Math 3

Study the english and nepali days in a week.

S. N. English days Nepali days

1. Sunday cfOtjf/
2. Monday ;f]djf/
3. Tuesday D+funjf/
4. Wednesday a'wjf/
5. Thursday ljlxjf/
6. Friday Zf'qmjf/
7. Saturday Zflgjf/

Study the english and nepali 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. September 9. Paush
10. October 10. Magh
11. November 11. Falgun
12. December 12. Chaitra

Mathematics 3 Approved by CDC 201

• 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

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

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

202 Approved by CDC Mathematics 3

See, feel and do.

1. 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

2. 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



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

Mathematics 3 Approved by CDC 203

Convert the following.

i) days into week and days ii) months in to years and months

45 days 30 months

45 days converting into weeks 30 months converting into

and days years and months.

7) 45 (6 weeks 12) 30 (2 years
− 42 days − 24 months
6
3

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

iii) minutes into hours and minutes.

140 minutes
140 minutes, converting into hours and minutes.

60) 140 (2 hours

− 120

20 minutes

∴ 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 5 3
+ 6 3 2
10 years 8 monthy 5 days

6 months 13 days from 9 months 20 days. Mathematics 3
month days
4 20
+ 6 13
3 monthy 7 days

204 Approved by CDC

See, feel and do.

1. Convert the following

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

2. Add the following: (b) years days
10 115
(a) year months weeks
2 7 1 + 26 95

+ 3 4 2

Mathematics 3 Approved by CDC 205

(c) year months weeks (d) year months weeks
15 0 4 4 5 6

16 1 1 3 3 13

+ 4 2 1 + 2 2 6

(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

3. Perform the following task:

(a) ye ars months (b) weeks days (c) years months days
11 10 7 6 9 10 21

− 7 8 − 2 2 − 6 6 13

(d) m onths day (e) years months (f) years months days
12 24 15 11 25 9 3

− 7 13 − 6 07 − 12 4 1

4. Perform the following task: ×=
a) How many days are there in a year? ×=
b) How many days are there in 4 months? ×=
c) How many weeks are there in a year? ×=
d) How many weeks are there in 3 months? ×=
e) How many days are there in 4 week? Mathematics 3

206 Approved by CDC

Unit Revision Test

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

11 12 1 11 12 1
10 2 10 2

93 93

84 84
765 765

8:20 40 minutes past 2

2. 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 =

3. 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.

4. 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.

Mathematics 3 Approved by CDC 207

5. 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.

6. 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.

7. Write the following dates in the short form:
(a) The year 1993, April 5th, Monday
(b) The year 2065, Poush 18th, Friday

Study the given calendar and answer the following:

(a) Which calendar is it? a}zfv @)&* Apr/May 2021

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

(c) How many days are there !@#$
in this month? 14 15 16 17

(d) Which months of English % ^ & * ( !) !!
calendar fall on this 18 19 20 21 22 23 24
month?
!@ !# !$ !% !^ !& !*
(e) How many holidays are 25 26 27 28 29 30 1
there including Saturdays
!( @) @! @@ @# @$ @%
2345678

in this month? @^ @& @* @( #) #!
f) Which day is the 9 10 11 12 13 14

celebrating day of new

year?

208 Approved by CDC Mathematics 3

7Unit

COMMUNICATION,
TECHNOLOGY AND MARKET

Estimated periods - 28

Objectives

At the end of this unit, students will be able to:
identify the coins and note of different denominations.
compare the capacity of vessels and their identification.
convert one unit to another unit upon length and addition and subtraction
of the units.
identify the weighting instruments and compare the weights during
buying and selling.
understand the tabulation of data and pictograph.

Teaching Materials

different coins, notes, weights, vessels of different capacities chart of
units upon money, capacity, weights, ruler, meter tape, pictograph, etc.

Activities

It is better to:
show coins and notes of different denominations and interpretation of
conversion of rupees to paisa.
demonstrate the vessels by taking liquids to show different capacities of
vessels.
show by making table for conversion of units of measurement of length,
weight and money.
demonstrate the weight devices of different units in practical way.
show the tabulation and pictograph of data to write answers.

