Prime Mathematics 3

70 74 37 324 123 610
×20 ×20 ×100 ×200 ×300 ×5000

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

12 78 678 309 2593
×10 ×10 ×10 ×10 ×10
120

13 69 978 7743
×100 ×100 ×100 ×100

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

Multiplication by two digit numbers

Study and Learn:

Multiply 27 by 13. There are three steps for
this multiplication.

Step 1 Step 2 Add Step 3 13 = 10 + 3
Multiply 27 by 3 Multiply 27 by 10 the products
27 1 81
27 2 ×1 0 +2 7 0
×1 3 270 351
27
81 ×3
+2 7 0 81

351 Exercise - 5.8

A. Multiply as shown above:

28 28 28 37 37 37

×1 6 × 6 × 1 0 + ×2 4 × 4 × 2 0 +

+ +

96 Prime Mathematics Book − 3

46 46 46 58 58 58

27 ×7 ×20 + 44 ×4 ×40 +

++

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

28 26 34 46 57 68
×1 4 ×1 7 ×2 3 ×3 5 ×4 5 ×7 3
112

+ 280 + + + + +
392

63 76 93 87 37 49
×5 9 ×6 7 ×5 8 ×6 4 ×9 6 ×8 5

++++++

Multiplication of three digit numbers by two digit numbers

Study and Learn:

Multiply 2 4 3 by 3 6 The process of multiplica-
tion of 243 by 36 is also
Step 1 Step 2 Step 3 same as above. So, look

2 43 21 1 1 at the process.
×36
1458 243 243 1458
×6 × 30 +7 2 9 0
7290 8748
1458

+7 2 9 0 36 = 30 + 6
8748

Exercise - 5.9

A. Multiply as shown above:

276 276 276 457 457 457

×24 ×4 ×20 + ×36 ×6 ×30 +

++

Prime Mathematics Book − 3 97

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

++

B. Multiply the following as shown in the example:

146 375 243 436 567
×2 4 ×42 ×39 ×56 ×64
584

+ 2920 + + + +

3504

289 521 124 648 973
×34 ×23 ×32 ×37 ×54

+++++

876 539 745 982 384
×47 ×38 ×94 ×43 ×57

+++++

Multiplication by three digit numbers

Study and Learn: There are four steps for this multiplication.
Multiply 135 by 243

243 = 200 + 40 + 3

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

98 Prime Mathematics Book − 3

Exercise - 5.10

A. Multiply as shown above:

147 147 147 147

×236 ×6 ×30 ×200

+

+ 273 273 273
×5 ×40 ×200
273
×2 4 5

+ 369 369 369
×8 ×50 ×400
369
×4 5 8

+ 584 584 584
×3 ×70 ×300
584
×3 7 3

+

B. Multiply the following as shown below:

248 346 457 673 429
×3 2 5 ×2 5 6 ×3 4 8 ×4 6 2 ×2 4 7
1240 + + + +

4960

+ 74 400
80600

Prime Mathematics Book − 3 99

578 638 289 547 789
×2 6 3 ×4 7 6 ×3 2 4 ×7 5 4 ×2 4 9

+ + + + +
239 526 747 256 745

×1 4 7 ×4 3 4 ×2 5 6 ×3 8 9 ×5 8 4

+++++

Word problems on multiplication

Study and learn:

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

Salim, can you solve the Yes, Sir! I can solve it. We have
above problem? to multiply, don't we ? We do so

Because, in 14 crates the
number of eggs are more
30 than that in 1 crate.
×1 4
120
+ 3 0 0 Therefore, there are 420
4 2 0 eggs in 14 crates.

Exercise - 5.11

A. Solve the following problems:

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

Therefore, bottles are in 8 cartons.

100 Prime Mathematics Book − 3

b) There are 78 chocolates in a packet. How many 78
×9
chocolates are there in such 9 packets ?

Therefore, chocolates are in 9 packets.

c) A man earns Rs. 375 in a day. How much does he earn 375
×7
in a week ?

Therefore, he earns in a week.

d) The cost of a pair of shoes is Rs. 890. What is the cost 890
×6
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 24
×30
in a month?

Therefore, hours in a month.

f) The price of a packet of chocolates is Rs. 75. What is 75
the price of 40 such packets of chocolates? ×4 0

Therefore, the price of 40 packets of chocolates is

.

g) There are 185 pages in a book. How many pages are 185
×24
there in such 24 books ?

Therefore, pages there in 24 books.

Prime Mathematics Book − 3 101

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.

102 Prime Mathematics Book − 3

Simplification

The students of class three wanted to buy a wall clock for their class.
There are 26 students in the class. Each student is ready to pay Rs. 7.
So, they paid
Rs. 7 × 26 = Rs. 182

Their class teacher gave them Rs. 25. Now, they have
Rs. 182 + Rs. 25 = Rs. 207

Some students went to the market and bought a clock for Rs. 150.

Now, they have left In short, your event gives the
Rs. 207 − Rs. 150 = Rs. 57 mathematical form :
7 × 26 + 25 – 150

7 × 26 + 25 − 150 Steps:
= 182 + 25 − 150 First, we multiply.
= 207 − 150 Then, we add the numbers.
= 57 Finally we subtract.

