Math 3

See, feel and do.

Perform the following problems:

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

Th H T O Th H T O Th H T O
6 8 3 5 5 4 3 6 4 3 7 5
− 4 5 1 3 − 2 4 1 5 − 2 0 5 4

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

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

Subtraction of 4 digit numbers with borrowing

See, feel and learn.

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

Yes, Jeena
you can try.

Mathematics 3 Approved by CDC 151

6 12 I think it is same as the
subtraction of 3 digit
Th H T O number, isn’t it Sir ?
4 5 7 2
− 2 3 4 7 Steps:
• 7 can’t be subtracted from 2. So, 2 can
2 2 2 5
borrow 1 ten from 7 tens.
∴ 1 ten + 2 ones = 12 ones
12 ones − 7 ones = 5 ones
• 7 tens has left 6 tens
• 6 tens − 4 tens = 2 tens
• 5 hundreds − 3 hundreds = 2 hundreds
• 4 thousands − 2 thousands = 2 thousands.

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

Jeena, can you subtract Yes, sir! I can.
3469 from 8652?
Let me try.
14
5 4 12

Th H T O
8 6 5 2
−3 4 6 9
5 1 8 3

152 Approved by CDC Mathematics 3

Step:
• First we subtract the digit of ones place. But 9 can’t be subtracted from 2.

So, 2 borrows 1 ten from 5 tens.
∴ 1 ten + 2 ones = 12 ones
12 ones − 9 ones = 3 ones
• Now, 5 tens has left 4 tens. But 6 tens can’t be subtraced from 4 tens. So,

4 borrows 1 hundred 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.

See, feel and do.

Perform the following problems:

Th H T O Th H T O Th H T O Th H T O
3 4 2 6 2 5 4 3 5 8 4 0 6 5 4 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
5 7 2 6 4 3 7 4 6 9 2 5 5 9 0 3
− 2 4 5 9 − 2 1 9 6 − 4 7 6 9 − 2 4 6 8

Adarsh, can you subtract Yes, sir! I can
5243 from 7042? do it.

9 13 Let me try.
6 10 3 12
153
Th H T O
7 0 4 2
− 5 2 4 3
1 7 9 9

Mathematics 3 Approved by CDC

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.

See, feel and do.

Perform the following problems:

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

Th H T O Th H T O Th H T O
7 6 4 7 5 4 0 3 3 5 4 0
− 4 7 6 3 − 2 5 7 6 − 1 7 6 2

Th H T O Th H T O Th H T O
6 4 8 2 5 3 6 1 4 0 7 0
− 2 6 9 3 − 3 4 7 4 − 2 9 8 4

154 Approved by CDC Mathematics 3

Subtraction of more than 4 digit numbers without borrowing

See, feel and learn.

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, first we should arrange the
numbers in their place value columns.

Ok Madan ! Let’s try one
example.
T Th Th H T O
5 6 3 2 4
−3 4 2 0 3

2 2 1 2 1

See, feel and do.

1. Perform the following problems:

4 3 2 4 5 5 2 6 7 3 4 6 7 3 4
− 2 1 0 3 2 − 2 1 4 5 1 − 3 5 7 1 4

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

5 7 3 7 4 7 3 5 2 6 4 8 8 4 3 6 7 3
− 2 6 3 5 4 3 − 1 4 0 3 2 5 − 6 2 1 5 4 2

Mathematics 3 Approved by CDC 155

2. Do the following task as shown below:

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

Subtraction of more than 4 digit numbers with borrowing

See, feel and learn.

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

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

First we subtract ones from ones, T Th Th H T O
then tens from tens, hundreds from hundreds
11
and so on by borrowing from the higher 1 14
place number of the left column
if necessary. 65 1TTh21 Th 111 76 1T 122
− 4 3 2 6 5
See, feel and do.
1 8 9 0 7

1. Perform the following problems:

2 5 3 2 4 4 3 2 5 3 4 2 3 5 4 6
− 1 3 1 7 6 − 3 1 0 6 8 − 2 4 1 6 5 4

156 Approved by CDC Mathematics 3

5 3 4 8 2 6 7 0 2 4 6 3 5 4 2
− 2 6 7 5 4 − 3 4 4 5 7 − 2 6 3 6 5

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

Word problems on subtraction without and with
borrowing

See, feel 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
= 2 1 7 4

∴ 2174 fishes are left in the pond.

See, feel and do.

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. .

Mathematics 3 Approved by CDC 157

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.