Mathematics 3 Approved by CDC 209

7.1 Money

The paper money was issued by
Emperor Hein Tsung in China

between 806 and 821 A.D.

See, feel and learn.

Our coins

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

Our notes

1 Rupee 2 Rupees 5 Rupees 10 Rupees

20 Rupees 25 Rupees 50 Rupees

100 Rupees 250 Rupees

210 Approved by CDC Mathematics 3

500 Rupees 1000 Rupees

See, feel and learn.

Students,
There are 100 paisa in a rupee.
i.e. Re. 1 = 1 × 100 paisa = 100 p
Rs. 2 = 2 × 100 paisa = 200 p
Rs. 3 = 3 × 100 paisa = 300 p

Here, Rupee = Re
Rupee = Rs
Paisa = p

Sir, What about paisa to rupees?

Is, 100 paisa = Re 1?

200 paisa = 200 = Rs. 2?
100
300
300 paisa = 100 = Rs. 3?

Absolutely right,
Divide by 100 have to be done to
convert in Rupees.

Mathematics 3 Approved by CDC 211

× 100

Rupees Conversion Paisa

÷ 100

In short rupee is written as Re., rupees as Rs. and paisa as p.
Re. 1 = 100p
To convert rupees to paisa we multiply by 100 and to convert paisa to rupees we
divide by 100.

To convert 5p into rupees:
5
5p = 100 Rs. which is 5 hundredth of a rupee or 0.05 of a rupee = Rs. 0.05

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

See, feel and do.

i) Convert 5 rupees 25 paisa into paisa.
As we know,

Re 1 = 100 paisa

\ 5 rupees 25 paisa = 5 × 100 + 25 p = 525 paisa.

ii) Convert Rs. 7 into paisa

\ Rs 7 = p= paisa.

iii) Convert 12 rupees 30 paisa into paisa

\ 12 rupees 30 paisa = × + p= paisa.

iv) Convert 400 paisa to rupees
As we know,

100 paisa = Re 1

400 paisa = Rs. 400 ÷ 100

= Rs. 400 = Rs. 4
100

212 Approved by CDC Mathematics 3

v) Convert 700 paisa to rupees
As we know,

100 paisa = Re 1

700 paisa = Rs.

= Rs. = Rs.

vi) Convert 900 paisa to rupees
As we know,

100 paisa = Re 1

900 paisa = Rs.

= Rs. = Rs.

See, feel and learn.

Addition

Pralika, you have 25 rupees 75 paisa and
you borrow 15 rupees 10 paisa. How much do

you have now.

Sir, I find my money by doing
addition as.

Rs Paisa
25 75
+ 15 10
40 85

I have 40 rupees 85 paisa now.

Yes, you are intelligent.
Your answer is correct.

Mathematics 3 Approved by CDC 213

Madhav, Cost of books of class two is 927
rupees 75 paisa and cost of exercise copies
is 340 rupees 75 paisa. how mucyh cost paid

by you for books & copies?

Cost of books Rs Paisa
Cost of copies 927 75
+ 340 75
1267 150
+ 1 – 100
1268 50

Sir, I know 100 paisa is equal to
1 rupee and the total money paid
by me is 1268 rupees 50 paisa

Subtraction

Pratik, you are given Rs. 225

and 75 paisa to buy a book

and Rs. 205 and 25 paisa is

paid. How much money do

you have left. Rs Paisa

225 75

– 205 25

20 50

Sir, I have only 20 rupees

50 paisa left. it is know

after subtraction sir.

Absolutes right, you
got it after subtraction

which is correct.

214 Approved by CDC Mathematics 3

Pranisha I have Rs 345 and I
gave to you Rs. 148.75.

How much money do I have left.

Rs Paisa

11
2 3 4 100

345 00
– 148 75

196 25
Sir, I know it very well.
You have Rs. 196.25 left
Where, Re 1 = 100 paisa

Yes, you are absolutely
right. It is difficult but

you did.