Exercise - 5.12

A. Simplify the following problem:

a) 5 × 6 + 28 b) 8 × 3 + 14 c) 7 + 4 + 8 d) 19 − 2 × 4
= = = =
= = = =

e) 6 × 3 + 17 − 10 f) 4 × 5 + 8 − 7 g) 57 + 4 × 9 − 6
= = =
= = =
= = =

h) 4 × 4 + 7 × 6 − 20 i) 27 − 3 × 6 + 2 × 5 j) 2 × 4 + 4 × 3 + 10 − 8
== =
== =
== =

Prime Mathematics Book − 3 103

Unit Revision Test

A. Multiply the following problems:

28 49 364 38 57
×7 ×6 ×4 ×40 ×38

583 127 269 547 628
×58 ×3 0 0 ×76 ×3 6 4 ×4 2 5

B. 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.

c) The cost of one litre petrol is Rs. 85. Find the cost of 256 litres of

petrol.

Therefore, the cost of 256 litres of petrol is .

Simplify: (iii) 36 × 8 + 24 × 12 − 205
(i) 17 × 5 + 18 − 9 (ii) 45 × 8 − 38 + 27

104 Prime Mathematics Book − 3

Unit

6

Estimated periods − 12

DIVISION

Objectives

At the end of this unit, the students will be able to :
• divide the numbers upto three digits by the number upto two digits.
• make and solve the simple word problems on division.
• explain the relation between multiplication and division.

Teaching Materials
• Chart of multiplication tables and division tables

Activities

It is better to:
• ask the students to write the multiplication and corresponding division table before start-

ing the lesson.
• drill and discuss the steps of division process on the basis of concept of previous knowl-

edge.
• ask the students to check the result of division by using the concept of previous knowledge

which is dividend = divisor x quotient + remainder.
• ask the students to write the word problems in mathematical form of division on the basis

of previous knowledge, concept, discussion and solve them.
• drill the concept of multiplication and division which are opposite process with discussion.

Revision

Division as repeated subtraction:

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
− 4

0

106 Prime Mathematics Book − 3

Exercise - 6.1

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

24 30 35 26
− 6 − 6 − 7 − 8
Quotient = Quotient = Quotient =
18 Remainder = Remainder = Remainder =
− 6

12
− 6

6
− 6

0
Quotient = 4
Remainder = 0

17 45
− 4 − 9

Quotient = Quotient = Quotient = Quotient =
Remainder = Remainder = Remainder = Remainder =

Division of two digit numbers by one digit number:

Study and learn: Steps :
Divide 49 by 3 • In division, single digit divides the single digit at first from the left.

3)49(16 So, 4 tens ÷ 3 = 1 tens and 1 ten is still the remainder.
− 3 Write 1 in tens place of the quotient.
Write the product of quotient and divisor i.e. 1 × 3 = 3
19 below the divided in the tens place. 4 – 3 = 1
−18 • Now, bring 9 ones down.
1 ten + 9 ones = 19 ones
1 19 ones ÷ 3 = 6 ones and remainder 1 one.
Quotient = 16 Write 6 in ones place of quotient.
Remainder = 1 write the product of quotient and divisor i.e.
Divisor = 3 6 × 3 = 18 below the dividend.
Dividend = 49 19 – 18 = 1

Prime Mathematics Book − 3 107

Can you verify Of course, I did
the result ? that in class two.

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

Exercise - 6.2

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

108 Prime Mathematics Book − 3

Division of 3 digit numbers by 1 digit numbers.

Divide 492 by 4.

4)492(123 Verification
−4 Divisor × quotient + remainder
= 4 × 123 + 0
09 = 492 + 0
−8 = 492 = dividend

12
−12

0
∴ Quotient = 123

Remainder = 0

Divide 329
by 4.

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

∴ Quotient = 82
Remainder = 1

Exercise - 6.3

Perform the following task and check your result:

345 ÷ 3 672 ÷ 6 634 ÷ 5 972 ÷ 9

Prime Mathematics Book − 3 109

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:

Study and learn:
Divide 4219 by 3.

3) 4219 (1406 Steps:
-3 4 > 3, so 4 ÷ 3 = 1 and remainder 1
12 Bring down 2 and 12 ÷ 3 = 4
-12 Bring down 1 but 1 < 3, so for 1÷3, quotient 0 remainder1 again bring
01 down 9 and 19 ÷ 3 = 6 and remainder 1.
-0
19 Exercise - 6.4
-18

∴ Quotient 1= 1406
Remainder = 1

Perform the following task:

744 ÷ 2 492 ÷ 3 7917 ÷ 7 5624 ÷ 4

110 Prime Mathematics Book − 3

7253 ÷ 6 9728 ÷ 9 4326 ÷ 6 4327 ÷ 5

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

Division of two digit numbers by two digit numbers:

Study and learn:
Divide : 78 ÷ 14

14)78(5 Before dividing 78 by 14, we write
−70 the multiplication table of 14.