7. Your father deposits Rs. 1,50,000 in a bank and

withdraw Rs. 75,000 at a time. How much money is

left in the bank as the principle?

∴ There is Rs. in the bank.

8. Pema earn Rs. 254 in dashain festival after Tika. If he

spends Rs. 1230 for new clothes, how much money left

to him?

∴ He has got Rs. left.

158 Approved by CDC Mathematics 3

5.3 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
×3
4 × 3 = 12 12

From the above example, it concludes that the multiplication
is repeated addition.

See, feel, learn and do.

Lakhan, Meera, Karan and Dhaniya are given 3 bananas each. How many bananas
are there altogether?

333 3
4 persons have 3 bananas each.
4 × 3 = 12

Complete the followings:

2×3 = 6 ×=
Mathematics 3
Approved by CDC 159

×= ×=
×= ×=
×= ×=

×= ×=

160 Approved by CDC Mathematics 3

Study the following tables.

Multiplication Table of 6

One times 6 6×1=6
6 × 2 = 12
Two times 6+6 6 × 3 = 18
6 × 4 = 24
Three times 6+6+6 6 × 5 = 30
6 × 6 = 36
Four times 6+6+6+6
161
Five times 6+6+6+6+6

Six times 6+6+6+6+6+6
Mathematics 3 Approved by CDC

Seven times 6+6+6+6+6+6+6 6 × 7 = 42

Eight times 6+6+6+6+6+6+6+6 6 × 8 = 48

Nine times 6+6+6+6+6+6+6+6+6 6 × 9 = 54

Ten times 6+6+6+6+6+6+6+6+6+6 6 × 10 = 60

Multiplication Multiplication Multiplication Multiplication
Table of 7 Table of 8 Table of 9 Table of 10

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

162 Approved by CDC Mathematics 3

Observe the multiplication table and fill.

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

Mathematics 3 Approved by CDC 163

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

See, feel and learn.

Multiply 43 by 2 Steps :
• First multiply the ones digit by 2, 2 × 3 = 6
43 • Then multiply the tens digit by 2, 2 × 4 = 8
×2
86

See, feel and do.

1. Perform the following task:

23 34 20 60 45 53
×2 ×2 ×4 ×3 ×1 ×2

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

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

See, feel and learn.

Multiply 2 3 3 by 3 Steps :
• First multiply the digit of ones, 3 × 3 = 9
233 • Then multiply the digit of tens, 3 × 3 = 9
×3 • Finally multiply the digit of hundred, 3 × 2 = 6

699

164 Approved by CDC Mathematics 3

3. Find the product of :

314 243 312 401 212
×2 ×2 ×3 ×3 ×4

423 503 610 423 720
×3 ×2 ×5 ×2 ×4

4. Find the product as shown:

2 1 3 × 2 = 5 0 2 × 3 = 3 0 4 × 2 =
2 3 4 × 2 = 4 2 3 × 3 = 7 1 2 × 4 =

Multiplication of two digits numbers by one digit
numbers with carrying

Jadu lal, can you Yes, sir ! I can multiply it.
multiply 46 by 2? I know the multiplication

table for 2.

Ok! Jadu lal.
Show your work

T O Steps:
• First multiply the digit of ones, 2 × 6 = 12 ones
1 12 ones = 1 ten + 2 ones.
Write 2 in the column of ones place and carry over 1
4 6
× 2 ten to the tens place.
9 2
• Then multiply the digit of tens. 2 × 4 = 8 tens
Mathematics 3 8 tens + 1 ten = 9 tens.
Now, write 9 in tens place.

Approved by CDC 165

See, feel and do.

1. Perform the following task:

T O T O T O T O T O

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

T O T O T O T O T O

4 7 6 5 7 6 3 9 4 7
× 3 × 5 × 7 × 6 × 5

T O T O T O T O T O

6 3 7 3 8 4 2 4 3 3
× 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 on

166 Approved by CDC Mathematics 3

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

See, feel and do.

1. Perform the following task:

247 164 253 343 354
×2 ×3 ×4 ×5 ×6

436 325 378 468 246
×3 ×5 ×4 ×2 ×7

436 325 378 468 246
×3 ×5 ×4 ×2 ×7

2. Perform the following problems in your exercise book :

a) 48 × 3 b) 39 × 2 c) 74 × 4 d) 54 × 6

e) 72 × 8 f) 324 × 5 g) 352 × 7 h) 426 × 9

Mathematics 3 Approved by CDC 167

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

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

168 Approved by CDC Mathematics 3

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.

