Math5

Example:

Find the interest of Rs 100 in 1 year if the rate of interest is (i) 10% (ii) 20%
(ii) 12%
Solution:
(i) The rate of interest = 10%
\ The interest of Rs 100 in 1 year = Rs 10

(ii) The rate of interest = 20%
\ The interest of Rs 100 in 1 year = Rs 20

(iii) The rate of interest = 12%
\ The interest of Rs 100 in 1 year = Rs 12

Example :
Find the simple interest of Rs 300 in 2 years at a rate of 12% per annum.
Solution:

Here, Rate = 12% per annum.

Interest of Rs 100 in 1 year = Rs 12 Interest in 1 yr = Rs 12
Interest of Rs 100 in 2 years = Rs 12x2 Interest in 2 yr = Rs 12 × 2

Interest of Rs 1 in 2 years = Rs 12 × 2 Interest of Rs 100 = Rs 12
100
Rs 12
Interest of Rs 300 in 2 years = Rs 12 × 2 × 300 Interest of Re 1 = 100
100
12 × 2 × 300 Rs 12
Required interest = Rs 100 Interest of Rs 300 = 100 × 300

= Rs 72

Exercise 7.4

1. Find the interest of Rs. 100 in 1 year with the given rate.

Rate 5% 10% 20% 18% 12%
Interest Rs ........ Rs ........ Rs ........ Rs ........ Rs ........

2. a. If the interest of Rs. 100 in 1 year is Rs. 8, what is the interest of Rs.
500 in 4 years?

b. If the interest of Rs. 100 in 1 year is Rs. 12, what is the interest of Rs.
600 in 3 years?

c. If the interest of Rs. 100 in 1 year is Rs. 24, what is the interest of Rs.
2000 in 4 years?

Oasis School Mathematics Book-5 151

3. Using unitary method, calculate the interest in each of the following
cases:

a. Rs. 500 for 2 years at the rate of 10% per annum.
b. Rs. 400 for 3 years at the rate of 12% per annum.
c. Rs. 3000 for 4 years at the rate of 20% per annum.
d. Rs. 4000 for 5 years at the rate of 10% per annum.

4. a. Sharmila deposited Rs. 5000 in a bank. If the bank gives interest at
a rate of 9% per year, how much interest does she get in 4 years?

b. Rajanee borrows Rs. 4500 for 3 years at 5% per year. What interest
does she have to pay?

c. Sharada deposited Rs. 3600 in a bank for 4 years at a rate of 12% per
year. How much interest does she receive?

1. Consult your teacher 2. a) Rs. 160 b) Rs. 216 c) Rs. 1920 3. a) Rs. 100
b) Rs. 144 c) Rs. 2400 d) Rs. 2000 4. a) Rs. 1800 b) Rs. 675 c) Rs. 1728

Profit & Loss

Look and learn:
I bought a doll for Rs. 600.
\ Cost price of the doll = Rs. 600.
I sold it for Rs. 650.
\ Selling price of the article = Rs. 650.
I paid Rs. 600 for an article and I sold it for 650. I made a profit of Rs. 650 – Rs 600
= Rs 50 \ Profit = Selling price – Cost price
Ram bought an article for Rs. 700.
He sold it for Rs. 600. There is a loss of Rs. 700 – Rs. 600 = Rs. 100.
\ Loss = Cost price – Selling price
Hence,
Cost price : The amount of money which we pay to buy an article is the cost
price. It is denoted by C.P.
Selling price : The amount of money at which we sell an article is the selling
price. It is denoted by S.P.

152 Oasis School Mathematics Book-5

Profit : The difference between the selling price and the cost price is the profit.

\ Profit = S.P. – C.P.

When S.P. is more than C.P., there is a profit.

Loss : The difference between the cost price • Profit : S.P. – C.P. • Loss = C.P. – S.P.
and the selling price is the loss. • C.P. = S.P. – profit • C.P. = S.P. + loss
• S.P. = C.P. + profit • S.P. = C.P. – loss
\ Loss = C.P. – S.P.

When C.P. is more than S.P., there is a loss.

Example :

Calculate profit or loss in the following cases.

a. C.P. = Rs. 240, S.P. = Rs. 300 b. C.P. = Rs. 450, S.P. = Rs. 400

Solution :

a. Here, C.P. = Rs. 240, S.P. = Rs. 300 S.P. > C.P. There is
since, S.P. > C.P, there is profit profit.

We have,
profit = S.P. – C.P
= Rs. 300 – Rs. 240 = Rs. 60

b. Here, CP = Rs. 450, S.P = Rs. 400 C.P. > S.P. There is
loss.
Since, S.P < C.P, there is loss

Loss = C.P – S.P

= Rs. 450 – Rs. 400

= Rs. 50

Exercise 7.5

1. Find profit or loss in each of the following cases.
a. CP = Rs. 320, SP = Rs. 350
b. CP = Rs. 625, SP = Rs. 600
c. CP = Rs. 1260, SP = Rs. 1110
d. CP = Rs. 1540, SP = Rs. 1810
e. CP = Rs. 2550, SP = Rs. 3000

Oasis School Mathematics Book-5 153

2. Find the SP in each of the following cases.
a. CP = Rs. 500, Profit = Rs. 25 b. CP = Rs. 750, Loss = Rs. 60
c. CP = Rs. 1270, Loss = Rs. 150 d. CP = Rs. 1800, Profit = Rs. 240
e. CP = Rs. 2540, Profit = Rs. 360

3. Find CP in each of the following cases.
a. SP = Rs. 1000, Profit = Rs. 70 b. SP = Rs. 1260, Loss = Rs. 85
c. SP = Rs. 1550, Profit = Rs. 150 d. SP = Rs. 1660, Loss = Rs. 165
e. SP = Rs. 3040, Profit = Rs. 275

4. a. A radio was bought at Rs. 1200 and sold at Rs. 1500. Find the gain.
b. Find the profit or loss if an article which cost Rs. 800 was sold at Rs.

900.
c. A man bought a mobile phone set at Rs. 2500 and sold it at Rs. 2400.

Find his gain or loss.

1. a) Profit = Rs. 30 b) Loss = Rs. 25 c) Loss = Rs. 150 d) Profit = Rs. 270
e) Profit = Rs. 450 2. a) Rs. 525 b) Rs. 690 c) Rs. 1120 d) Rs. 2040
e) Rs. 2900 3. a) Rs. 930 b) Rs. 1345 c) Rs. 1400 d) Rs. 1825 e) Rs. 2765
4. a) Rs. 300 b) Profit = Rs. 100 c) Loss = Rs. 100

Ratio

Sharada and Manisha got 30 marks and 60 marks respectively.

Let's compare their marks.

Manisha got 30 marks more than Sharada, this is the comparison by difference.

Sharada's marks to Manisha's marks = 30 63=0021=
60
2
or, Manisha's marks to Sharadas marks = 1

This is a comparison by division.

Hence, comparison by division is called ratio.

154 Oasis School Mathematics Book-5

Let's take two quantities ‘a’ and ‘b’ of same unit.

The ratio of a to b = a : b or a Write: a : b Read : a is to b
b Write b : a Read : b is to a

The ratio of b to a = b : a or b
a

• A ratio is the comparison of two quantities of same unit by division.

• Ratio is a number with no unit.

Example : 25:60 = 25
60
Find the ratio of Rs 25 to Rs 60.

Solution:

Ratio of Rs to Rs 60 = 25:60

= 25
60
5
= 12

= 5 : 12

Example : While taking ratio, both quantities
should be in same unit.
Find the ratio of 50cm to 2m.
Solution: We have to convert the ratio
into its lowest form.
Here, 2m = 2 × 100 cm = 200 cm

Ratio of 50 cm to 200 cm = 50 : 200

= 50
200

= 5
20
1
= 4

Exercise 7.6

1. Represent the following as the ratio of first number to the second
number and write it in the simplest form:

a. 6, 9 b. 12, 24 c. 9, 27 d. 16, 8

e. 25, 15 f. 96, 36 g. 36, 8

Oasis School Mathematics Book-5 155

2. Find the ratio of the following quantities and express it in the simplest
form:

a. Rs 20 to Rs 50 b. 35 cm to 65 cm c. 24 l to 36 l

d. 12 oranges to 14 oranges e. 40 minutes to 55 minutes

3. Find the ratio of following quantities and express it in the simplest
form:

a. 25 paise to Re 1 b. 2 kg to 800 gm c. 75 cm to 2m

d. 35 minutes to 1 hr e. 50 seconds to 2 minutes f. 5 days to a week

4. a. The length and breadth of a rectangular field are 25m and 10 m respectively.