8

∴ Quotient = 5 Steps : 1 × 14 = 14
Remainder = 8 7 < 14, so we take 78. 2 × 14 = 28
78 is less than 84 but 3 × 14 = 42
more than 70. 4 × 14 = 56
So, 78 is divided by 14 5 × 14 = 70
for 5 times. 6 × 14 = 84

Prime Mathematics Book − 3 111

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

12)37(3 Verification:
−36 Divisions × quotient + remainder
= 12 × 3 + 1
1 = 36 + 1
∴ Quotient = 3 = 37 = dividend

Remainder = 1

13)72(

17)87(

21)85(

18)95(

112 Prime Mathematics Book − 3

24)67(

37)98(

34)78(

Division of three digit numbers by two digit numbers:
Study and learn: Remainder:
Divide 243 by 18 1 × 18 = 18
Steps: 2 × 18 = 36
3 × 18 = 54
18)243(13 In 243, 24>18 but 24<36, 4 × 18 = 72
−18 5 × 18 = 90
so 18 divides 24 for 1 6 × 18 = 108
63 time. 7 × 18 = 126
−54 8 × 18 = 144
In the table of 18, 63>54 9 × 18 = 162
9 but 63 < 72. So, 63 is
∴ Quotient = 13
divided by 18 for 3 times.
Remainder = 9

Exercise - 6.6 10 × 18 = 180

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

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

4 Prime Mathematics Book − 3 113
∴ Quotient = 32

Remainder = 4

16)774(
17)934(
15)765(
19)589(

114 Prime Mathematics Book − 3

23)492(
32)744(
20)840(

60)360(

Prime Mathematics Book − 3 115

Word problems on division 13)676(52
−65
Study and learn:
26
If the cost of 13 kg of apples is Rs. 676, find −26
the cost of 1 kg of apples.
Therefore the cost of 1 kg of apples is Rs. 52 0

Exercise - 6.7

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 12 pens is Rs 516, what is the cost of 1

pen ?

Therefore, the cost of 1 pen is .

116 Prime Mathematics Book − 3

Simplification

Things to remember for simplification
First do the work of division. Then do the work of

multiplication. Then do the work of addition.
At last do the work of subtraction.

Can you simplify Yes, sir ! I can simplify
24 – 8 ÷ 4 × 7 according to the above rule.

24 – 8 ÷ 4 × 7
= 24 – 2 × 7 [First divide 8 by 4, 8 ÷ 4 = 2]
= 24 – 14 [Then multiply 2 by 7, 2 × 7 = 14]
= 10 [Then subtract 14 from 24, 24 – 14 = 10]

Exercise - 6.8

Simplify the following problems:

7 + 5 × 16 ÷ 4 42 ÷ 7 × 6 − 25 18 ÷ 3 − 2 + 4 × 2 60 ÷ 12 + 5 × 3

5 × 40 ÷ 8 − 7 104 ÷ 13 × 3 − 15 8 + 144 ÷ 12 × 3 − 17

3 × 45 ÷ 9 + 12 × 2 12 × 45 ÷ 5 – 25 + 12 6 × 132 ÷ 11 + 42

60 ÷ 12 – 4 × 6 + 42 46 + 26 – 3 × 117 ÷ 13 14 + 12 × 126 ÷ 9 − 107

Prime Mathematics Book − 3 117

Unit Revision Test

A. Divide: 8)91( 7)126( 4)824(
6)45(

8)3296( 12)364( 24)508( 17)553(

B. Solve the following problems:

A man sold 288 pens in 16 days. How many pens did he sell in 1 day ?

Therefore he sold pens in 1 day.

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.

C. Simplify the following problems::

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

118 Prime Mathematics Book − 3

Unit Estimated periods − 10

7

TIME

Objectives

At the end of this unit, the students will be able to :
• tell time in hours and minutes.
• tell the time with A.M. and P.M.
• convert the times from one unit to another.
• perform addition and subtraction of time (seconds, minutes, hours, days, weeks, months

and years)

Teaching Materials
• Wrist watch, clock, model clock, calendar etc.

Activities

It is better to:
• discuss with the students to tell time showing watch, clock, model clock.
• 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 (min-

utes, hours, days, weeks, months, years etc).
• ask the students to perform the problem on addition and subtraction of times as in given

in the curriculum prescribed by CDC.

Time Study and learn.

The face or dial of a clock or watch is numbered

from 1 to 12. It consists of a short hand or hour Minute hand
hand to indicate hours, a long hand or minute
hand to indicate minutes and a thin hand or Hour hand
second hand to indicate seconds. Counting starts Winding screw
Second hand
Face or dial

from 12 or 0 and the hands move towards right

from 12.
1 complete rotation of the second hand is 60 seconds and 1 complete

rotation of the minute hand is 60 minutes and 1 complete rotation of

the hour hand is 12 hours.

One complete rotation by the second hand is 60 seconds during which the
1
minute hand moves 6=01 of 1 complete rotation which is 1 minute.
∴ 60 seconds minute
1
Or 1 second = 60 minute

When the minute hand makes one complete rotation, the hour hand moves
1
12 of one complete rotation which is 1 hour.
1
∴ 60 minutes = 1 hour, or 1 minute = 60 hour

In 1 day (day and night), the hour hand rotates twice which is 2 × 12 hours
= 24 hours.
∴ 24 hours = 1 day

60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day

Telling time
We tell the time in hours and minutes indicated by the hour hand and
minute hand.