See, feel and do. 23 × 200 =
8 × 5000 =
1. Complete the following boxes: 75 × 3000 =
8 × 60 =
2 × 10 = 42 × 400 =
3 × 100 = 12 × 3000 =
5 × 1000 = 9 × 50 =
26 × 30 = 71 × 200 =
4 × 20 = 125 × 100 =
5 × 300 =
7 × 2000 =
52 × 600 =
5 × 40 =

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

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

70 37 324 123 610
×20 ×100 ×200 ×300 ×5000

Mathematics 3 Approved by CDC 169

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

12 78 678 309 2593
×10 ×10 ×10 ×10 ×10

120 7743
×100
13 69 978
×100 ×100 ×100

179 46 347 6379
×1000 ×1000 ×1000 ×1000

Multiplication by two digit numbers

See, feel and learn.

Multiply 27 by 13.

There are three steps for
this multiplication.

13 = 10 + 3

27 Step 1 Step 2 Step 3
×1 3 Multiply 27 by 3 Multiply 27 by 10 Add the products

81 2 27 1
+2 7 0 ×1 0
27 270 81
351 ×3 +2 7 0
81
351

170 Approved by CDC Mathematics 3

See, feel and do.

1. Multiply as shown above:

28 28 28 37 37 37
×16 ×6 ×10 ×24 ×4 ×20

46 46 46 58 58 58
×27 ×7 ×20 ×44 ×4 ×40

2. Multiply the following as shown in the example below:

28 26 46 57 68
×14 ×17 ×35 ×45 ×73

112 49
+ 280 ×85

392

63 76 87 37
×59 ×67 ×64 ×96

Mathematics 3 Approved by CDC 171

See, feel and learn. 36 = 30 + 6

Multiply 243 by 36

The process of multiplication of
243 by 36 is also same as above.

So, look at the process.

243 Step 1 Step 2 Step 3
×36
1458 21 1 1
+7290
8748 243 243 1458
×61 ×30 +7290
458 7290
8748

See, feel and do.

1. Multiply as shown above:

278 278 278 457 457 457
×36 ×6 ×30
×24 ×4 ×20

648 648 648 783 783 783
×65 ×5 ×60
×57 ×7 ×50

172 Approved by CDC Mathematics 3

2. Multiply the following as shown in the example:

146 375 243 436
×2 4 ×42 ×39 ×56
58 4
124
+2 9 2 0 ×32

3504

567 289 521
×64 ×34 ×23

648 973 876 539
×37 ×54 ×47 ×38

745 982 384 436
×94 ×43 ×57 ×56

845 222 334 433
×84 ×44 ×77 ×96

Mathematics 3 Approved by CDC 173

Multiplication by three digit numbers

See, feel and learn.

Multiply 135 by 243

There are four steps for
this multiplication.

243 = 200 + 40 + 3

135 Step 1 Step 2 Step 3 Step 4
×243 405
11 135 35
405 ×40 ×200 5400
5400 135 5400 27000 +2 7 0 0 0
+2 7 0 0 0 ×3
32805 32805
405

See, feel and do.

1. Multiply as shown above:

147 147 147 147
×236 ×6 ×30 ×200

174 Approved by CDC Mathematics 3

27.3 273 273 273
×245 ×5 ×40 ×200

369 369 369 369
×458 ×8 ×50 ×400

584 584 584 584
×373 ×3 ×70 ×300

2. Multiply the following as shown below:

248 346 457 429
×3 2 5 ×2 5 6 ×3 4 8 ×2 4 7
1240

4960

74400

80600

Mathematics 3 Approved by CDC 175

578 638 289 789
×2 6 3 ×4 7 6 ×3 2 4 ×2 4 9

239 526 747 745
×1 4 7 ×4 3 4 ×2 5 6 ×5 8 4

Word problems on multiplication

See, feel and learn.

There are 30 eggs in a crate. How many eggs are there in such 14 crates?

Salim, can you solve the
above problem?

3 0 Yes, Sir! I can solve it.
×1 4 We have to multiply, don't we ?
12 0 We do so Because, in 14 crates the
+3 0 0 number of eggs are more than that

42 0 in 1 crate.

Therefore, there are 420 eggs in 14 crates.

176 Approved by CDC Mathematics 3

See, feel and do.