See, feel and do.

1. Write the short form as given in the example:
Example: 7 rupees 5 paisa = Rs. 7.05
(a) 2 rupees 4 paisa =
(b) 8 rupees 20 paisa =
(c) 10 rupees 25 paisa =
(d) 15 rupees 5 paisa =
(e) 51 rupees 10 paisa =
(f) 115 rupees 50 paisa =
(g) 200 rupees 75 paisa =
(h) 85 rupees 95 paisa =

Mathematics 3 Approved by CDC 215

2. 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 =

3. Convert the following into paisa.

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

4. Convert the following rupees into paisa:

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

(g) Rs. 50.90

(h) Rs. 125.75

216 Approved by CDC Mathematics 3

5. Convert the following paisa into rupees:

(a) 235p Example:
(b) 205p To convert 123p into rupees:
(c) 1012p 123p = 100p + 23p
(d) 987p
(e) 12340p = Re. 1 + 23p
(f) 850p = Rs. 1.23
(g) 10025p
(h) 100005p

6. Perform the following task:

Rs. p Rs. p Rs. p
87 32 42 18 45 48
+ 25 38 + 34 32 + 125 50

112 70 Rs. p
200 87
Rs. p Rs. p + 750 43
134 20 720 65
+ 252 40 + 350 45

Rs. p Rs. p Rs. p
51 56 180 81 85 95
+ 34 84 + 250 53 + 16 76
17 18
Rs. p Rs. p
Rs. p 486 70 549 51
185 74 + 247 46 + 159 72
+ 895 56

Mathematics 3 Approved by CDC 217

6. Perform the following task:

Rs. p Rs. p Rs. p
87 32 42 18 45 48
– 25 38 – 34 32 – 125 50

112 70 Rs. p
200 47
Rs. p Rs. p – 50 33
134 20 720 65
– 52 40 – 50 25 Rs. p
85 95
Rs. p Rs. p − 16 76
51 52 180 81
− 34 34 − 50 33 Rs. p
17 18 549 51
Rs. p − 159 12
Rs. p 486 70
185 74 − 247 26
− 95 56

7. 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?
218
Approved by CDC Mathematics 3

7.2 Capacity

To pots of given capacity are given to
your Pasang. How can you fill the bigger
one by using smaller with water?

250 milliliters When big bottle is filled
by smaller pot, there will
1 liters be 4 times needed to fill

madam.

1 liters = 4 × 250 milliliters.
= 1000 milliliters.
2 liters = 2000 milliliters

Liter unit should be used to fill the bigger pots where milliliter should be used
to fill the smaller vessels.

10 liters 100 milliliters 20 liters 200 milliliters

When a cubical vessel 1cm
long 1cm wide and 1cm
high is filled with a liquid,
the liquid is said to occupy a
space of 1 cubic centimetre
or 1 cu. cm or 1cm3 or 1
millilitres or 1ml.

1000 litres 1 litre 500 ml
Approved by CDC
Mathematics 3 219

Similarly, when a cubical 1cm 1m
vessel 1m in length is 1cm 1cm 1m
filled with liquid, the
liquid is said to occupy a 1m
space of 1 cubic metre or
1cu.m or 1m3.

The volume of liquid that a vessal can hold is called its capacity.
Standard units of measuring the capacity of liquid are litres and milliliters.
1000 millilitres = 1 litre

See, feel and do.

1. Fill in the blanks.

Mug

Bucket 1 litres

The capacity of bucket is 20 times to fill with smaller
10 times to fill with bottle

10 litres Jar Bottle

The capacity of bottle is 200 ml
1 litres Glass
Pot

times is needed to fill the pot with glass.

220 Approved by CDC Mathematics 3

1000 Tank
litres 20 litres Jar

The capacity of bottle is

2. Convert litres into millilitres.

a) 2l = 2 × 1000 ml = 2000 ml.
b) 7l = 7 × ml = ml.
c) 14l = 7 × ml = ml.
d) 16l = 7 × ml = ml.
e) 25l = 7 × ml = ml.
f) 33l = 7 × ml = ml.