Hour hand is nearly at 12 and the minute hand is at
1. It is 5 minutes past 12 or 5 past 12
We write 12:05

120 Prime Mathematics Book − 3

11 12 1 It is 15 minutes past 12 or 15 past 12
10 2 [Quarter past 12]
We write 12:15
93

84
765

It is 30 minutes past 12 or 30 past 12 11 12 1
[Half past 12] 10 2

We write 12:30 93

84
765

11 12 1 It is 45 minutes past 12 or 15 minutes
10 2 to 1 [Quarter to 1]
We write 12:45
93
It is 1 o’clock
84 We write 1:00
765

11 12 1
10 2

93

84
765

11 12 1 It is 50 minutes past 5 or 10
10 2 minutes to 6
We write 5:50
93

84
765

It is 55 minutes past 3 or 5 11 12 1
minutes to 4 10 2

We write 3:55 93

84
765

In a day, the hour hand makes two revolutions (rotation). Time before

noon [mid night to mid day] is called ante meridiem or A.M. meaning

before noon and the time after noon [ Mid day to mid night] is called post

meridiem or P.M. meaning after noon. 11 12 1

This clock is showing the time in the morning. 10 2
93

It is 25 minutes past 2 in the morning. 84
We write 2:25 A.M. 765

This clock is showing the time in the evening. 11 12 1
It is 15 minutes to 8 in the evening. 10 2
We write 7:45 P.M.
93

84
765

Prime Mathematics Book − 3 121

Exercise - 7.1

A.Write the time shown by the given clocks:

11 12 1 5 minute past 4 11 12 1
10 2 4:05 10 2

93 93

84 84
765 765

11 12 1 11 12 1
10 2 10 2

93 93

84 84
765 765

11 12 1 11 12 1
10 2 10 2

93 93

84 84
765 765

11 12 1 11 12 1
10 2 10 2

93 93

84 84
765 765

11 12 1 11 12 1
10 2 10 2

93 93

84 84
765 765

B. Draw the hour and minute hands to show to the
given time.

11 12 1 11 12 1 11 12 1 11 12 1
10 2 10 2 10 2 10 2
93 93
93 93 84 84

84 84 765 765
765 765
Quarter to 11 Half past 4
6 O’clock Quarter past 8

11 12 1 11 12 1 11 12 1 11 12 1
10 2 10 2 10 2 10 2
93
93 93 84 93

84 84 765 84
765 765 765
8 : 20
2 : 35 7 : 05 12: 55

122 Prime Mathematics Book − 3

C. Write in digital form: (e) Quarter past eight
(f) 35 minutes past 6
(a) Half past two (g) 25 minutes to 7
(b) 12 minutes past 7 (h) 5 minutes to 11
(c) Quarter to nine
(d) 20 minutes to 10

D. Provide A.M. or P.M. for the following times:

(a) It is time to get up. (b) Today it’s a little late for
my breakfast.

The time is ............................ The time is ...........................
(c) Today is Friday. Students are at (d) School is just over.

the special assembly.

The time is ............................ The time is ...........................
(e) The family is having dinner (f) Good night. Have a nice sleep.

together.

The time is ............................ The time is ...........................

E. Rewrite the following times using A.M. or P.M.

(a) 5:40 in the morning. (b) 10 minutes to 7 in the evening.

(c) quarter past 9 in the evening. (d) Quarter to 6 in the evening.

(e) Half past 2 in the afternoon. (f) 25 minutes past 9 at night.

Prime Mathematics Book − 3 123

Conversion of time

Recall the following:

• 60 seconds = 1 minute
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.

Example 1: Convert 40 minutes into seconds. 60
Solution: 1 minute = 60 seconds. × 40
2400
∴ 40 minutes = 60 × 40 seconds = 2400 seconds
60
Example 2: Convert 6 hours into minutes. ×6
Solution: We know 360
24
1 hour = 60 minutes ×3
∴ 6 hours = 60 × 6 minutes 72

= 360 minutes

Example 3: How many hours are there in 3 days?
Solution: We know

1 day = 24 hours
∴ 3 days = 24 × 3 hours = 72 hours.

Example 4: Convert 75 minutes to hours and minutes.

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

1 hour 15 minutes

124 Prime Mathematics Book − 3

Exercise - 7.2

A. 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

B.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

C. 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

D. 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) 135 minutes to hours and minutes

(g) 48 hours to days (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

5 30 Arrange vertically

+ 6 15 Add minutes

11 45 Add hours

= 11 hours and 45 minutes

To subtract 15 minutes 15 seconds from 24 minutes 32 seconds
minutes seconds

24 32 Arrange vertically

− 15 15 Subtract seconds

9 17 Subtract minutes

= 9 minutes 17 seconds

Prime Mathematics Book − 3 125

Exercise - 7.3

A. Perform the following task:

hours minutes hours minutes hours minutes
10 15 9 28
9 12
+ 25 20 + 16 17 +24 17
+7 05

hours minutes hours minutes hours minutes
30 12 21 31
5 20
+ 25 35 + 35 24 7 00
+ 32 08

days hours days hours hours minutes seconds
7 14 12 13 5 22 44

+ 15 7 +5 7 + 11 12 14

days hours minutes hours minutes seconds days hours minutes

10 10 20 14 15 16 56 7

+ 7 11 39 20 25 30 8 9 10

+8 7 6 + 11 2 3

B. 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

126 Prime Mathematics Book − 3

C. Perform the following task:

minutes seconds days hours hours minutes seconds
21 50
30 12 20 34 36
− 12 38
− 25 35 − 9 14 27

hours minutes hours minutes seconds hours minutes seconds
32 46 45 30 24
42 19 36
− 14 18 − 8 11 17
− 12 17 07