Find the ratio of the length and breadth.

b. The length of the yellow and green pencils are 12 cm and 8 cm
respectively. Find the ratio of their length.

c. There are 45 boys and 35 girls in class V. Find the ratio of the number
of boys to the number of girls.

d. A man earns Rs 25,000 per month and saves Rs 15000 per month.
Find the ratio of his earning and saving.

5. Find the ratio of the height of: c. Ram and Hari
a. Ram and Shyam b. Shyam and Hari

150cm 160cm 175cm

Ram Shyam Hari

1. a) 2 : 3 b) 1 : 2 c) 1 : 3 d) 2 : 1 e) 5 : 3 f) 8 : 3 g) 9 : 2 2. a) 2 : 5 b) 7 : 13
c) 2 : 3 d) 6 : 7 e ) 8 : 11 3. a) 1 : 4 b) 5 : 2 c) 3 : 8 d) 7 : 12 e) 5 : 12
f) 5 : 7 4. a) 5 : 2 b) 3 : 2 c) 9 : 7 d) 5 : 3 5. Consult your teacher.

156 Oasis School Mathematics Book-5

Objective Questions

Colour the correct alternatives:

1. Aadhya gets 60 marks out of 100 full marks. Her marks in percent is

100% 60% 60 %
100

2. Percentage of shaded part in this figure is

50% 75% 25%

3. 45% is equal to 9 45
45 20 20
50
5
4. 5% of 20 is equal to

1

5. Cost of a pen is Rs 30. Then the cost of 3 pens is

Rs 30 Rs 90 Rs 10

6. The rate of interest is 10%. Then the interest of Rs 100 in 1 year is

Rs 10 Rs 100 Rs 1000

Oasis School Mathematics Book-5 157

Unit Test

Full marks: 22

1. Find the ratio of (a) 50 cm to 1m (b) Rs. 3 to 70 Paise. 2

2. a. Cost price of an article is Rs. 400 and it is sold at Rs. 350. Find profit or

loss. 2

b. An article is sold for Rs. 950 which was bought for Rs. 800. Find the

profit or loss. 2

3. a. A man earns Rs. 4,500 and saves Rs. 1500. Find the ratio of his saving

and earning. 2

b. An article was bought at Rs. 1500 and sold at the profit of Rs. 450.

Find the selling price of the article. 2

4. Find the value of: 2
a. 15% of 900
b. 5% of 3000

5. In a class, there are 60 students. If 10% students are absent find the
number of absent students. 2

6. a. If the cost of an article is Rs. 20, what is the cost of 14 such

articles? 2

b. The cost of 8 balls is Rs. 192. What is the cost of a ball? 2

7. a. Find the interest of Rs. 100 in one year with the given rate:

i. 5%, ii. 12% 2

b. Using unitary method, calculate the interest of Rs. 500 for 2 years at

a rate of 10% per annum. 2

158 Oasis School Mathematics Book-5

UNIT Measurement of
Time and Money
8

12 Estimated Teaching Hours: 15
93

6

Contents • Measurement of time

• Addition and subtraction of time

• Multiplication and division of time by a
number

• Measurement of money

• Addition and subtraction of money

• Multiplication and division of money by a
number

Expected Learning Outcomes

Upon completion of this unit, students will be able
to develop the following competencies:

• To convert one unit of time into another unit
• To add and subtract the time
• To multiply and divide the time by a number
• To convert one unit of money into another unit
• To add and subtract the amount of money
• To multiply and divide money by a number

Materials Required : Clock, calendar, paper notes, etc.

Oasis School Mathematics Book-5 159

Measurement of time

Review

We have already discussed the units of time and their relation in previous
classes. Let's revise it.

60 seconds = 1 minute
60 minutes = 1 hour
24 hours = 1 day
7 days = 1 week
30 days = 1 month
12 months = 1 year
365 days = 1 year
10 years = 1 decade
100 years = 1 century

Example :

Convert 24 minutes 35 seconds into seconds

Solution: I have to multiply minute by 60
24 mins 35 sec to convert it into seconds.

= 24 × 60 sec + 35 sec

= 1440 sec + 35 sec

= 1475 sec

Example :

Convert 2 hours 45 minutes 26 seconds into seconds

Solution: 1 hr = 60 mins
2 hours 45 minutes 26 seconds 2 hrs = 2 × 60 mins
= 2 × 60 mins + 45 mins + 26 sec = 120 mins

= 2 × 60 × 60 sec + 45 × 60 sec + 26 sec

= 7200 sec + 2700 sec + 26 sec

= 9926 sec

Do you know !

• A leap year occurs in every four years.
• 1 leap year = 366 days.

160 Oasis School Mathematics Book-5

Example :

Convert 324 minutes into hours and minutes.

Solution:

324 minutes 60 mins = 1 hr

= 324 hours 1 min = 1 hr
60 60

= 5 hours 24 minutes 324 mins = 324 hr
60

60) 324 ( 5 hrs
- 300
24 mins

Example :

Convert 8246 seconds into hours, minutes and seconds.

Solution: Steps:
8246 seconds • Convert seconds into minutes and

= 8246 minutes seconds.
60
• Convert minutes into hours and
minutes.

60) 8246( 137 minutes While converting seconds into
- 60 minutes
224
- 180 • We divide given seconds by 60
446
- 420 • quotient represents minutes and
26 seconds remainder represents second.

Again, While converting minutes into hour

137 minutes = 137 hours • Divide given minutes by 60.
60
• Quotient represents hours and the
60) 137(2 hours remainder represents minutes.
- 120
17 minutes

\ 8246 seconds = 2 hours 17 minutes 26 seconds.

Oasis School Mathematics Book-5 161

Example :

Convert 83 months into years and months.
Solution:
83 months

= 83 years
12

12) 83( 6 years
- 72
11 months

\ 83 months = 6 years 11 months

Exercise 8.1

1. Convert into seconds:

a. 4 mins b. 8 mins 24 sec c. 3 hrs 40 mins 25 sec

2. Convert into minutes:

a. 6 hrs b. 7 hrs 25 mins c. 18 hrs 16 mins

3. Convert into months:

a. 7 years b. 8 years 6 months c. 9 years 10 months

4. Convert into days: b. 7 weeks c. 3 months 18 days
e. 4 years f. 3 years 2 days
a. 8 months
d. 7 weeks 4 days

5. Convert into minutes and seconds:

a. 274 seconds b. 336 seconds c. 450 seconds

6. Convert into hours and minutes:

a. 86 minutes b. 144 minutes c. 224 minutes

7. Convert into days and hours:

a. 38 hours b. 67 hours c. 132 hours

8. Convert into weeks and days:

a. 85 days b. 122 days c. 138 days

9. Convert into years and months:

a. 42 months b. 127 months c. 226 months

10. Convert into hours, minutes and seconds:

a. 5660 seconds b. 10824 seconds c. 12420 seconds

162 Oasis School Mathematics Book-5

1. a) 240 sec. b) 504 sec. c) 13225 sec. 2. a) 360 mins b) 445 mins.
c) 1096 mins. 3. a) 84 months b) 102 months c) 118 months 4. a) 240 days
b) 49 days c) 108 days d) 53 days e) 1460 days f) 1097 days 5. a) 4 mins 34 sec.
b) 5 mins 36 sec c) 7 mins 30 sec. 6. a) 1 hrs. 26 mins b) 2 hrs. 24 mins
c) 3 hrs. 44 mins. 7. a) 1 day 14 hrs. b) 2 days 19 hrs. c) 5 days, 12 hrs.
8. a) 12 weeks, 1 day b) 17 weeks, 3 days c) 19 weeks, 5 days
9. a) 3 yrs, 6 months b) 10 yrs, 7 months c) 18 yrs, 10 months.
10. a) 1 hrs. 34 mins 20 sec. b) 3 hrs, 24 sec. c) 3 hrs, 27 mins.