3. Change millilitres into litres ÷ 1000 =3 l
÷ =l
(a) 3000ml = 3000 ÷ =l
(b) 5000ml = ÷ =l
(d) 15000ml = ÷ =l
(e) 20000ml = ÷ =l
(f) 36000ml =
(h) 84000ml = 221

Mathematics 3 Approved by CDC

4. Convert the following into millilitres.

(a) 4l 235ml = 4 × 1000 ml + 235 ml = 4000 ml +

235 ml = 4000 ml

(b) 8l 428ml = × ml + ml = ml +

ml = ml

(c) 9l 150ml = × ml + ml = ml +

ml = ml

d) 11l 570ml = × ml + ml = ml +

ml = ml

(e) 52l 25ml = × ml + ml = ml +

ml = ml

(f) 75l 5ml = × ml + ml = ml +

ml = ml

See, feel and do.

To convert ml into l and ml
9 7 5 3 ml
Separate three digits from right to left.

Remaining will be thousand millilitre.

9000ml + 753ml

Leave as it is

Convert thousand ml to litres by dividing by 1000.

= 9l + 753ml Approved by CDC Mathematics 3

= 9l 753ml

222

1. Convert the following in litres and millilitres.

(a) 6334ml = 6000 ml + 334 ml = 6 l + 334 ml = 6 l 334 ml.

(b) 9126ml = ml + ml = l + ml = l ml.

(c) 1357ml = ml + ml = l + ml = l ml.

(d) 7008ml = ml + ml = l + ml = l ml.

(e) 12007ml = ml + ml = l + ml = l ml.

(f) 44074ml = ml + ml = l + ml = l ml.

2. Complete the following:

l ml l ml l ml
74 373 25 275 437 200
+ 19
78 + 375 385 + 63 560
93 451

93l 451ml

l ml l ml l ml
315 250 478 456 87 200

+ 365 315 + 78 543 + 43 250

3. Complete the following:

l ml l ml l ml
86 445 144 379 94 89

– 19 345 – 88 295 – 74 19

l ml l ml l ml
124 348 456 789 8 500

– 94 109 – 234 567 – 3 480

Mathematics 3 Approved by CDC 223

7.3 Measurement of LengthInches

The Nile river of Africa starting
from Lake Victoria and ending in
Mediterranean sea is 4,145 miles

about 6669 km long.

See, feel and learn.

• 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.

Centimeters

The given figure is a ruler or scale

2cm
10mm 10mm

• 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

224 Approved by CDC Mathematics 3

Conversion ÷100

÷10 cm m ÷1000
mm cm ×100 m km
×1000
×10

Bigger unit to smaller unit ⇒ multiply cm is the bigger
Smaller unit to bigger unit ⇒ divide unit, mm is the
smaller unit. Bigger

Example 1 : convert 5cm into millimetres. to smaller unit, we
Solution: we know multiply

1cm = 10mm

∴ 5cm = 5 × 10mm = 50mm cm is the smaller

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

See, feel and do.

1. 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.

Mathematics 3 Approved by CDC 225

c) The length of book is cm.

d) The length of instrument box is cm.

e) The length of instrument broom is cm.

2. Convert centimetres into millimetres.

(a) 2 cm = 2 × 10 mm = 20 mm
(b) 5 cm = × =
(c) 8 cm = × =
(d) 11 cm = × =
(e) 15 cm = × =

226 Approved by CDC Mathematics 3

3. Convert metres into centimetres:

(a) 3 m = 3 × 100cm = 300cm
(b) 6 m = × =
(c) 10 m = × =
(d) 16 m = × =
(e) 34 m = × =

4. Change the following into metres:

(a) 400 cm = ÷ m =
(b) 700 cm = ÷ m =
(c) 800 cm = ÷ m =
(d) 1200 cm = ÷ m =
(e) 1800 cm = ÷ m =