D. 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

The calendar

Recall the following:
Nepali calendar 2077

a}zfv 2077 Apr/May 2020 hi] 7 2077 May/June 2020 cfiff9 2077 June/July 2020

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

3114 14 15 1 164 2 175 1 15 2 16 3 17 4 18 5 19 6 20 1 15 2 16 3 17

3 186 4197 5 2108 6 2119 7 220 8 231 9 242 7 21 8 22 9 23 1024 1125 1226 1327 418 5 19 6 20 7 21 8 22 9 23 1024

10253 11264 12275 13286 14297 153208 16219 1428 1529 1630 1731 181 19 2 203 1125 1226 1317 1428 1529 1630 171

17320 1831 1942 2053 2164 2275 2386 21 4 225 23 6 247 258 26 9 2710 182 193 204 215 226 237 248

2497 25180 26191 27120 28131 29142 3013 2811 2912 3013 3114 259 2610 2711 2812 2913 3014 3115

Prime Mathematics Book − 3 127

>fj0f 2077 July/Aug 2020 efb| 2077 Aug/Sep 2020 cflZjg 2077 Sep/Oct 2020

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

1 16 2 17 3 18 4 19 5 20 6 21 7 22 1 17 2 18 3 19 1 17 2 18 3 19 4 20 5 21 6 22 7 23

823 9 24 1025 1126 1227 1328 1429 4 20 5 21 6 22 7 23 8 24 9 25 1026 8 24 9 25 1026 1127 1228 1329 1430

1530 1631 171 182 193 204 215 1127 1228 1329 1430 1531 16 1 172 15 1 16 2 17 3 184 19 5 206 21 7

226 237 248 259 2610 2711 2812 183 194 205 216 227 238 249 228 23 9 2410 2511 2612 2713 2814

2913 3014 3115 3216 2510 2611 2712 2813 2914 3015 3116 2915 3016 3117

sflt{s 2077 Oct/Nov 2020 d+l;/ 2077 Nov/Dec 2020 kf}if 2077 Dec2020/Jan 2021

cfO{ ;f]d du+ n aw' ljlx z'qm zlg cfO{ ;fd] du+ n 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

1 18 2 19 3 20 4 21 1 17 2 18 3014 1 16
5 22 6 23 7 24 8 25 9 26 1027 1128 3 19 4 20 5 21 6 22 7 23 8 24 9 25
1229 1330 1431 15 1 16 2 17 3 184 1026 1127 1228 1329 1430 15 1 16 2 2 17 3 18 4 19 5 20 6 21 7 22 8 23
19 5 206 21 7 22 8 23 9 2410 2511 17 3 184 19 5 206 21 7 22 8 23 9
2612 2713 2814 2915 3016 2410 2511 2612 2713 2814 2915 9 24 1025 1126 1227 1328 1429 1530

1631 17 1 182 19 3 204 21 5 22 6

23 7 248 25 9 2610 2711 2812 2913

df3 2077 Jan/Feb 2021 kmfNug' 2077 Feb/Mar 2021 rq} 2077 Mar/Apr 2021

cfO{ ;f]d d+un aw' 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

1 15 2 16 3 17 4 18 5 19 6 20 1 13 2 14 3 15 4 16 5 17 1 15 2 16 3 17

7 21 8 22 9 23 1024 1125 1226 1327 6 18 7 19 8 20 9 21 1022 1123 1224 4 18 5 19 6 20 7 21 8 22 9 23 1024

1428 1529 1630 1731 181 19 2 203 1325 1426 1527 1628 17 1 182 19 3 1125 1226 1327 1428 1529 1630 1731
21 4 22 5 23 6 247 25 8 26 9 2710 204 21 5 22 6 23 7 248 259 2610 181 192 203 21 4 22 5 23 6 247

2811 2912 2711 2812 2913 3014 258 26 9 2710 2811 2912 3013

Exercise - 7.4

Answer the following :

1. How many months have 31 days ? ..................................................................

2. How many months have 30 days ? ..................................................................

3. What day is Asoj 25 ? ..................................................................

4. How many days are there in Kartik ? ..................................................................

5. How many full weeks are there in Falgun ? ...................................................................

6. How many weeks are there in December ? ..................................................................

7. How many full weeks are there in May ? ...................................................................

8. Which month of English Calendar falls on Bhadra. ..................................................................

128 Prime Mathematics Book − 3

There are seven days in a week.

S. N. English days Nepali days
1. Sunday cfOtjf/
2. Monday ;fd] jf/
3. Tuesday D+funjf/
4. a'wjf/
5. Wednesday ljlxjf/
6. Thursday Zfq' mjf/
7. Zflgjf/
Friday
Saturday

There are 12 months in a year.

S. N. English months S. N. Nepali months
1. January 1. Baishak
2. February 2. Jestha
3. March 3. Ashadh
4. April 4. Shrawan
5. May 5. Bhadra
6. June 6. Ashwin
7. July 7. Kartik
8. August 8. Mangsir
9. 9. Paush
10. September 10. Magh
11. October 11. Falgun
12. 12. Chaitra
November
December

• The order of English and Nepali months are not same.
• The English year starts from the about the middle of the ninth month

of the Nepali calendar.
• There are different calendars in use. English calendar is also called

Christian Calendar or Gregorian calendar. Nepali calendar is known as
Bikram Calendar

Prime Mathematics Book − 3 129

7 days = 1 week
30 days = 1 month (generally)
12 months = 1 year
365 days = 1 year
52 weeks = 1 year

To convert week into days multiply by 7. To convert years into months multiply by 12.
To convert days into weeks divide by 7. To convert months into year divide by 12.
To convert months into days multiply by 30. To convert years into days multiply by 365.
To convert days into months divide by 30. To convert days into years divide by 365.