1. Solve the following problems:

a) There are 24 bottles in a carton. How many bottles 24
×8
are there in such 8 cartons ?
78
Therefore, bottles are in 8 cartons. ×9

b) There are 78 chocolates in a packet. How many 375
×7
chocolates are there in such 9 packets ?
890
Therefore, chocolates are in 9 packets. ×6

c) A man earns Rs. 375 in a day. How much does he earn 24
×30
in a week ?
75
Therefore, he earns in a week. ×4 0

d) The cost of a pair of shoes is Rs. 890.What is the cost 185
×24
of such 6 pairs of shoes ?

Therefore, the cost of 6 pairs of shoes is .

e) There are 24 hours in a day. How many hours are

there in a month?

Therefore, hours in a month.

f) The price of a packet of chocolates is Rs. 75. What is
the price of 40 such packets of chocolates?

Therefore, the price of 40 packets of chocolates is
.

g) There are 185 pages in a book. How many pages are

there in such 24 books ?

Therefore, pages there in 24 books.

Mathematics 3 Approved by CDC 177

h) There are 37 students standing in each line for the

morning assembly. How many students are there

altogether if there are 18 such lines?

Therefore, students are there altogether.

i) Ram spends Rs. 45 in a day for his tiffen. How

much does he spend in 3 weeks ?

Therefore, he spends in 3 weeks.

j) The cost of a watch is Rs. 375. How much will be

the cost of 28 such watches ?

Therefore, the cost of 28 watches is .

k) There are 247 candles in a box. How many candles

will be there in 48 such boxes ?

Therefore, there are candles in 48 boxes.

l) If the cost of one table is Rs. 876, find the cost of

56 such tables.

Therefore, the cost of 56 such tables is .

m) There are 365 days in a year. How many days are

there in 28 years ?

Therefore, there are days in 28 years.

178 Approved by CDC Mathematics 3

5.4 Division

See, feel, learn and do.

Three micro - buses are ready to move to their destination from Kathmandu
valley in dashain. There are 36 passengers altogether. How many passengers
are sitted in each micro-buses?

Microbus - 1 12 passengers

Microbus - 2 12 passengers

Microbus - 3 12 passengers

3 × 12 = 36
36 ÷ 3 = 12

Mathematics 3 Approved by CDC 179

Division as repeated subtraction:

See, feel and learn.

Let us recall the things which we
learnt about division in class 2.

There are 20 pencils. Share them
equally among 4 boys.

1st time : 20
−4
16

2nd time : 16
−4
12

3rd time : 12
−4

8

4th time : 8
−4

4

5th time : 4 Mathematics 3
−4
180
0

Approved by CDC

See, feel and do.

Perform the following as given in the example by the process of
repeated subtractions:

24 30 35 26
−6 −6 −7 −8

18 Quotient = Quotient =
−6 Remainder = Remainder =

12
−6

6
−6

0

Quotient = 4 Quotient =
Remainder = 0 Remainder =

17 45 35 26
−4 −9 −7 −8

Quotient = 4 Quotient = Quotient = Quotient =
Remainder = 0 Remainder = Remainder = Remainder =

Mathematics 3 Approved by CDC 181

Division of two digit numbers by one digit number:

Divide 49 by 3 See, feel and learn.

3) 49 (16 Steps :
−3 • In division, single digit divides the single digit at first

19 from the left.
−18 So,4 tens ÷ 3 = 1 tens and 1 ten is still the remainder.
Write 1 in tens place of the quotient.
1 Write the product of quotient and divisor i.e. 1 × 3 = 3
below the divided in the tens place. 4 – 3 = 1

Quotient = 16 • Now, bring 9 ones down.
Remainder = 1 1 ten + 9 ones = 19 ones
Divisor = 3 19 ones ÷ 3 = 6 ones and remainder 1 one.
Dividend = 49 Write 6 in ones place of quotient.

Write the product of quotient and divisor i.e.
6 × 3 = 18 below the dividend.
19 – 18 = 1

Can you verify
the result ?

Of course, I did that
in class two.

Divisor × quotient + remainder = dividend
= 3 × 16 + 1
= 48 + 1
= 49 dividend.

182 Approved by CDC Mathematics 3

See, feel and do.

Perform the following task and verify your result.

69 ÷ 2 87 ÷ 3 36 ÷ 9 56 ÷ 5

84 ÷ 6 74 ÷ 5 98 ÷ 7 89 ÷ 8

59 ÷ 4 84 ÷ 9 79 ÷ 7 92 ÷ 3

Mathematics 3 Approved by CDC 183

Division of 3 digit numbers by 1 digit numbers.