5. Change the following into centimetres:

3m 40cm = 3 × 100cm + 40cm 6m 84cm =
= 300cm + 40cm =
= 340cm =

9m 75cm = 5m 94cm =
= =
= =

6. Convert into metres and centimetres:

345cm = 300 cm + 45 cm 848cm =
= 3m + 45 cm =
= 3m 45cm =

Mathematics 3 Approved by CDC 227

708cm = 1234cm =
= =
= =

879cm = 720cm =
= =
= =

7. Convert kilometers into metres:

(a) 4 km = 4 × 1000m = 4000m
(b) 5km = × =
(c) 8km = × =
(d) 10km = × =
(e) 15km = × =

8. Change the following into kilometres:

(a) 2000 m = ÷ km = km.
(b) 3000 m =
(c) 8000 m = ÷ km = km.
(d) 12000 m =
(e) 19000 m = ÷ km = km.

÷ km = km.

÷ km = km.

9. Convert the following into metres:

(a) 7km 850m = 7 × 1000m + 850m = 7000m + 850m = 7850m
(b)
(c) 2km 340m = = =
(d)
(e) 1km 234m = = =

228 8km 15m = = =

9km 5m = = =
Mathematics 3
Approved by CDC

10. Convert into kilometres and metres as shown in the first one:

(a) 7524m = 7000m + 524m + 7km + 524m = 7km 524cm

(b) 1234m = + ++ =

(c) 3579m = + ++ =

(d) 9876m = + ++ =

(e) 10980m = + ++ =

11. Perform the following sum:

m cm m cm m cm
4 25 21 57 55 48
+ 7 39 + 42 34 + 44 42

km m km m km m
15 150 7 456 413 705
+ 12 350 + 113 514 + 247 225

m cm m cm m cm
120 85 43 92 205 82
− 49 28 − 23 75 − 66 48

km m km m km m
9 349 28 788 535 125
− 4 155 − 17 579 − 210 25

Mathematics 3 Approved by CDC 229

12. Word problems on addition of lengths:

(a) If two pieces of clothes 7m 40cm
and 5m 25cm long are joined, what
will be the total length?

(b) A bench is 2m 55cm long and
second bench is 3m 30cm long.
What is the total length when they
are connected together?

(c) Sangita walks 2km 520m on foot
and travels 8km 230m by bus.What
is distance she travel altogether?

(d) The place B is 25km 350m east of
the place A and the place C is 41km
450m east of the place B. What is
the distance between A and C?

13. Word problems on subtraction of lengths:

(a) Kristina’s school is 7km 420m from
her home. She walks 1km 100m on
(b) foot and then she takes school bus to
(c) reach her school. How far does she
(d) travel by bus?

Anima bought 7m 88cm of ribbon.
She gave 2m 45cm to Binu. What
length of ribbon is left with her?

Ashok’s height is 1m 65cm and
Binay’s height is 1m 42cm. By how
much is Ashok taller than Binay?

Distance between two places is 79 km
840m. If 40 km 220m road between
the two places is pitched and rest is
just gravelled.What length of the road
that is not pitched?

230 Approved by CDC Mathematics 3

7.4 Weight

50kg 500gm 500gm

See, feel and understand.

500gm
200gm

50gm

750gm 750gm

Here are two types of measuring instruments used to know the weight of
cauliflower.

• The first one is the weight machine.

• The second one is the beam balance.

• Comparing the weights of two different things to know which is heavier and
which is lighter.

Mathematics 3 Approved by CDC 231

It's weight is 600gm. It's weight is 200gm.

Hence,The book is heavier than exercise copy.

These are the standard weights issued by the bureau of measurements.

50gm 100gm 200gm 250gm

500gm 1kg 2kg 5kg

10kg 20kg 50kg

• Weights of lighter objects are measured in grams and weights of heavier objects
are measured in kilograms.

• Kilogram is written as ‘kg’ and gram is written as ‘g’ or ‘gm’ in short.
∴ 1000 gm = 1 kg

232 Approved by CDC Mathematics 3

• To convert kilograms into grams we multiply by 1000 and to convert grams
into kilogram we divide by 1000.