Addition and subtraction of time

Let's learn the process of addition and subtraction of time from the following
example.

Example :

Add: 6 hrs 48 mins 38 sec and 5 hrs 51 mins 32 sec:

Solution: hrs mins sec 70 sec = 1 min 10 sec
6 48 38
+ 5 51 32 99 mins + 1 min = 100 mins
11 99 70
12 40 10 = 1 hr 40 mins

11 hrs + 1 hr = 12 hrs

Alternative method: 38 sec
6 hrs 48 mins 32 sec
+ 5 hrs 51 mins 70 sec
11 hrs 99 mins

1 hrs 1 hr 39 mins 1 min 10 sec
12 hrs 40 mins 10 sec

Example : mins sec
Subtract:
hrs 79 85 1 min 25 sec = 85 sec
11
20 25 1 hr 19 mins = 79 mins
12
- 8 50 45
3 29 40 \ 12 hrs 20 mins 25 sec - 8 hrs 50 mins 45 sec

= 3 hrs 29 mins 40 sec

Oasis School Mathematics Book-5 163

Example : months days 1 month 12 days = 42 days
Subtract: 18 42 1 yr 6 months = 18 months

years 7 12
12 9 20
9 22
13
- 6
6

Class Assignment 85 mins = 1 hr 25mins
95 mins = ............ hr ............ mins
Convert as follows: 100 mins = ............ hr ............ mins
80 sec = 1 mins 20 sec 105 mins = ............ hr ............ mins
95 sec = ............ mins ............ sec 110 mins = ............ hr ............ mins
75 sec = ............ mins ............ sec 115 mins = ............ hr ............ mins
100 sec = ............ mins ............ sec

45 days = 1 hrs 15 days
50 days = ............ hr ............ days
35 days = ............ hr ............ days
42 days = ............ hr ............ days
22 months = ............ hr ............ days
18 months = ............ hr ............ days
17 months = ............ hr ............ days

Multiplication and division of time
Let's learn the multiplication and division of time from the following examples:

Example :

Multiply: hours minutes seconds 105 sec = 1 min 45 sec
5 24 35
×3 72 mins + 1 min = 73 mins
15 72 105
16 13 45 = 1 hr 13 mins

15 hrs + 1 hr = 16 hrs

164 Oasis School Mathematics Book-5

5 hours 24 mins 35 seconds
× 3
15 hours 72 mins 105 seconds

15 hours 1 hr 12 mins 1 min 45 sec
16 hours 13 mins 45 sec

Example :

Divide: 13 hours 48 mins 32 seconds by 5.

hrs mins sec

5 13 48 30 2 hrs

-10

3 hrs 48 mins

= (3 × 60 + 48) mins

= 228 mins

5 228 mins 45 mins • Divide hrs, 13 ÷ 5 = 2 hrs, remainder = 3 hrs
- 20
28 • Convert the remainder of hrs into mins, 3 × 60
- 25 mins = 180 mins

3 mins 30 sec • Add the minutes, 180 mins + 48 mins = 228
= 3 × 60 sec 30 sec mins
= 210 sec
• Divide minutes, 228 ÷ 5 = 45 mins, remainder = 3
5 210 sec 42 sec mins
- 20
10 • Convert remainder of mins into sec 3 × 60 sec =
- 10 180 sec
0
= 2 hrs 45 mins 42 sec • Add seconds, 180 sec + 30 sec = 210 sec

• Divide seconds, 210 sec ÷ 5 = 42 sec

Oasis School Mathematics Book-5 165

Exercise 8.2 b. Hours Minutes Seconds
8 40 35
1. Addthefollowing: + 9 25 40
a. Hours Minutes Seconds
5 45 35
+ 6 25 40

c. Years Months Days d. Years Months Days

5 8 24 8 9 19

+ 6 9 25 + 12 7 25

2. Subtract the following: b. Hours Minutes Seconds

a. Hours Minutes Seconds 28 25 30
12 45 25
- 6 55 30 - 24 45 42

c. Years Months Days d. Years Months Days

8 3 15 12 4 13

- 3 8 22 - 8 9 18

3. Multiply the following: b. Hours Minutes Seconds
a. Hours Minutes Seconds 8 45 32
7 25 35 × 5
× 4

c. Years Months Days d. Years Months Days

7 8 15 12 9 24

× 3 × 7

4. Divide:
a. 15 minutes 30 seconds by 6
b. 12 hours 30 minutes by 5
c. 15 hours 30 minutes 48 seconds by 4

166 Oasis School Mathematics Book-5

d. 15 hours 50 minutes 15 seconds by 7

e. 10 years 7 months 12 days by 6

f. 18 days 20 hours 40 minutes by 5

5. a. A man walked for 2 hours 25 minutes 45 seconds on the first day
and he walked for 3 hours 46 minutes 26 second on the second day.
How much did he walk altogether?

b. Suresh worked for 2 days 15 hours 29 minutes to complete a work.
He worked for 5 days 13 hours 55 minutes to complete another
work. How many hours did he work altogether?

6. a. Date of birth of Anasuya is 2064/4/12. Calculate her age in years ,
months and days.

b. Ananya’s age is 7 years 8 months 16 days and Abha’s age is 4 years 10
months 25 days. By how much Abha is younger than Ananya?

7. a. A teacher teaches for 4 hours 25 mintues in a day. For how long will he
teach in 6 days?

b. A pipe takes 2 hours 25 minutes 45 seconds to fill a cistern. How long
does it take to fill 4 such cisterns?

8. One tap can fill a tank in 5 hours 45 minutes 12 second. How long will 4 pipes
take to fill the same tank?

9. The following table shows the time of departure of the buses from Kathmandu
and the time of arrival to different places. Observe this table and answer the
following questions:

Place Time of departure Time of arrival

Pokhara 7:00 A.M. 1:30 P.M.

Biratnagar 5:30 A.M. 4:15 P.M.

Nepalgunj 5:00 A.M. 4:30 P.M.

Bharatpur 8:00 A.M. 12:30 P.M.

Find how long do the buses take to arrive at:

a. Pokhara b. Biratnagar c. Nepalgunj d. Bharatpur

Oasis School Mathematics Book-5 167

10. The following table shows the time of departure of the buses from
Kathmandu:

Place Time of departure Duration of
journey

Ghorahi 6:00 A.M. 10 hours

Malangawa 5:30 A.M. 9 hours

Birgunj 5:00 A.M. 6 hours 15 minutes

Gorkha 6:30 A.M. 4 hours 30 minutes
c. Birgunj d. Gorkha
Find the time of arrival at:

a. Ghorahi b. Malangawa

Answers: Consult your teacher

Measurement of money

Rs. 10 Re. 1 Rs. 2 Rs. 5
Rs. 20 Rs. 50 Rs. 100

Rs. 500 Rs. 100

Our money is measured in Paise (P) and Rupees (Rs).
Notation

25 Rupees = Rs 25

1 Rupee = Re 1

85 Paise = 85 P

168 Oasis School Mathematics Book-5

Conversion of money
To convert rupees into Paise and Paise into rupees we have to use the relation.

Re 1 = 100 Paise

Example : I understand! To convert Rs into Paise
we have to multiply Rs by 100. To
Convert Rs 5 into Paise. convert Paise into rupees we have to
Solution: divide Paise by 100.
Rs 5 = 5 × 100 Paise
= 500 Paise Example :
Convert Rs 6.25 into Paise.
Example : Solution:
Rs 6.25 = 6.25 × 100 Paise
Convert 450 Paise into rupees. = 625 Paise

Solution: Remember !
• 5 rupees 35 Paise = Rs 5.35
450 Paise = Rs 450 • 12 rupees 45 Paise = Rs 12.45
100 • 30 rupees 25 Paise = Rs 30.25

= Rs 4.50

Example :

Convert Rs 5 and 35 p into Rs.

Solution:

Rs 5 + Rs 35
100

= Rs 5 + Rs 0.35

= Rs 5.35

Addition and subtraction of money

Let’s learn the process of addition and subtraction of money from the given
example.