Divide 492 4)492(123 Verification
by 4. −4 Divisor × quotient + remainder
= 4 × 123 + 0
09 = 492 + 0
−8 = 492 = dividend
12
−12 ∴ Quotient = 123
Remainder = 0
0

Divide 329 Steps :
by 4. In the number 329, the digit at
hundreds place is less than divisor.
4)329(82 So, let’s take the digit at tens place
−32 also, then divide 32 ÷ 4 = 8
Now, bring 9 ones down.
09 9 ÷ 4 = 2 ones + 1 ones
−8
1

∴ Quotient = 82
Remainder = 1

See, feel and do.

Perform the following task and verify your result.

345 ÷ 3 672 ÷ 6 634 ÷ 5 972 ÷ 9

184 Approved by CDC Mathematics 3

824 ÷ 8 945 ÷ 7 734 ÷ 8 237 ÷ 4

476 ÷ 5 304 ÷ 6 738 ÷ 8 567 ÷ 6

Division of 4 and 5 digit numbers by 1 digit number:

See, feel and learn.

Divide 4219 by 3. Steps:
4 > 3, so 4 ÷ 3 = 1 and remainder 1
3) 4219 (1406 Bring down 2 and 12 ÷ 3 = 4
-3 Bring down 1 but 1 < 3, so for 1÷3, quotient
12 0 remainder 1 again bring down 9 and 19 ÷
-12 3 = 6 and remainder 1.
01
-0
19
-18
1

∴ Quotient = 1406
Remainder = 1

Mathematics 3 Approved by CDC 185

See, feel and do.

Perform the following task:

744 ÷ 2 492 ÷ 3 7917 ÷ 7 5624 ÷ 4

7253 ÷ 6 9728 ÷ 9 4326 ÷ 6 4327 ÷ 5

37264 ÷ 3 56246 ÷ 5 63217 ÷ 7 82824 ÷ 9

186 Approved by CDC Mathematics 3

Division of two digit numbers by two digit numbers:

See, feel and learn.

Divide 78 by 14. Before dividing 78 by 14,
we write the multiplication
14)78(5
−70 table of 14.
8
Steps: 1 × 14 = 14
∴ Quotient = 5 7 < 14, so we take 78. 2 × 14 = 28
Remainder = 8 78 is less than 84 but more than 70. 3 × 14 = 42
So, 78 is divided by 14 for 5 times. 4 × 14 = 56
5 × 14 = 70
6 × 14 = 84

See, feel and do.

Perform the following task as given in the example and verify your
result.

14)452(32 ∴ Quotient = 32 Verification:
−42 Remainder = 4 Quotient × divisor + remainder
32 = 32 × 14 + 4
−28 = 448 + 4
4 = 452 = dividend.

13)72( Verification:

Mathematics 3 Approved by CDC 187

17)87( Verification:
21)85( Verification:
18)95( Verification:
24)67( Verification:
37)98( Verification:
34)78( Verification:

188 Approved by CDC Mathematics 3

Word problems on division

See, feel and learn. 13)676(52
−65
If the cost of 13 kg of apples is Rs. 676, find the cost of 1 kg 26
of apples.Therefore the cost of 1 kg of apples is Rs. 52 −26
0

See, feel and do.

Solve the following problems:

a) 48 pencils are shared equally among 8 girls.
How many pencils does each girl get ?

Therefore each girl gets pencils.

b) 72 sweets are shared equally among 6 boys.
How many sweets does each boy get?

Therefore, each boy gets sweets.

c) There are 522 students in a school. They are
lined up in 9 rows equally. How many students
are there in each row ?

Therefore, students are in each row.

d) If the cost of 8 pens is Rs 512, what is the cost

of 1 pen ?

Therefore, the cost of 1 pen is .

Mathematics 3 Approved by CDC 189

Unit Revision Test

1. Perform the following task:

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

2. Perform the following task:

a) 23 + 159 + 2345 =
b) 403 + 2351 + 76 =
c) 251 + 6254 + 252 =
d) 965 + 2458 + 365 =

3. 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. .

4. Do the following task :

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

190 Approved by CDC Mathematics 3

5. 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.

6. Simplify: b) 35 − 14 + 21 c) 46 − 28 + 53 − 45
= =
a) 19 + 12 – 8 = =
= = =
= = =
=
=

7. Multiply the following problems:

28 38 57 547 628
×7 ×40 ×38 ×64 ×25

8. Solve the following problems:

a) There are 45 apples in a basket. How
many apples are there in such 24
baskets ?