Example 1: Convert 5 kilograms into grams × 1>000
Solution: We know, Kg gm
1 kg = 1000 gm
∴ 5 kg = 5 × 1000 gm >
= 5000 gm ÷ 1000

Example 2: Convert 6000 grams into kilogram.
Solution: We know
1000 gm = 1 kg
∴ 6000 gm = 6000 ÷ 1000 kg
= 6 kg

See, feel and do.

1. Practical work
a) Provide different standard weights and balance, let the students
weights the given objects.

Weight Weight

Mathematics 3 Weight Weight
Approved by CDC
233

Weight Weight

b) Use the weight machine and estimate the weight of followings:

Weight Weight Weight

Weight Weight Weight
Mathematics 3
234 Approved by CDC

2. Convert the following into grams:

(a) 2 kg = 2 × 1000 gm = 2000 gm
=
(b) 5 kg = × =
=
(c) 8 kg = × =
=
(d) 20 kg = ×

(e) 24 kg = ×

(f) 50 kg = ×

3. Convert the following into kilogram:

(a) 3000gm = 3000 ÷ 1000 kg = 3 kg
= ÷ =

(b) 7000gm = ÷ =
= ÷ =

(c) 10000gm = ÷ =
= ÷ =

(d) 14000gm = ÷ =
= ÷ =

(e) 26000gm = ÷ =
= ÷ =

(f) 32000gm = ÷ =
= ÷ =

4. Convert kilograms and grams into grams:

(a) 2 kg 250 gm = 2 kg + 250 gm

= 2 × 1000 g + 250 gm

= 2000 gm + 250 gm

= 2250 gm

Mathematics 3 Approved by CDC 235

(b) 4 kg 400 gm (c) 9 kg 125 gm
(d) 16 kg 240 gm (e) 20 kg 200 gm
(f) 42 kg 750 gm (g) 50 kg 550 gm
(h) 80 kg 100 gm (i) 12 kg 990 gm

5. Convert grams into kilograms and grams:

(a) 1234 gm = 1000gm + 234gm
= 1 kg + 234 gm
= 1 kg 234 gm

(b) 2345 gm (c) 6210gm
(d) 8035gm (e) 12345gm
(f) 22200gm (h) 30205gm
(i) 3450gm (j) 5555gm

6. Perform the following task: kg gm
4 370
kg gm kg gm + 8 430
2 240 4 235
+ 5 350 + 6 455 kg gm
4 150
7 590 + 50 500

7kg 590gm

kg gm kg gm
15 345 23 629
+ 8 90 + 45 21

kg gm kg gm kg gm
234 385 500 789 750 245
+ 456 185 + 276 8 + 25 15

236 Approved by CDC Mathematics 3

7. Add the following:

(a) 4 kg 240 gm and 7 kg 360 gm.
(b) 1 kg 700 gm and 9 kg 280 gm.
(c) 9 kg 12 gm and 15 kg 88 gm.
(d) 23 kg 8 gm and 7 kg 880 gm.
(e) 49 kg 750 gm and 7 kg 150 gm.
(f) 123 kg 605 gm and 654 kg 155 gm.

8. Perform the following task:

kg gm kg gm kg gm
18 340 8 456 25 570
− 5 120 − 5 167 − 13 180

13 220

13kg 220gm

kg gm kg gm kg gm
27 855 143 408 432 725
− 14 257 − 97 283 − 234 530

kg gm kg gm kg gm
246 700 642 841 765 200
− 98 206 − 352 261 − 175 165

9. Subtract:

(a) 64 Kg 174 gm from 95 kg 393 gm.
(b) 45 Kg 345 gm from 662 kg 535 gm.
(c) 405 Kg 729 gm from 800 kg 800 gm.
(d) 235 Kg 105 gm from 500 kg 300 gm.
(e) 94 Kg 148 gm from 138 kg 493 gm.
(f) 77 Kg 345 gm from 144 kg 370 gm.