Writing dates: Date is the time when an event happens. Which year?
Which month? Which day of the month? In English system, date is written
in the order of day,month,year.

03 – 20 – 6 – 2010

Year Read as Tuesday 20th June 2010
month
day of month
day of week
In Nepali system date is written in the order year – month – day

2067 − 2 − 7 − 3 Day of week
Day of month
Month
Year

Generally year, month and day of the month are enough to locate the date of
particular event. For example: 2067.01.25

Convert the following

i) 45 days into week and days

ii) 30 months in to years and months

iii) 140 minutes into hours and minutes. ii) 30 months
i) 45 days 30 months converting into years
45 days converting into weeks and days and months.

= 7) 45 (6 weeks = 12) 30 (2 years
− 42 days − 24 months

3 6

∴ 45 day = 6 weeks 3 days ∴ 30 months = 2 years 6 months

130 Prime Mathematics Book − 3

iii) 140 minutes
140 minutes, converting into hours and minutes.

= 60) 140 (2 hours
− 120 minutes

20

∴ 140 minutes = 2 hours 20 minutes.
Example

Add 4 year, 5 months 3 days and 6 years 3 months 2 days ?

years month days
4 53

+6 3 2
10 years 8 monthy 5 days

6 months 13 days from 9 months 20 days.

month days
4 20

+ 6 13
3 months 7 days

Exercise - 7.5

A. Study the given calendar and answer the following:

(a) Which calendar is it? efb| @)&$ Aug/Sep 2017
cfO{ ;fd]
(b) How many Saturdays are there in d+un aw' ljlx z'qm zlg

this month? Sun Mon Tue Wed Thu Fri Sat

(c) How many days are there in this 1 17 2 18 3 19

(d) month? 420 5 21 6 22 7 23 8 24 9 25 1026
Which months of English calendar
1127 1228 1329 1430 1531 161 172
fall on this month?

(e) How many holidays are there 183 194 205 216 227 238 249

including Saturdays in this month? 2510 2611 2712 2813 2914 3015 3116
(f) On which day does Teej lie?
5 - Fater Days, 8 - Teej, 10 - Rishipanchami

(g) Write the date Wednesday 21st

September 2017 according to the

Nepali Calendar.

Prime Mathematics Book − 3 131

B.Write the following dates in short form (digital form)

(a) The year 2074, Ashadh 25th, Friday 2067.03.25.06

(b) The year 2072, Shrawan 32nd, Saturday

(c) The year 2065, Jesth 7th, Tuesday

(d) The year 2007, May 14th, Friday

(e) The year 2010, November 27th, Thursday

(f) The year 1993, April 5th, Monday

C.Write the following dates in full form:

(a) 2067/10/18/6 (b) 2064/9/22/1

(c) 2019/2/7/3 (d) 7/31/10/2010

(e) 5/16/6/2008 (f) 6/14/5/2007

D. Convert the following

(a) 28 days to weeks (b) 40 days to weeks and days
(c) 90 days to months (d) 130 days to months and weeks
(e) 2 weeks to days (f) 7 weeks 6 days to days
(g) 3 months 10 days to days (h) 3 years to days
(i) 1460 days to years (j) 27 months to years and months

E. Add the following: (b) years days
(a) years months weeks 10 115

27 1 + 26 95
+3 4 2

(c) years months weeks (d) years months weeks
15 0 4 45 6
16 1 1 3 3 13
+4 2 1
+2 2 6

132 Prime Mathematics Book − 3

(e) 5 years 3 months 2 weeks; 6 years 4 months 1 week
(f) 4 years 2 months 15 days and 6 years 7 months 12 days
(g) 9 years 100 days; 11 years 65 days and 2 years 65 days

F. Perform the following task:

1. years months 2. weeks days 3. years months days

11 10 76 9 10 21

− 7 8 − 2 2 − 6 6 13

4. months days 5. years months 6. years months weeks

12 24 15 11 25 9 3

− 7 13 − 6 07 − 12 4 1

7. Subtract 2 week 3 days from 7 weeks 6 days.
8. Subtract 6 years 2 months 13 days from 9 years 10 months 21 days.

Unit Revision Test

A. Draw the minute and hour hands in the given
clocks indicating the given time.

8:20 40 minutes past 2

Prime Mathematics Book − 3 133

B.Write the following times in digital form:

(a) 25 minutes past 10 = (b) 10 minutes to 5 =
(c) Half past 2 = (d) Quarter to 6 =

C. Rewrite the following times in digital form
providing A.M. or P.M.

(a) 46 minutes past 5 in the morning.
(b) Quarter past 7 in the evening.
(c) Half past 3 at night.
(d) Quarter to 10 in the morning.

D. Convert the following:

(a) 6 hours into minutes. (b) 2 days 6 hours into hours.