Therefore, apples in 24
baskets.

b) A person earns Rs. 375 in a day. How
much does he earn in one weeks ?

Therefore, he earns in one
weeks.

Mathematics 3 Approved by CDC 191

9. Simplify: b) 45 × 8 − 38 + 27 c) 36 × 8 + 24 × 12 − 205
= =
a) 17 × 5 + 18 − 9 = =
= = =
= = =
=
=

10. Divide:

6)45( 8)91( 7)126( 4)824(

11. Solve the following problems:

a) A man sold 288 pens in 6 days. How many
pens did he sell in 1 day ?

Therefore he sold pens in 1 day.

b) There are 128 students in a hall. They are
divided into 8 equal groups. How many
students are there in each group ?

Therefore there are students in
each group.

12. Simplify the following problems::

24 – 15 ÷ 5 × 6 6 × 8 – 45 ÷ 9 + 2 76 ÷ 19 × 4 + 5 × 3 − 25

192 Approved by CDC Mathematics 3

6Unit

OUR DAILY LIFE

Estimated periods - 6

Objectives

At the end of this unit, students will be able to:
tell the relation of day, week, hour, minute and second.
convert the time from one unit to the another and perform the addition
and subtraction upon time.
study the calendar of English and Nepali months.

Teaching Materials

Wrist watch, clock, model clock, Nepali calendar, English Calendar, etc.

Activities

It is better to:
show yearly calendar and ask the students to give information about
days, weeks, months, years etc.
discuss and perform the activities of conversion of time from one unit to
another (minutes, hours, days, weeks, months, years etc).
interpret the process of answering by the study of given calendar.
ask the students to perform the problem on addition and subtraction of
times as in given in the curriculum prescribed by CDC.

Mathematics 3 Approved by CDC 193

6.1 Time

Conversion of time

Sir,
I understand about minute hand and
second hand in previous chapter. But
what about hour hand in a clock?
Is hour hand makes one complete
rotation in 24 hours?

No, it is not.
Hour hand makes one complete rotation in 12 hours which is
called only a half day.
Where,
Half day = 12 hours.
1 day = 24 hours
Also observe the following relations carefully.

• 60 seconds = 1 minute Mathematics 3
60 minutes = 1 hour
24 hours = 1 day

• To convert day to hours, multiply by 24.
To convert hours to minutes, multiply by 60.
To convert minute to seconds, multiply by 60.

• To convert seconds to minutes, divided by 60.
To convert minutes to hours, divided by 60.
To convert hours to days, divided by 24.

194 Approved by CDC

See, feel and understand.

Example 1: Convert 40 minutes into seconds. 60
Solution: 1 minute = 60 seconds. × 40
∴ 40 minutes = 60 × 40 seconds 2400
= 2400 seconds

Example 2: Convert 6 hours into minutes. 60
Solution: We know ×6
1 hour = 60 minutes 360
∴ 6 hours = 60 × 6 minutes
= 360 minutes

Example 3: How many hours are there in 3 days? 24
Solution: We know ×3
1 day = 24 hours
∴ 3 days = 24 × 3 hours 72
= 72 hours.

Example 4: Convert 75 minutes to hours and minutes.

Solution: = 60 minutes + 15 minutes 75 ÷ 60 75 minutes
75 minutes = 1 hour + 15 minutes
= 1 hour 15 minutes − 60 minutes

60) 75 (1 15 minutes

− 60
15 1 hour 15 minutes

See, feel and do.

1. Convert the following to seconds:

(a) 2 minutes (b) 12 minutes
(c) 20 minutes (d) 2 hours
(e) 3 hours 10 minutes (f) 10 hours 20 minutes

Mathematics 3 Approved by CDC 195

2. Convert the following to minutes:

(a) 4 hours (b) 7 hours
(c) 15 hours (d) 2 hours 15 minutes
(e) 1 hour 30 minutes (f) 13 hours 42 minutes

3. Convert the following to hours:

(a) 3 days (b) 5 days
(c) 10 days (d) 16 days
(e) 1 day 6 hours (f) 4 days 12 hours

4. Convert the following:

(a) 120 seconds to minutes (b) 90 seconds to minutes

(c) 240 seconds to minutes (d) 200 seconds to minutes

(e) 180 minutes to hours (f) 48 hours to days

(g) 135 minutes to hours and minutes

(h) 50 hours to days and hours

(i) 200 minutes to hours and minutes

(j) 210 minutes to hours and minutes

Addition and subtraction of times

To add 5 hours 30 minutes and 6 hours 15 minutes:

hours minutes Arrange vertically
5 30 Add minutes
Add hours
+ 6 15
11 45

= 11 hours and 45 minutes

To subtract 15 minutes 15 seconds from 24 minutes 32 seconds

minutes seconds Arrange vertically
24 32 Subtract seconds
15 Subtract minutes
− 15 17
9

= 9 minutes 17 seconds

196 Approved by CDC Mathematics 3

See, feel and do.