Mathematics 3 Approved by CDC 237

10. Word Problems:

a) Rashmi is carrying 3 kg 340 gm of books and 1 kg kg gm

450 gm of fruits in her bag. Find the total weight

she is carrying in her bag.

She carrying .

b) Mother bought 12kg 600gm of rice and 9kg kg gm

175gm of pulses. What is the total weight of rice

and pulses?

The total weight is .

c) Asha’s bag weighs 5 kg 345 gm and Amar’s bag kg gm

weighs 4 kg 645gm. What is the total weight of the

two bags?

The total weight of two bags is .

d) A porter with sack weighs 120kg 675gm. If the kg gm

weight of the sack is 50kg 185gm, find the weight

of the porter.

The weight of the porter is .

e) A fruit seller had 38kg 600gm of apples. If 13 kg kg gm

235gm of apples were rotten, find the weight of the

good apples.

The weight of the good apples is .

f) A sack contains 32kg 500gm of potatoes. If 12 kg kg gm
600gm of potatoes are removed how much potatoes
are left in the sack?

of potatoes is left in the sack.

238 Approved by CDC Mathematics 3

7.5 Pictograph

See, feel and understand.

The marks obtained by a student of class two is given below.

Maths Nepali Serofero English GK
100 60 70 80 50

A symbol represents the 10 marks. The symbol can be used for the
student to represents the marks.

Maths 100

Nepali 60

English 70

Serofero 80

GK 50

It can be represents in bar graph as follows.

The bar graph given below shows
the marks obtained by a student in

a terminal test.

Mathematics 3 Approved by CDC 239

100
80

80

70

Marks obtained 60

50

40

30

20

10

0 Maths Nepali English Serofero GK

Subjects

Answer the questions given below with the help of above informations.

What is the mark obtained in Maths ?

What is the mark obtained in Nepali ?

What is the mark obtained in English?

What is the mark obtained in Serofero?

What is the mark obtained in GK ?

Which subject obtained highest mark ?

Which subject obtained lowest mark ?

240 Approved by CDC Mathematics 3

The number of students enrolled in different years in a school are
given below.

2073 2074 2075 2076
50 30 70 60

A symbol represents the 10 students. The symbol can be used for the
number to represents the students.

2073 50

2074 30

2075 70

2076 60

It can be represents in bar graph as follows.

Number of students80
70
60 2064 B.S 2065 B.S 2066 B.S
50 Years
40 241
30 Approved by CDC
20
10

2063 B.S

Mathematics 3

Answer the questions given below with the help of above informations.
In which year, the maximum number of students had passed ?
What is the number of students who passed in the year 2066 B.S. ?
In which year, the least number of students had passed ?
What is the number of students who passed in the year 2063 B.S ?
What is the number of students who passed in the year 2065 ?

The price list of the different books of class 3 are given below. Draw a bar graph
and answer the given questions.
Name of books: Nepali English Maths Serofero G.K.
Price (In Rs.) 275 225 325 300 250

350

300

Price (In Rs.) 250

200

150

100

50

0

Nepali English Maths Serofero G.K.
Subjects

What is the cost of Science book?

Which book's price is maximum?

What is the cost of Social studies book?

Write the name of the book with minimum price.

By how much is the Science book cheaper than the English book?

Note: The width of the bar should be equal.The distance between two bars should be equal.

242 Approved by CDC Mathematics 3

Unit Revision Test

1. Convert 7kg into grams. Convert 25000gm into kilogram.
7kg = × = 25000gm = ÷ =

2. Convert 3kg 450gm into grams: Convert 23456gm into kilogram and grams.

3kg 450gm = kg + gm 23456gm = kg + gm
= gm + gm = gm + gm
= gm + gm = gm + gm

3. Perform the following task:

kg gm kg gm
47 560 234 456
− 15 375 − 50 344

4. Perform the following:

A porter is carrying 43kg 450gm. If 17kg 450gm is kg gm
added, how much weight is he carrying in total?

Now he is carrying .

5. Perform the following:

Jitendra’s weight was 67kg 789gm. With hard kg gm
exercise in a week, 5kg 679gm of weight was reduced.
What is his weight now?