(c) 145 minutes to hours and minutes. (d) 6 weeks 6 days to days.

E. Add the following:

(a) 12 hours 14 minutes 22 seconds and 3 hours 25 minutes 34 seconds.
(b) 6 years 3 months 2 weeks and 4 years 5 months 1 week.

F.Subtract the following.
a) Subtract 4 years 5 months from 6 years 8 months.
b) Subtract 3 week 5 days from 7 week 6 days.

G.Write the following dates in the short form:

(a) The year 1993, April 5th, Monday
(b) The year 2065, Poush 18, Friday

134 Prime Mathematics Book − 3

Unit

8

Estimated periods − 8

MONEY

Objectives

At the end of this unit, the students will be able to:
• convert rupees into paisa and paisa into rupee.
• add or subtract different amounts of money.
• solve the word problems involved with addition and subtraction of different amounts

of money.

Teaching Materials
• different coins and notes in current use.

Activities

It is better to
• show coins and notes of different denominations.
• demonstrate to develop the concept that 100p is equivalent to 1 rupees (exchanging 1

rupee note and equivalent coins etc)
• let the students practise conversion of paisa to rupees and rupees to paisa.

Money The paper money was issued by
Emperor Hein Tsung in China between
806 and 821 A.D.

Learn the following:
Our coins

5 Paisa 10 Paisa 25 Paisa 50 Paisa 1 Rupee 2 Rupees 5 Rupees 10 Rupees

Our notes

1 Rupee 2 Rupees 5 Rupees 10 Rupees

20 Rupees 25 Rupees 50 Rupees

100 Rupees 250 Rupees

500 Rupees 1000 Rupees

136 Prime Mathematics Book − 3

In short rupee is written as Re., rupees as Rs. and paisa as p.

Re. 1 = 100p × 100
To convert rupees to paisa we multiply by 100 and Rs. conversion P
to convert paisa to rupees we divide by 100.

To convert 5p into rupees: ÷ 100

5p = 5 Rs. which is 5 hundredth of a rupee or 0.05 of a rupee
100
= Rs. 0.05

Thus, we write 3 rupees 25 paisa in short as Rs. 3.25

Exercise - 8.1

A. Write the short form as given in the example:

Example: 7 rupees 5 paisa = Rs. 7.05
(a) 2 rupees 4 paisa = ......... (e) 51 rupees 10 paisa = .........

(b) 8 rupees 20 paisa = ......... (f) 115 rupees 50 paisa = .........

(c) 10 rupees 25 paisa = ......... (g) 200 rupees 75 paisa = .........

(d) 15 rupees 5 paisa = ......... (h) 85 rupees 95 paisa = .........

B.Write as rupees and paisa as given in the example:

Example: Rs. 8.25 = Rs. 8 rupees 25 paisa

(a) Rs. 4.05 = ..................................

(b) Rs. 9.25 = ..................................

(c) Rs. 14.06 = ..................................

(d) Rs. 24.55 = ..................................

(e) Rs. 34.50 = ..................................

(f) Rs. 50.75 = ..................................

(g) Rs. 1.80 = ..................................

(h) Rs. 1.50 = .................................. Prime Mathematics Book − 3 137

C. Convert the following into paisa.

(a) 3 rupees 15 paisa Example:
(b) 7 rupees 20 paisa To convert 5 rupees 25 paisa
(c) 12 rupees 35 paisa into paisa:
(d) 16 rupees 50 paisa
(e) 45 rupees 60 paisa 5 rupees 25 paisa
(f) 80 rupees 75 paisa = Rs. 5 + 25p
(g) 92 rupees 5 paisa = 5 × 100p + 25p
= 500p + 25p
= 525p

D. Convert the following rupees into paisa:

(a) Rs. 4 (b) Rs. 9 Example:
(c) Rs. 5.20 (d) Rs. 13.14 To convert Rs. 2.08 into paisa:
(e) Rs. 10.50 (f) Rs. 28.20
(g) Rs. 50.90 (h) Rs. 125.75 Rs. 2.08 = Rs. 2 + Rs. 0.08
= 2 × 100p + 0.08 ×100p
= 200p + 8p
= 208p

E. Convert the following paisa into rupees:

(a) 235p (b) 205p Example:
(c) 1012p (d) 987p To convert 123p into
(e) 12340p (f) 850p rupees:
(g) 10025p (h) 100005p 123p = 100p + 23p

= Re. 1 + 23p
= Rs. 1.23

F. Perform the following task:

A p Rs. p Rs. p
Rs. 32 18 48
38 42 32 45 50
87 70
+ 34 +125
+ 25 = =
= 112

138 Prime Mathematics Book − 3

Rs. p Rs. p Rs. p
134 20 720 65 200 47
+52 40 + 50 25 + 50 33
= = =

= = =

B Rs. p Rs. p Rs. p
51 52 180 81 85 95
34 − 50 33 − 16 76
−34 18 = =
= 17
= = =

Rs. p Rs. p Rs. p
185 74 486 70 549 51
− 95 56 − 247 26 − 159 12
= = =

= = =

G. Solve the following word problem:

(a) Anita has Rs. 650 and 47 paisa and Kusum has Rs. 234 and 33
paisa. How much money do they have altogether?

(b) A kg of apples cost Rs. 65 and 35paisa and a kg of oranges cost Rs.
75 and 45 paisa. Find the total cost of 1 kg of apples and 1 kg of
oranges.