1. Perform the following task:

hours minutes hours minutes hours minutes
10 15 9 28 9 12

+ 25 20 + 16 17 + 24 17

hours minutes hours minutes days hours
30 12 21 31 7 14

+ 25 35 + 35 24 + 15 7

days hours days hours days hours
12 13 14 12 15 16

+ 5 7 + 5 6 + 5 7

hours minutes hours minutes hours minutes
5 20 5 40 8 20

7 00 5 40 8 45
+ 32 08 + 35 02 + 38 80

hours minutes seconds hours minutes seconds
10 10 20 5 22 44

+ 7 11 39 + 11 12 14

hours minutes seconds hours minutes seconds
5 6 7
14 15 16
8 9 10
20 25 30 + 11 2 3

+ 8 7 6

Mathematics 3 Approved by CDC 197

2. Add the following:

(a) 27 minutes 23 seconds and 7 minutes 22 seconds
(b) 18 hours 19 minutes and 16 hours 21 minutes
(c) 15 days 12 hours and 8 days 9 hours
(d) 10 hours 12 minutes 14 seconds and 8 hours 18 minutes 26 seconds
(e) 6 days 12 hours 24 minutes and 10 days 6 hours 24 minutes

3. Perform the following task:

minutes seconds days hours hours minutes seconds
30 12 21 50 20 34 36

− 25 35 − 12 38 − 9 14 27

hours minutes hours minutes seconds hours minutes seconds
32 46 42 19 36 45 30 24

− 14 18 − 12 17 07 − 8 11 17

4. Subtract the following:

(a) 6 minutes 34 seconds from 8 minutes 44 seconds
(b) 49 hours 39 minutes from 59 hours 58 minutes
(c) 12 days 19 hours from 21 days 23 hours
(d) 7 hours 39 minutes 40 seconds from 17 hours 49 minutes 52 seconds
(e) 21 days 15 hours 55 minutes from 25 days 23 hours 57 minutes

198 Approved by CDC Mathematics 3

6.2 Calendar

See, feel, learn and do.

az} fv @)&* Apr/May 2021 hi] 7 @)&* May/June 2021 cfiff9 @)&* June/July 2021

cfO{ ;f]d du+ n a'w ljlx z'qm zlg cfO{ ;f]d d+un a'w ljlx zq' m zlg cfO{ ;fd] du+ n a'w ljlx z'qm zlg

Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat

!@#$ #) #! ! !@#$%
14 15 16 17 13 14 15 15 16 17 18 19

% ^ & * ( !) !! @#$%^&* ^ & * ( !) !! !@
18 19 20 21 22 23 24 16 17 18 19 20 21 22 20 21 22 23 24 25 26

!@ !# !$ !% !^ !& !* ( !) !! !@ !# !$ !% !# !$ !% !^ !& !* !(
25 26 27 28 29 30 1 23 24 25 26 27 28 29 27 28 29 30 1 2 3

!( @) @! @@ @# @$ @% !^ !& !* !( @) @! @@ @) @! @@ @# @$ @% @^
2345678 30 31 1 2 3 4 5 4 5 6 7 8 9 10

@^ @& @* @( #) #! @# @$ @% @^ @& @* @( @& @* @( #) #!
9 10 11 12 13 14 6 7 8 9 10 11 12 11 12 13 14 15

>fj0f @)&* July/Aug. 2021 efb| @)&* Aug./Sep. 2021 cflZjg @)&* Sep./Oct. 2021

cfO{ ;f]d du+ n aw' ljlx z'qm zlg cfO{ ;f]d d+un a'w ljlx zq' m zlg cfO{ ;fd] d+un a'w ljlx z'qm zlg

Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat

#! #@ !@ !@#$% #! ! @
15 16 16 17 17 18 19 20 21 17 17 18

#$%^&*( ^ & * ( !) !! !@ #$%^&*(
18 19 20 21 22 23 24 22 23 24 25 26 27 28 19 20 21 22 23 24 25