Example :

Add: 25 rupees 65 Paise and 36 rupees 75 Paise.

Solution: Paise 140 P = 1 rupee 40 Paise

Rs

25 65

+ 36 75

61 140

62 40

Oasis School Mathematics Book-5 169

Alternative method: Steps:
25 rupees 65 Paise = Rs 25.65 • Convert Rs and Paise into Rs

36 rupees 75 Paise = + Rs 36.75 (in decimal).

Rs 62.40 • Add rupees.

62 rupees 40 Paise

Example : 1 rupee 45 Paise = 145 P

Subtract: 25 Rupees 45 Paise - 18 Rupees 75 Paise
Solution:

Rs Paise Alternative method:
24 145 25 Rupees 45 Paise = Rs 25.45
25 45 18 Rupees 75 Paise = – Rs 18.75
- 18 75 Rs 6.70
6 70 = Rs 6 and 70 Paise

Multiplication and division of money by a whole number
Let’s learn the process of multiplication and division of money by a whole
number from the given example.

Example :

Add: 25 Rupees 65 Paise and 36 Rupees 75 Paise.
Solution:

Rs Paise Alternative method:
12 Rupees 25 Paise = Rs 12.25
12 25 ×7
Rs 85.75
× 7 = 85 Rupees 75 Paise

84 175
85 75

= 85 Rupees 75 Paise

170 Oasis School Mathematics Book-5

Example :

Divide: 33 Rupees 48 Paise by 4

Solution: Rs Paise Alternative method:
4 33 48 8
– 32 Rs 33 and 48 Paise = Rs 33.48
Re. 1 48 Paise
= 148 Paise Now,

4 148 37 Paise 4) 33.48 (8.37
- 12
28 - 32
- 28
14

- 12

28

- 28 \ Rs 8.37
0 = Rs 8 and 37 Paise

0

\ 33 Rupees 48 Paise ÷ 4 = 8 Rupees 37 Paise

Example : 5 254.75 50.95
A man bought 5 kg of rice at Rs 254 and 75 P. - 25
Find the cost of 1 kg of rice. 47
Solution: - 45
25
Cost of 5 kg rice = Rs. 254 and 75 P - 25
0
= Rs. 254.75
Now, cost of 1kg rice = Rs. 254.75

5
\ Cost of 1 kg rice = Rs. 50.95

Exercise 8.3

1. Convert into Paise:

a. Rs 6 b. Rs 12 c. 10 Rupees 50 P d. Rs 12 and 60 P

e. Rs 5.60 f. Rs 12.75 g. Rs 25.60

2. Convert into Rupees:

a. 800 Paise b. 600 Paise c. 45 Paise
f. 4570 Paise
d. 75 Paise e. Rs 1375 Paise i. Rs 240 and 75 Paise

g. Rs 45 and 25 Paise h. Rs 62 and 45 Paise

j. Rs 125 and 40 Paise

Oasis School Mathematics Book-5 171

3. Add the following:
a. Rs. 16 and 65 P + Rs. 35 and 70 P b. Rs. 20 and 35 P + Rs. 86 and 85 P
c. Rs. 123 and 65 P + Rs. 56 and 70 P d. Rs. 26.85 + Rs. 37.35
e. Rs. 384.75 + Rs. 65.85 f. Rs. 47.80 + Rs. 464.75

4. Find the difference:

a. Rs. 48 and 65 Paise - Rs. 36 and 95 Paise

b. Rs. 248 and 35 Paise - Rs. 165 and 50 Paise

c. Rs. 345 and 70 Paise - Rs. 268 and 85 Paise

d. Rs. 268.65 - Rs. 184.25 e. Rs. 384.25 - Rs. 296.75

f. Rs. 457.45 - Rs. 227.65 g. Rs. 4578.30 - Rs. 3357.45
5. Multiply:

a. Rs. 45 and 25 Paise × 4 b. Rs. 135 and 45 Paise × 7

c. Rs. 186 and 75 Paise × 5 d. Rs. 243 and 55 Paise × 6

e. Rs. 45.35 × 7 f. Rs. 332.65 × 8

g. Rs. 524.80 × 12 h. Rs. 612.65 × 8

6. Divide: b. Rs. 48 and 75 P by 5
a. Rs. 36 and 24 P by 4 d. Rs. 508.65 ÷ 5
c. Rs. 359 and 10 P by 7 f. Rs. 656.80 ÷ 4
e. Rs. 595.53 ÷ 9
g. Rs. 750.42 ÷ 6

7. a. Sumnima bought a saree for Rs. 1386.25 and a pair of shoes for
Rs. 668.85. How much did she spend in all?

b. Himanka ordered a sandwich for Rs. 124.75 and Zenith ordered an ice
cream for Rs. 96.35. How much should they pay?

8. a. Asmita had Rs. 3520.85. She bought a jacket for Rs. 2635.25. How much
money is left with her?

b. Roshan had Rs. 1500. He went to the market and bought a bag for Rs.
375.25 and a shirt for Rs. 620.85.

i. How much money did he spend in the market?

ii. How much money is left with him?

9. a. A pen costs Rs. 25.85. What will 8 pens cost?
b. A bicycle costs Rs. 1485.35. Find the cost of 9 such bicycles?

10. a. The cost of 1 dozen copy is Rs. 219.60. What is the cost of one copy?
b. A man spends Rs. 375.20 in a week. How much does he spend in a day?

Answers: Consult your teacher

172 Oasis School Mathematics Book-5

Objective Questions

Colour the correct alternatives:
1. 2 hours 2 minutes 2 seconds is equal to

6362 seconds 7322 seconds 7200 seconds

2. 450 minutes is equal to 6hrs 30 mins. 7 hrs
4 hrs 520 m

3. A man walks 6 hours 25 minutes and 30 seconds on the first day and 7 hours
23 minutes 45 seconds on the second day. How much does he walk in 2 days?

13 hrs 48 mins 15 sec. 13 hrs 49 mins 15 sec. 14 hrs 49 mins 15 sec.

4. (15 hours 35 mins 20 sec) – (6 hrs 12 mins 15 sec) is equal to

9 hrs 23 mins 5 sec. 10 hrs 23 mins 35 sec. 9 hrs 23 mins 35 sec.

5. Rs 35.60 is equal to Rs. 35 and 6Paise Rs. 35 and 160 Paise
Rs. 35 and 60 Paise

6. Rs 112.35 – Rs 95 and 60 Paise is equal to Rs. 16 and 75 Paise
Rs. 16 and 25 Paise Rs. 15 and 75 Paise

7. If the cost of one copy is Rs 23.35, then the cost of 5 copies is

Rs. 115.75 Rs. 116.75 Rs. 115.25

8. Time period from 6:30 A.M to 7:15 P.M is

45 mins 1 hrs 45 mins 12 hrs 45 mins

Number of correct answers

Oasis School Mathematics Book-5 173

UNIT Measurement of

9 Length, Weight and
Capacity

12 Estimated Teaching Hours: 15
93

6

Contents • Measurement of length
• Measurement of weight
• Measurement of capacity

Expected Learning Outcomes

Upon completion of this unit, students will be able to
develop the following competencies:

• To convert one unit of length into another
• To add and subtract the length
• To multiply and divide the length by a number
• To convert one unit of weight into another unit
• To add and subtract the weight
• To multiply the weight by a number
• To convert one unit of capacity into another unit
• To add and subtract the capacity
• To multiply and divide the capacity by a number

Materials Required : Measuring tape, ruler, spring balance, pan balance etc.

174 Oasis School Mathematics Book-5

Measurement of length
Units of measuring length are kilometre (km), metre (m), centimetre (cm) and
millimetre (mm).
To measure a short distance we use millimetre (mm) and centimetre (cm) . To
measure long distance we use metre (m) and kilometre (km).

We use ‘cm’ to measure the length of
a line segment.

We use ‘m’ to measure the length of
a classroom.

We use ‘km' to measure the distance
between two places.

Conversion of units of lengths
To convert the units of length we use the following relations.