(c) A copy costs Rs. 20 and 40 paisa and a pencil costs Rs. 4 and 30
paisa. Find the total cost of a copy and a pencil.

(d) If your father gave you Rs. 12 and 25 paisa. and mother gave you
Rs. 8 and 20 paisa, how much money you have altogether?

Prime Mathematics Book − 3 139

Unit Revision Test

1. (a) Write 6 rupees 12 paisa in short form.
(b) Write Rs. 15.24 as rupees and paisa.

2. (a) Convert 8 rupees 20 paisa into paisa.
(b) Convert Rs. 27.20 into paisa.

3. (a) Convert 876p into rupees?
(b) Convert 567p into rupees and paisa.

4. Perform the following task:

Rs. P Rs. P
24 48 127 91
+ 38 22 − 37 51
= =

= =

5. (a) Add: Rs. 5 and 27 paisa with Rs. 15 and 13 paisa.
(b) Subtract 7 rupees 45 paisa from 19 rupees 75 paisa.

6. (a) Richa has 32 rupees 25 paisa and Nita has 74 rupees 50 paisa.
How much money do they have altogether?

(b) Arya has 54 rupees 60 paisa. She gave 23 rupees 25 paisa to her
sister. How much money is left with her now?

140 Prime Mathematics Book − 3

Unit Estimated periods − 7

9

LENGTH

Objectives

At the end of this unit, the students will be able to:
• convert metres into centimeters.
• convert centimeters into metres and centimetres.
• convert km into metres and metre into km and metres.
• measure the length of objects using scales.

Teaching Materials
• ruler, metre scale, measuring tape, etc.

Activities

It is better to
• show different length measuring devices.
• make discussion about parts of scale.
• demonstrate the activities of measuring the lengths of different objects around the

class.
• perform activities of conversion of length.
• perform addition and subtraction related to metres and centimetres and kilometres and

metres.

Length

The Nile river of Africa starting from Lake
Victoria and ending in Mediterranean sea is
4,145 miles about 6669 km long.

Learn the following:

• We often use questions like ‘How long?’ ‘How high?’, ‘How far?’ to
know the lengths, heights and distances.

• Standard units for measuring lengths are millimetre, centimetre,
metre, kilometre etc. Small lengths are measured in millimetres or
centimetres. Lengths of long objects are measured in metres and
kilometres. Distance between two places is measured in kilometres.

mm 1 cm 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Centimeters

0 Inches 1 2 3 4 5 6
0 Inches 1 2 3 4 5 6
The given figure is a ruler or scale

2cm
10mm 10mm

mm 1 cm 2 34 5 78 9 10 11 12 13 14 15

Centimeters

• Millimetre is written as mm, centimetre as cm, metre as m

and Kilometre as km, in short.

10 millimetres = 1 centimetre i.e. 10 mm = 1 cm

100 centimetres = 1 metre i.e. 100cm = 1 m

1000 metres = 1 kilometre i.e. 1000m = 1 km

142 Prime Mathematics Book − 3

Conversion >÷10 >÷100
mm cm m
cm

×10> ÷>1000 ×100>
m Km

Bigger unit to smaller unit ⇒ multiply ×1000>
Smaller unit to bigger unit ⇒ divide
Example 1 : convert 5cm into millimetres. cm is the bigger unit,
Solution: we know 1cm = 10mm mm is the smaller unit.
Bigger to smaller unit,
∴ 5cm = 5 × 10mm = 50mm
we multiply

Example 2 : Convert 400 centimetres into metres. cm is the smaller
Solution: We know 100cm = 1m unit, m is the bigger
∴ 400cm = (400 ÷ 100)m = 4m unit Smaller to bigger

unit, we divide.

Exercise - 9.1

A. Measure the following object using a ruler and find
the length of the objects.

a) The length of pencil is ............ cm.

b) The length of blackboard is ................ cm.

c) The length of book is ................... cm.

Prime Mathematics Book − 3 143

Instrumet Box

d) The length of instrument box is ............ cm.

e) The length of instrument broom is ............ cm.

B. Convert centimetres into millimetres.

(a) 2 cm = 2 × 10mm = 20mm

(b) 5 cm = × =

(c) 8 cm = × =

(d) 11 cm = × =

(e) 15 cm = × =

(f) 27 cm = × =

C. Convert metres into centimetres:

(a) 3m = 3 × 100cm = 300cm

(b) 6m = × =

(c) 10m = × =

(d) 16m = × =

(e) 34m = × =

(f) 40m = × =

144 Prime Mathematics Book − 3

E. Change the following into metres:

(a) 400 cm = ÷ m = ...........
÷ m = ...........
(b) 700 cm = ÷ m = ...........
÷ m = ...........
(c) 800 cm = ÷ m = ...........
÷ m = ...........
(d) 1200 cm =

(e) 1800 cm =

(f) 2300 cm =

E. Change the following into centimetres:

3m 40cm = 3 × 100cm + 40cm 6m 84cm = ...........
9m 75cm = 300cm + 40cm 5m 94cm = ...........
= 340cm 16m 17cm = ...........

= = ...........
= = ...........
= = ...........

14m 72cm = = ...........
= = ...........
=
= ...........

Prime Mathematics Book − 3 145