

632 = 4 H + 20 T + 32 O

= 4 H + 20 T + 3 T + 2 O [∴32 ones = 3 tens

= 4 H + 23 T + 2 O + 2 ones]

= 4 H + 2 H + 3 T + 2 O [∴23 tens = 2 hundred

= 6 H+ 3 T+ 2 O + 3 tens]

= 600 + 30 + 2 O = 632

3. Multiply and complete the following:

456 = H+ T+ O O
×6 ×O O

= H+ T+ O Mathematics 2
= H+ T+ T+
= H+ T+ O
= H+ H+ T+
= H+ T+ O
=
+ + O=
144
Approved by CDC

456 = H+ T+ O
×4 × O

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

473 = H+ T+ O
×9 × O

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

Multiplication by carrying over short cut method:

To multiply 143 by 4. 11
Steps:
143
* First multiply the digit of ones place. ×4

3 × 4 = 12 ones = 1 ten + 2 ones. 572

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

place.

* Then multiply the digit of tens place.

4 × 4 = 16 tens

16 tens + 1 ten = 17 tens

= 1 hundred + 7 tens

* Write 7 in the column of tens place and carry 1 hundreds over to

hundreds place.

* Last multiply the digit of hundred place.

4 × 1 = 4 hundred

4 hundreds + 1 hundred = 5 hundreds

* Write 5 in the column of hundreds.

Mathematics 2 Approved by CDC 145

See, feel and do.

1. Perform the following multiplication:

11 164 258 384 546
×3 ×5 ×7 ×4
275
×2 567 246
×5 ×7
550

723 463 347
×9 ×8 ×3

176 285 734 842 372
×8 ×4 ×6 ×9 ×7

2. Word problems on multiplication without carrying over.

A cat has 4 legs. How many legs do 6 cats have? 6
6 cats have 24 legs. ×4

The price of one apple is Rs. 8. What is the price of 7 apples?

The price of 7 apples is . ×

146 Approved by CDC Mathematics 2

The cost of one pen is Rs. 20.
What is the cost of 4 pens?

The cost of 4 pens is . ×

4 students can sit on one ×
bench. How many students
can sit on 13 benches? ×

students can sit on 13 benches. 3

There are 232 mangoes 46
in a basket. How many ×6
mangoes are there in 3 276
baskets?
×
There are mangoes.
147
3. Word problems on multiplication with carrying.

The cost of 1 kg tomatoes is Rs. 46. What
is the cost of 6 kg of tomatoes?

The cost of 1 kg of tomatoes = Rs. 46
The cost of 6 kg of tomatoes = Rs. 46 × 6
= Rs. 276

The cost of 1 kg of apples is Rs. 85. What
is the cost of 7 kg of apples?

The cost of 1 kg of apples = Rs. ×
The cost of 7 kg of apples = Rs.
= Rs.

Mathematics 2 Approved by CDC

There are 24 pencils in a packet. How ×
many pencils are there in 8 packets?

In 1 packet = pencils
In 8 packet = pencils ×
= pencils

Dorje spends Rs. 95 every day. How much ×
money does he spend in 9 days?
×
The money Dorje spends in 1 day = Rs.
The money Dorje spends in 9 days =Rs.
=Rs.

There are 150 pages in a book. How many pages will
be there in 5 same type of book?

Number of page in a book = Rs. ×

Number of books = Rs.
Total pages = Rs. × =

Arif has 4 friends. Each friends give him
Rs. 230 How much money has Arif?

Number of friends = Rs. ×
Money given by each = Rs.

Total money = Rs. × =

Salma earns Rs. 525 in a day. How much
earns by her in a week?

Income of a day = Rs. ×
=
No. of days in a week = Rs. ×
Total income = Rs. Mathematics 2

148 Approved by CDC

5.4 Division

Study and learn. How, ........, ?
Harish
Lakhan, I have six chocolates.
Can you distribute them in two

equal parts?

• 6 chocolates are distributed equally among Harish and Lakhan. Each
of them gets 3 chocolates.

• 6 chocolates divide into 2 equal parts means 6 is divided by 2, i.e. 3
• Mathematically, 6 ÷ 2 = 3
• In mathematics, the symbol (÷) denotes 'divided by'.

Lakhan, can you make Of course,
5 equal groups of 15 I can.

pencils? There are 3 pencils
in each group.

Well done, Lakhan! I understand
You know that, 15 is divided into 5 very well Sir.
equal parts that means 15 is divided
149
by 5. It is written as 15 ÷ 5 = 3

Mathematics 2 Approved by CDC

See, feel and learn.

1. Complete the following as shown below in the example:
Divide into 4 equal parts 12 ÷ 3 = 4
Divide into 3 equal parts 18 ÷ =
Divide into 5 equal parts ÷ =

Divide into 6 equal parts ÷ =
Divide into 3 equal parts ÷ =
2. Complete the following:

2 pencils + 2 pencils + 2 pencils + 2 pencils 8 ÷ 2 = 4

4 books + 4 books + 4 books ÷=

150 Approved by CDC Mathematics 2