10 mm = 1 cm To convert cm into mm, we have
100 cm =1m to multiply cm by 10 and to
1000 m = 1 km convert mm to cm we have to
divide mm by 10.

Multiply m by 100 to convert it into cm. 1000 m = 1km
Divide cm by 100 to convert it into m. 1
1m = 1000 km

Example :

Convert 5 cm 3 mm into mm. 1 cm = 10 mm
Solution: 5 cm = 5 × 10 mm

5 cm 3 mm = 5 × 10 mm + 3 mm

= 50 mm + 3 mm

= 53 mm

Oasis School Mathematics Book-5 175

Example : 1 km = 1000 m
Convert 8 m 65 cm into cm. 5 km = 5 × 1000 m
Solution: 5000 m
8 m 65 cm = 8 × 100 cm + 65 cm
= 800 cm + 65 cm
= 865 cm

Example :
Convert 5 km 330 m into metre.
Solution:
5 km 330 m = 5 × 1000 m + 330 m
= 5000 m + 330 m
= 5330 m
Example :

Convert 4 cm 8 mm into cm. 10mm = 1 cm
Solution:

4 cm 8 mm = 4 cm + 8 cm 1 mm = 1 cm
10 10

= 4 cm + 0.8 cm 8 mm = 8 cm
10
= 4.8 cm

Example : 1 cm = 1 m
Convert 8 m 25 cm into m. 100
Solution:

8 m 25 cm = 8 m + 25 m 25 cm = 25 m
100 100
= 8 m + 0.25m

= 8.25 m 1000m = 1 km
Example :

Convert 5 km 450 m into km.
Solution:

5 km 450 m = 5 km + 450 km 1 m = 1 km
1000 1000

= 5 km + 45 km = 450 km
100 1000

= 5 km + 0.45 km

= 5.45 km

176 Oasis School Mathematics Book-5

Exercise 9.1

1. Convert into mm:
a. 3 cm b. 2 cm c. 4 cm 3 mm d. 5 cm 6 mm e. 12 cm 7 mm f. 21 cm 8 mm

2. Convert into cm: e. 35 m 45 cm
a. 4 m b. 5 m 35 cm c. 8 m 15 cm d. 20 m 35 cm

3. Convert into meter (m):

a. 2 km b. 3 km 450 m c. 6 km 950 m d. 12 km 850 m e. 16 km 750 m

4. Convert into cm:

a. 15 mm b. 40 mm c. 56 mm d. 75 mm e. 94 mm

5. Convert into m:

a. 500 cm b. 325 cm c. 6 m 40 cm d. 7 m 20 cm e. 12 m 40 cm

6. Convert into km:

a. 3000 m b. 4320 m c. 7645 m d. 6 km 500 m e. 12 km 425 m

7. Convert into m and cm: c. 880 cm d. 1240 cm
a. 250 cm b. 475 cm c. 7500 m d. 16324 m

8. Convert into km and m:
a. 3420 m b. 5726 m

1. a) 30 mm b) 20 mm c) 43 mm d) 56 mm e) 127 mm f) 218 mm 2. a) 400 cm
b) 535 cm c) 815 cm d) 2035 cm e) 3545 cm 3. a) 2000 m b) 3450 m c) 6950 m
d) 12850 m e) 16750 m 4. a) 1.5cm b) 4 cm c) 5.6 cm d) 7.5 cm e) 9.4 m
5. a) 5m b) 3.25m c) 6.4 m d) 7.2 m e) 12.4 m 6. a) 3 km b) 4.32 km c) 7.645 km d) 6.5

km e) 12.425 km 7. a) 2m 50 cm b) 4m 75 cm c) 8m 80cm d) 12m 40 m 8. a) 3 km 420
m b) 5km 726 m c) 7km 500 m d) 16 km 324 m.

Addition and subtraction of length

Let's learn the process of addition and subtraction of length from the given
example.

Example : • 85 cm + 75 cm = 160 cm

Add: = 1 m 60 cm

km m cm • 650 m + 640 m = 1290 m

5 650 85 • 1290 m + 1 m = 1291 m
+ 4 640 75
9 1290 160 = 1 km 291 m
10 291 60
• 15 km + 4 km = 9 km

• 19 km + 1 km = 10 km

Oasis School Mathematics Book-5 177

Example :

Subtract: 12 km 300 m 45 cm from 18 km 200 m 25 cm

km m cm

17 1199 1 m = 100 cm 125 • 1m 25 cm = 125 cm
18 200 25 • 125 cm - 45 cm = 80 cm

- 12 300 45 • 1 km 199 m = 1199 m

5 899 80 • 1199 m - 300 m = 899 m

= 5 km 899 m 80 cm • 17 km - 12 km = 5 km

Multiplication and division of length
Let's learn the multiplication and division of length from the given example.

Example :

Multiply 6 m 45 cm 8 mm by 6 48 mm = 4 cm 8 mm

m cm mm 270 cm + 4 cm = 274 cm

6 45 8 = 2 m 74 cm

× 6 36 m + 2 m = 38 m

36 270 48

38 74 8

Example :

Divide 7 km 25 m 74 cm by 6

km m cm

6 7 25 76 1 km

-6

1 km

= (1 × 1000) m

= (1000 + 25) m

= 1025 m

6 1025 m 17m 6 576 96 m
-6 - 54
42 36
- 42 - 36
5m 0
= (5 × 100) cm
= 500 cm + 76 m \ (7 km 25 m 76 cm) ÷ 6
= 576 cm = 1 km 17 m 96 cm

178 Oasis School Mathematics Book-5

Exercise 9.2

1. Add the following: b. 9 km 450 m 75 cm + 8 km 780 m 55 cm
a. 5 km 25 m 35 cm + 12 km 215 m 85 cm d. 16 m 68 cm 6 mm + 25 m 92 cm 7 mm
c. 13 m 86 cm 8 mm + 16 m 55 cm 6 mm

2. Subtract the following:
a. 12 km 640 m 45 cm - 7 km 850 m 55 cm
b. 27 km 560 m 20 cm - 19 km 870 m 35 cm

c. 25 m 65 cm 4 mm - 16 m 90 cm 7 mm

d. 32 m 75 cm 6 mm - 15 m 95 cm 9 mm

3. Multiply: b. 4 km 350 m 80 cm by 7
a. 3 km 225 m 35 cm by 4 d. 10 km 225 m 65 cm by 9
c. 9 km 125 m 52 cm by 8 f. 216 m 85 cm 7 mm by 6
e. 425 m 70 cm 8 mm by 5

4. Divide: b. 18 km 325 m 44 cm by 12
a. 6 km 325 m 44 cm by 4

c. 17 km 645 m 76 cm by 16 d. 6 m 25 cm 6 mm by 4

5. From the given figure, find the distance from:

a. the school to the
playground then the
hostel.

c. the gate to the playground
then the school.

d. the gate to school then the
hostel.

6. a. A man walks 5 km 240 m and 6 cm in a day. How far does he walk in 5 days?
b. The length of a piece of wire is 8 m 62 cm 6mm. Find the total length of

6 such wires.
7. If a man travels 17 km 130 m 40 cm in 7 hours, how much distance will he cover in

one hour?

1. 2. 3. Consult your teacher 4. a) 1 km 581m 36 cm, b) 1 km 527m 12 cm
c) 1 km 102 m 86 cm d) 1 m 56 cm 4 mm 5. a) Consult your teacher 6. Consult your teacher

Oasis School Mathematics Book-5 179

Measurement of weight

To measure the weight of an object, we use pan balance, spring balance, dial
balance etc.

Weight of an object is measured in kilogram (kg), gram (gm), milligram (mg).
Short form of kilogram = kg, gram = gm, milligram = mg

Heavier objects are measured in kilogram (kg) and lighter objects are measured
in gram (gm).

Conversion of units of weight 1000 mg = 1 gm
1000 gm = 1 kg
To convert the units of weight, let's remember the
following relations.