!) !! !@ !# !$ !% !^ !# !$ !% !^ !& !* !( !) !! !@ !# !$ !% !^
25 26 27 28 29 30 31 29 30 31 1 2 3 4 26 27 28 29 30 1 2

!& !* !( @) @! @@ @# @) @! @@ @# @$ @% @^ !& !* !( @) @! @@ @#
1234567 5 6 7 8 9 10 11 3456789

@$ @% @^ @& @* @( #) @& @* @( #) #! @$ @% @^ @& @* @( #)
8 9 10 11 12 13 14 12 13 14 15 16 10 11 12 13 14 15 16

sflQs{ @)&* Oct./Nov. 2021 dl+ ;/ @)&* Nov./Dec 2021 kfi} f @)&* Dec. 2021/Jan 2022

cfO{ ;fd] du+ n a'w ljlx z'qm zlg cfO{ ;fd] du+ n aw' ljlx z'qm zlg cfO{ ;f]d d+un a'w ljlx zq' m zlg

Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat

!@#$%^ !@#$ !@#
18 19 20 21 22 23 17 18 19 20 16 17 18

& * ( !) !! !@ !# % ^ & * ( !) !! $ % ^ & * ( !)
24 25 26 27 28 29 30 21 22 23 24 25 26 27 19 20 21 22 23 24 25

!$ !% !^ !& !* !( @) !@ !# !$ !% !^ !& !* !! !@ !# !$ !% !^ !& 1
31 1 2 3 4 5 6 28 29 30 1 2 3 4 26 27 28 29 30 31

@! @@ @# @$ @% @^ @& !( @) @! @@ @# @$ @% !* !( @) @! @@ @# @$
7 8 9 10 11 12 13 5 6 7 8 9 10 11 2345678

@* @( #) @^ @& @* @( @% @^ @& @* @( #)
14 15 16 12 13 14 15 9 10 11 12 13 14

df3 @)&* Jan./Feb. 2022 kmfNu'g @)&* Feb./Mar. 2022 r}q @)&* Mar./Apr. 2022

cfO{ ;fd] d+un a'w ljlx zq' m zlg cfO{ ;fd] d+un aw' ljlx z'qm zlg cfO{ ;fd] d+un aw' ljlx zq' m zlg

Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat Sun Mon Tue Wed Thu Fri Sat

! !@#$%^& !@#$%
15 13 14 15 16 17 18 19 15 16 17 18 19

@#$%^&* * ( !) !! !@ !# !$ ^ & * ( !) !! !@
16 17 18 19 20 21 22 20 21 22 23 24 25 26 20 21 22 23 24 25 26

( !) !! !@ !# !$ !% !% !^ !& !* !( @) @! !# !$ !% !^ !& !* !(
23 24 25 26 27 28 29 27 28 1 2 3 4 5 27 28 29 30 31 1 2

!^ !& !* !( @) @! @@ @@ @# @$ @% @^ @& @* @) @! @@ @# @$ @% @^
30 31 1 2 3 4 5 6 7 8 9 10 11 12 3456789

@# @$ @% @^ @& @* @( @( #) @& @* @( #)
6 7 8 9 10 11 12 13 14 10 11 12 13

Mathematics 3 Approved by CDC 199

Observe the above calanders and answer the questions.

a) How many months have 31 days ?
b) How many months have 30 days ?
c) What day is Asoj 25 ?
d) How many days are there in Kartik ?
e) How many full weeks are there in Falgun ?
f) How many weeks are there in December ?
g) How many full weeks are there in May ?
h) Which month of English Calendar falls on Bhadra.

Study the given calendar and answer the following:

(a) Which calendar is it? cflZjg @)&* Sep./Oct. 2021

(b) How many Saturdays are cfO{ ;f]d d+un aw' ljlx zq' m zlg
there in this month? Sun Mon Tue Wed Thu Fri Sat

(c) How many days are there #! ! @
in this month? 17 17 18

(d) Which months of English #$%^&*(
calendar fall on this 19 20 21 22 23 24 25
month?
!) !! !@ !# !$ !% !^
(e) How many holidays are 26 27 28 29 30 1 2
there including Saturdays
in this month? !& !* !( @) @! @@ @#
3456789
(f) On which day does Teej
lie? @$ @% @^ @& @* @( #)
10 11 12 13 14 15 16

(g) Write the date Wednesday 21st September 2017 according to the

Nepali Calendar.

200 Approved by CDC Mathematics 3