Example : I understand! To convert gm into
mg, I have to multiply gm by
Convert 3 gm into mg. 1000.
Solution:
3 gm = 3 × 1000 mg
= 3000 mg

Example :

Convert 5 kg 450 gm in gm. 1 kg = 1000 gm
Solution: 3 kg = 3 × 1000 gm
5 kg 450 gm
= 5 × 1000 gm + 450 gm
= 5000 gm + 450 gm
= 5450 gm

Example :

Convert 360 mg into gm. 1000 mg = 1 gm

Solution: 1 mg = 1 gm
1000
360mg = 360 gm
1000 360 mg = 360 gm
1000
= 0.36 gm

180 Oasis School Mathematics Book-5

Example : Example :

Convert 25 gm 350 mg in gm. Convert 7 kg 600 gm into kg.

Solution: Solution: To convert mg into gm, we
have to divide mg by 1000.
25 gm 350 gm 7 kg 600 gm

= 25 gm + 350 mg = 7 kg + 600 kg
1000 1000

= 25 gm + 0.35 gm = 7 kg + 6 kg
10
= 25.35 gm
= 7 kg + 0.6 kg

= 7.6 kg

Exercise 9.3

1. Convert the following into milligram (mg):

a. 15 gm b. 22 gm c. 25 gm 250 mg d. 20 gm 340 mg

e. 7 gm 650 mg f. 350 gm 540 mg

2. Convert the following into gm:

a. 5 kg b. 9 kg c. 12 kg 350 gm d. 18 kg 640 gm

e. 15 kg 450 gm f. 10 kg 650 gm

3. Convert the following into gm:

a. 450 mg b. 640 mg c. 8 gm 300 mg

d. 210 gm 750 mg e. 105 gm 500 mg

4. Convert the following into kilogram (kg):

a. 500 gm b. 750 gm c. 8 kg 400 gm d. 9 kg 650 gm

e. 15 kg 850 gm f. 24 kg 370 gm

5. Convert the following into gm and mg:

a. 5732 mg b. 6385 mg c. 5284 mg

d. 9231 mg e. 6576 mg

1. a) 15000 mg b) 22000 mg c) 25250 mg d) 20340 mg e) 7650 mg
f) 350540 mg 2.a) 5000 gm b) 9000 gm c) 12350 gm d) 18640 gm
e) 15450 gm f) 10650 gm 3.a) 0.45 gm b) 0.64 gm c) 8.3 gm
d) 210.75 gm e) 105.5 gm 4.a) 0.5 kg b) 0.75 kg c) 8.4 kg
d) 9.65 kg e) 15.85 kg f) 24.37 kg 5.a) 5 gm 732 mg
b) 6gm 385 mg c) 5 gm 284 mg d) 9 gm 231 mg e) 6gm 576 mg

Oasis School Mathematics Book-5 181

Addition and subtraction of weight

Let's learn the addition and subtraction of weight from the given examples.
Example :

Add: Kg gm mg 1180 mg = 1 gm 180 mg
25 960 750
+ 14 670 430 1630 mg + 1 gm = 1631 gm

= 1 kg 631 gm

39 1630 1180 39 kg + 1 kg = 40 kg

40 631 180
Example :

Subtract: mg 1 gm 175 mg = 1175 mg
Kg gm 1175 mg - 325 mg = 850 mg

64 1 kg 1349 1 gm 1175 1 kg 349 gm = 1349 gm
1349 gm - 840 gm = 509 gm
65 1000 gm 350 1000 mg 175 64 kg - 35 kg = 29 kg
- 35 840 325
29 509 850

Multiplication and division of weight by a whole number

Let's learn the multiplication and division of weight from the given example.

Example :

Multiply: 700 × 6 = 4200 mg

Kg = 4 gm 200 mg
8
gm mg 450 × 6 = 2700 gm
48 450 700
50 × 6 2700 gm + 4 gm = 2704 gm
2700 4200
704 200 = 2 kg 704 gm

8 × 6 = 48 kg

48 kg + 2 kg = 50 kg

Example :

Divide 7 kg 450 gm by 5. 5 2450 490 gm
Solution: - 20
45
Kg gm - 45
5 7 450 1 kg 0
-5 ( 7 kg 450 gm) ÷ 5
2 kg = 2 × 1000 gm = 1 kg 490 gm
= 2000 gm + 450 gm
= 2450 gm

182 Oasis School Mathematics Book-5

Exercise 9.4

1. Add the following:
a. 12 kg 640 gm + 15 kg 830 gm
b. 18 kg 350 gm 680 mg + 35 kg 790 gm 740 mg
c. 25 kg 880 gm 740 gm + 38 kg 570 gm 635 mg
d. 55 kg 710 gm 815 mg + 87 kg 380 gm 738 mg

2. Subtract the following:
a. 8 kg 650 gm from 15 kg 350 gm
b. 540 gm 680 mg from 750 gm 825 mg
c. 15 kg 350 gm 675 mg from 28 kg 640 gm 375 mg
d. 12 kg 630 gm 720 mg from 17 kg 310 gm 415 mg
e. 25 kg 840 gm 655 mg from 40 kg 525 gm 335 mg

3. Multiply:
a. 5 kg 450 gm by 6
b. 8 kg 220 gm by 9
c. 320 gm 750 mg by 5
d. 450 gm 640 mg by 8
e. 6 kg 340 gm 450 mg by 5
f. 8 kg 680 gm 370 mg by 6

4. Divide:
a. 640 gm 350 mg by 5
b. 815 gm 255 mg by 7
c. 15 kg 618 gm by 6
d. 11 kg 720 gm 241 mg by 3
e. 18 kg 640 gm 750 mg by 5

5. a. A packet contains 5 kg 640 gm of rice. Find the quantity of rice in 7
such packets.

b. 15 kg 840 gm potatoes are distributed equally among 9 families. How
much potatoes does a family get?

Answers: Consult your teacher

Oasis School Mathematics Book-5 183

Measurement of capacity
The amount of liquid that a vessel can hold in it is called capacity. Capacity of
a vessel is measured in litre (l) and millilitre (ml).
Conversion of units of capacity
The commonly used units of capacity are litre (l) and millilitre (ml). We can
convert the units of capacity using the relation,
1 litre = 1000 ml
1000 litres = 1 kilolitre
Example :

Convert 3 litre 250 ml into ml. We can convert litre (l) into
Solution: millilitre, multiplying litre by
3 litre 250 ml
= 3 × 1000 ml + 250 ml 1000.
= 3000 ml + 250 ml
= 3250 ml

Example :

Convert 2750 ml into litre ( l ) and millilitre (ml)

Solution:

2750 ml 1000 2750 2 litre

= 2750 litre - 2000
1000 750 ml

= 2 litre 750 ml

Example :

Add: 15 litres 885 ml + 24 litres 725 ml

Solution: 1610 ml = 1 l 610 ml

litre ml

15 885

+ 24 725

39 1610

40 610

= 40 litres 610 ml

184 Oasis School Mathematics Book-5

Example :
Subtract: 25 litres 240 ml - 17 litres 620 ml
Solution: litre ml

24 1 l = 1000 ml 1240

25 240
- 17 620
7 620

= 7 l 620 ml

Multiplication of capacity by a whole number

Let’s observe the following examples and get the idea of multiplication of
capacity by a whole number.

Example : • 570 × 6 = 3420 ml
= 3 l 420 ml
Multiply: • 6 × 6 = 36 l
litre ml • 36 l + 3 l = 39 l
6 570
× 6
36 3420
39 420
\ 39 litres 420 ml

Division of capacity by a whole number

Let’s observe the following examples and get the idea of division of capacity
by a whole number.

Example :

Division: 6 2322 ml 387 ml
- 18
litre ml 52
6 26 322 4 litre - 48
-24 42
- 42
2 × 1000 ml 0
\ 26 l 322 ml ÷ 6 = 4l 387 ml
= 2000 ml + 322 ml

= 2322 ml

Oasis School Mathematics Book-5 185

Exercise 9.5

1. Convert the following into millilitre (ml):

a. 2 l b. 5 l c. 6 l 350 ml d. 7 l 250 ml

e. 8 l 640 ml f. 15 l 840 ml g. 18 l 320 ml

2. Convert the following into litre (l):

a. 500 ml b. 350 ml c. 450 ml d. 1250 ml

e. 1500 ml f. 2700 ml g. 3500 ml

3. Convert the following into litre (l) and millilitre (ml):

a. 1350 ml b. 2460 ml c. 3500 ml d. 5500 ml

e. 12650 ml b. l ml c. l ml
4. Add the following: 15 640 24 620
+ 18 820 + 21 680
a. l ml
4 450
+ 8 840

d. 11 l 725 ml + 13 l 540 ml e. 18 l 940 ml + 12 l 360 ml

f. 25 l 560 ml + 18 l 745 ml g. 28 l 380 ml + 15 l 870 ml

5. Subtract the following: b. l ml c. l ml
a. l ml

6 450 14 240 38 150

- 2 850 - 6 570 - 15 840

d. 15 l 350 ml - 9 l 700 ml e. 28 l 20 ml - 19 l 450 ml

f. 21 l 650 ml - 16 l 960 ml g. 45 l 240 ml - 18 l 825 ml

6. Multiply: b. l ml c. l ml
a. l ml

5 250 8 640 12 120

× 6 × 8 × 6

d. 12 l 350 ml by 8 e. 15 l 450 ml by 7 f. 16 l 150 ml by 5 g. 18 l 240 ml by 4

7. Divide:
a. 16 l 480 ml by 4 b. 24 l 486 ml by 11

c. 9 l 126 ml by 3 d. 16 l 900 ml by 9

8. a. A bucket contains 10 l 452 ml of water. Find the quantity of water in 6
such buckets.

b. A jar contains 15 l 322 ml of milk. Find the quantity of milk in 7 such jars.

9. 3 l 500 ml milk was distributed equally among 20 children. How much milk
was given to each?

Answers: Consult your teacher

186 Oasis School Mathematics Book-5

More information about units of measurement of length,
weight and capacity

Measurement of length

10 millimetre (mm) = 1 centimetre (cm)

10 centimetre (cm) = 1 decimetre (dm)

10 decimetre (dm) = 1 metre (m)

10 metre (m) = 1 decametre (dam)

10 decametre (dam) = 1 hectometre (hm)

10 hectometre (hm) = 1 kilometre ( km)

Measurement of weight

10 milligram (mg) = 1 centigram (cg)

10 centigram(cg) = 1 decigram (dg)

10 decigram (dg) = 1 gram (g)

10 gram (g) = 1 decagram (dag)

10 decagram (dag) = 1 hectogram (hg)

10 hectogram (hg) = 1 kilogram ( kg)

Measurement of capacity

10 millilitre(ml) = 1 centilitre (cl)

10 centilitre(cl) = 1 decilitre (dl)

10 decilitre (dl) = 1 litre (l)

10 litre (l) = 1 decalitre (dal)

10 decalitre (dal) = 1 hectolitre (hl)

10 hectolitre (hl) = 1 kilolitre ( kl)

Oasis School Mathematics Book-5 187

Objective Questions

Colour the correct alternatives:
1. 25 mm is equal to

2cm 5 mm 20cm 5 mm 1cm 5 mm

2. Which of the following relation is not true?

1kg = 1000gm 1l = 1000ml 1m = 1000cm

3. 1565 gm is equal to 1kg 565gm 156kg 5 gm
15kg 65gm

4. 2345ml is equal to 23l 45ml 234l 5ml
2l 345ml

5. If 10 decimetre = 1 cm and 10 cm = 1 decametre then how many decimetre is
equal to decametre?

10 100 1000

6. The sum of 12km 350m 80cm and 10 km 800 m 60cm is equal to

22km 150m 40cm 23km 15m 40cm 22km 151m 40cm

7. The difference of 123 kg 540gm 300 mg and 65kg 850gm 200mg is equal to
58kg 690gm 100mg 58kg 590gm 100mg 58kg 310gm 100mg

Number of correct answers

188 Oasis School Mathematics Book-5

Unit Test Full marks: 20
3
1. Convert as given:
a. 3 kg 150 gm 30 mg into mg 1.5×2=3
b. 5 l 315 ml into l
c. 5km 450m 32cm into cm

2. Add:
a. 8 km 250 m 75 cm and 18 km 960 m 85 cm
b. 12 kg 450gm 680 mg and 18kg 750gm 340mg

3. Subtract: 1.5×2=3
a. 5 kh 840 gm 740 mg from 18 kg 225 gm 115 mg 1.5×2=3
b. 12l 640ml from 18l 850ml

4. Multiply:
a. 5 km 240 m 80 cm by 8
b. 13 l 350 ml by 3

5. Divide: 2×2=4
a. 18 km 325 m 44 cm by 12
b. 11 kg 720 gm 240 mg by 3

6. Solve the following problems: 2×2=4

a. If a man travels 17 km 130 m 40 cm in 7 hours, how much distance
does he cover in one hour?

b. A jar contains 15 l 322 ml of milk. Find the quantity of milk in 7 such
jars.

Oasis School Mathematics Book-5 189

UNIT Perimeter, Area
and Volume
10

12 Estimated Teaching Hours: 15
93

6

Contents • Perimeter
• Area
• Volume

Expected Learning Outcomes
Upon completion of this unit, students will be able to
develop the following competencies:

• To find the perimeter of a triangle, quadrilateral and polygon
• To find the perimeter of rectangle and square by using formula
• To find the area of plane figure by counting the unit square
• To find the area of rectangle and square by using formula
• To find the volume of given object by counting the unit cubes
• To volume of cube and cuboid by using the formula

Materials Required : • Model of triangle, quadrilateral and polygons, model of

cube, cuboid etc.

190 Oasis School Mathematics Book-5

Perimeter

Let's observe the given figure and get the idea about the perimeter of a plane

figure. 4 cm A
In the quadrilateral ABCD,
2.5 cm

length of AB = 2.5 cm D B
length of BC = 3 cm 4.5 cm 3 cm
length of CD = 4.5 cm

length of AD = 4 cm C
Total length of the boundary = AB + BC + CD + AD

= (2.5 + 3 + 4.5 + 4) cm = 14 cm

Hence, the perimeter of a plane To obtain perimeter, we have to add the length of
figure is the total length of its outer all sides of a plane figure.
boundary.

Perimeter of a triangle:

The given figure ABC is a triangle. AB, BC and AC are its
three sides.

\ Perimeter of DABC = AB + BC + AC.

Perimeter of a quadrilateral:
The given figure ABCD is a quadrilateral. AB, BC,
CD and AD are its four sides.
\Perimeter of quadrilateral ABCD
= AB + BC + CD + AD

Perimeter of a polygons:
The given figure ABCDEF is a polygon having
six sides AB, BC, CD, DE, EF and AF.
\ Perimeter of polygon ABCDEF
= AB + BC + CD + DE + EF + AF

Note: Polygon having 5 sides = pentagon
Polygon having 6 sides = hexagon
Polygon having 7 sides = heptagon
Polygon having 8 sides = octagon

Remember ! A polygon is a closed figure having more than 3 sides.

Oasis School Mathematics Book-5 191

Perimeter of a rectangle, using formula: A 5cm B
ABCD is a rectangle. D 2cm
Its length are AB and DC. C
Its breadth are AD and BC.
\ AB = DC = l
AD = BC = b
Now,
Perimeter of a rectangle = AB + BC + CD + AD
= l + b + l + b
= 2l + 2b
= 2(l + b)
\ Perimeter of a rectangle = 2(l + b)
Example :
Find the perimeter of rectangle ABCD.
Solution:
Here, length (l) = 5 cm
breadth (b) = 2 cm
We have, perimeter of a rectangle = 2(l + b)
= 2(5 + 2) cm
= 14 cm

Perimeter of a square, using formula:
ABCD is a square. Its four sides are AB, BC, CD and AD.
All four sides of a square are equal.
AB = BC = CD = AD = l
Perimeter of a square = AB + BC + CD + AD
= l + l + l + l = 4l

\ Perimeter of a square = 4l

Example :

Find the perimeter of the given square.
Solution:
Here,length (l) = 3 cm
We have, perimeter of a square = 4l
= 4×3
= 12 cm

192 Oasis School Mathematics Book-5

Exercise 10.1

1. Find the perimeter of the following closed figures:

Oasis School Mathematics Book-5 193

2. a. If three sides of a triangle are 2.6 cm, 4.2 cm and 5.1 cm, find its
perimeter.

b. If all five sides of a pentagon are 5.5cm, find its perimeter.

3. Find the perimeter of rectangles whose length and breadth are given below:
a. length = 6 cm, breadth = 5 cm
b. length = 8 cm, breadth = 6 cm
c. length = 4.5 cm, breadth = 3.5 cm
d. length = 5.6 cm, breadth = 4.2 cm
e. length = 6.3 cm, breadth = 5.1 cm

4. Find the perimeter of squares whose lengths are given below:
a. length = 6 cm b. length = 5 cm c. length = 4.5 cm

d. length = 5.5 cm e. length = 4.8 cm f. length = 3.7 cm

5. Solve the following problems:

a. A rectangular room is 12 m long and 8 m wide. Find its perimeter.

b. A square field is 46.5 m long. Find its perimeter.

c. A rectangular garden is 24 m long and 16 m wide. Find the length of
wire required to fence the garden.

d. A man wishes to enclose a square field having each side of 18 m with
a wire. Find the length of the wire required to fence it,

i. once ii. twice iii. thrice

e. A rectangular garden is 20 m long and 12 m wide. A man runs round
the garden 5 times. What distance does he cover?

1. a) 13.5 cm b) 14 cm c) 12 cm d) 14 cm e) 18 cm f) 20 cm g) 19 cm
h) 20 cm i) 21 cm j) 18 cm k) 32 cm l ) 31 km m) 35.4 cm 2. a) 11.9 cm
b) 27.5 cm 3. a) 22cm b) 28cm c) 16 cm d) 19.6 cm e) 22.8 cm
4. a) 24 cm b) 20 cm c) 18 cm d) 22cm e) 19.2 cm f) 14.8 cm
5. a) 40 cm b) 186 cm c) 80m d) (i) 72 m (ii) 144m (iii) 216 m e) 320 m

194 Oasis School Mathematics Book-5

Area

If we paste a picture on the wall, it covers some
surface of the wall. The space covered by the
surface of an object is its area.

Let's observe these two figures. Surface of the
book is greater than that of the box. So the area
of the book is greater than that of the box.

The unit of the area:
Generally square cm and square metre are the units of area.
The given figure ABCD is a square. Each of its sides is 1 cm. So the area of the
square ABCD is 1 cm² or 1 square cm.

If the side of a square is 1 cm, its area is 1
cm² (sq. cm).

The area of a figure formed by the squares of side 1 cm each:

The area of a figure formed by the squares having sides 1 cm each can be
obtained by counting the number of squares.

In the given figure, 12 squares having
each side 1 cm are shaded.
Note:

area = 1 sq. cm

area = 1 sq. cm
2

\ Area of shaded parts = 12 sq. cm or 12 cm².
Example :

Find the area of the shaded part in the given
figure.

Solution:

In the given figure, number of completely
shaded square box = 12

Its area = 12 sq. cm.

Number of half-shaded square box = 4
1
Its area = 4 × 2 sq.cm = 2 sq. cm

Oasis School Mathematics Book-5 195

\ Area of the shaded part

= 12 sq. cm + 2 sq. cm

= 14 sq. cm.

Area of rectangle:
In the given figure, rectangle ABCD is formed by the combination of 15 squares
having each side 1 cm.
Therefore, area of rectangle ABCD = 15 sq. cm
Again,
Number of squares along the length of ABCD = 5
Number of squares along the breadth of ABCD = 3
Now,
Area of rectangle ABCD = 15 sq.cm
= 5 × 3 sq. cm

length
breadth

= length × breadth
\ Area of a rectangle = l × b

Area of square:
A square is also a rectangle. Its length and breadth are equal.
Area of a square = length × breadth
= length × length
= (length)²
\ Area of a square = l²

Example :

Find the area of the given figures:

Solution: Solution:
a. Here, b. Here,
length (l) = 7 cm length (l) = 3 cm
breadth (b) = 3 cm We have, area of a square = l²
We have, area of a rectangle = l × b = (3cm)²
= 7 cm × 3 cm = 9 sq. cm
= 21 sq. cm

196 Oasis School Mathematics Book-5

Example :
Find the area of the shaded region:
Solution:
Area of bigger rectangle = 8 m × 6 m
= 48 m²
Area of smaller rectangle = 6 m × 4 m
= 24 m²
Area of the shaded part
= Area of the bigger rectangle - Area of the smaller rectangle
= 48 m² - 24 m² = 24 m²

Exercise 10.2

1. Find the area of the following figures by counting the number of unit squares:

d

2. Find the area of the following shapes by counting the squares:

Oasis School Mathematics Book-5 197

3. Find the area of the given figures (using formula):

4. Find the area of the rectangles whose length and breadth are given below:
a. length (l) = 5 cm, breadth (b) = 4 cm b. length (l) = 6 cm, breadth (b) = 5 cm
c. length (l) = 4.5 cm, breadth (b) = 3.5 cm d. length (l) = 5.5 cm, breadth (b) = 3.2 cm
e. length (l) = 4.2 cm, breadth (b) = 3.1 cm

5. Find the area of the squares having:
a. length (l) = 5 cm b. length (l) = 6 cm
c. length (l) = 4.5 cm d. length (l) = 5.5 cm e. length (l) = 5.1 cm

6. a. A rectangular ground has length 25 m and breadth 20m. Find the area
of the ground.

b. A rectangular plot of land is 35 m long nad 22 m wide. Find its area.
c. A square garden has length 40 m. Find its area.
7. Find the area of the shaded part in each of the given figures.

1. Consult your teacher 2. Consult your teacher 3. a) 12cm2 b) 9 cm2 c) 10cm2 d) 13cm2
e) 12.25 cm2 f) 21.16cm2 4. a) 20cm2 b) 30cm2 c) 15.75cm2 d) 17.6cm2 e) 13.02 cm2

5. a) 25cm2 b) 36cm2 c) 20.25cm2 d) 3025cm2 e) 26.01cm2
6. a) 500m2 b) 770 m2 c. 1600m2 7. a) 16cm2 b) 20cm2 c) 7cm2 d) 26cm2

198 Oasis School Mathematics Book-5

Volume

Every solid object occupies some space. The space occupied by any object is
called volume. We express volume in cubic units.

Volume of a cuboid:
It is a cuboid. Its three dimensions are length, breadth
and height.
The length, breadth and height of a cuboid are not
equal. Volume of the cuboid = length × breadth x height
Volume of a cube
It is a cube. Its three dimensions length, breadth and
height are equal.
Volume of the cube = length × length × length
= l³
Volume of unit cube
This is a cube. Its all three dimensions are 1 cm.
\ Volume of this cube = 1 cu. cm
= 1 cu. cm

1 cu. cm = 1 cm³ = 1c.c.

Remember: 4cm
• 1000 cu. cm = 1 litre

Volume of this figure = 4 cu. cm
Example :

Find the volume of the given cuboid.
Solution:
Number of cubes along the length (l) = 4
Number of cubes along the breadth (b) = 2
Number of cubes along the height (h) = 2
Volume of the cube = 4 × 2 × 2
= 16 cu. cm

Oasis School Mathematics Book-5 199

Example :

Find the volume of a room whose length, breadth and height are 6m, 4.5 m and
3 m respectively.
Solution:
Here,
length (l) = 6 m
breadth (b = 4.5 m
height (h) = 3 m
We have,
Volume (v) = l × b × h
= 6 m × 4.5 m × 3 m
= 81 cu. m

Example :

Find the volume of a cubical box whose length is 6 cm.
Solution:
Volume (v) = l³
= (6cm)³
= 216 cu. cm

Example :

Length, breadth and height of a vessel are 24 cm, 10 cm and 8 cm respectively.
Find its volume in litre.

Solution:

Here,

length (l) = 24 cm 1000 cu. cm = 1 litre
breadth (b) = 10 cm 1
height (h) = 8 cm
We have, 1 cu. cm = 1000 litre
Volume = l × b × h
1920
1920m cu. cm = 1000 litre

= 24 × 10 × 8 cu.cm

= 1920 cu.cm

= 11092000litre
= 1.92 litre

200 Oasis School Mathematics Book-5