Now his weight is .

6. Fill in the blanks.

a) 10 mm = cm b) cm = 1 m
c) 1 km = m d) mm = 2cm

Mathematics 3 Approved by CDC 243

7. Perform the following task:

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

8. Convert:

a) 3cm into mm.

×= mm

b) 8000 g into kg

÷= kg

c) 5m 60cm into cm

×+ = cm
cm
d) 378cm into m and cm
ml
÷= m

e) 5l 720ml into ml

×+ =

9. Perform the following task :

m cm km m m cm km m
5 35 4 120 84 44 7 734
+ 6 47 + 16 450 − 49 38 − 2 456

10. Solve the following problems: Mathematics 3

a) Two pipes 15m 240cm and 16m
360cm long are joined. Find the
total length of the pipe.

b) A shopkeeper had 59m 67cm of
cotton cloth. He sold 34m 28cm of
the cloth. How much cloth is left?

244 Approved by CDC

8Unit

MEASUREMENT

Estimated periods - 5

Objectives

At the end of this unit, students will be able to:

understand area and concept of unit area [unit square].

find the area of objects by counting the unit squares. 1 1
2 2
find the area of half unit square by counting and concept of + = 1
unit square.

Teaching Materials

Geo-board, unit square model, different objects to find area.

Activities

It is better to:
show the geo-board to understand unit squares.
demonstrate the finding of area of objects by counting unit square.
demonstrate the counting of half unit squares to make single.

Mathematics 3 Approved by CDC 245

Area

See, feel and learn.

Students, Here we are going
to discuss the concept of unit
square and measurement of

area of objects.

Yes sir,
Can I try to say about unit
square? It is the square having

all sides one unit.

Well done,
It is the square having

all sides one unit.
1 unit

1 unit

• Area of unit square = 1 unit × 1 unit 1 unit
= 1 square unit 1 unit

• Area of unit square = 1 cm × 1 cm 1 cm
= 1cm2 or square cm. 1 cm

• Area of unit square = 1 mm × 1 mm 1 mm
= 1 mm2 or square mm 1 mm

• Area of unit square = 1 m × 1 m 1m
= 1 m2 or square m 1m

246 Approved by CDC Mathematics 3

See, feel and do.

Count the unit squares from the following shapes.

AD K N ABCD = squares
BC L M squares
squares
PS WZ PQRS = squares

QR KLMN =
WXYZ =
XY

Find the area of objects.

See, feel and learn.

• Count the units squares which are included in the given shape.

• Number of unit squares is the actual area of the given shape.

• If half of unit square is present there, area will be 1 sq. unit.
2
• Such type of two halfs makes a complete square.

1 cm

area = 1 square cm

1 cm

1 cm area = 2 square cm
area = 3 square cm
1 cm

1 cm 1 cm

1 cm 1 cm area = 1 + 1 square cm
2 2

= 1 square cm

Mathematics 3 Approved by CDC 247

See, feel and do.

1. Count the square each 1cm2 and write the area of the figures.
(a) (b)

Area = cm2 Area = cm2
(c) (d)

Area = cm2 Area = cm2

2. Find the area of the following figures where length of each square is
1 cm.

(a) (b)

Area = sq.cm Area = sq.cm
(c)

Area = sq.cm

248 Approved by CDC Mathematics 3

(c) (d)

Area = sq.cm Area = sq.cm

3. Fill in the blanks in the following.

a) The area of a square of length 1m is .

b) The area of a square field of length 1km is .

c) 4 half sq.cm make sq.cm.

d) The surface covered by an object or a figure is called .

4. Count the unit squares of shaded region and write down the area of
objects.

AD PS • Area of shape sq.cm
BC QR sq.cm
ABCD = sq.cm
K RD • Area of shape sq.cm
L
QI E PQRS =
• Area of shape
M P H F
N O G KLMNOPQR =
• Area of shape

DEFGHI =

Mathematics 3 Approved by CDC 249

5. Count the unit square for the following having 1cm long sides and
find the area.

Number of unit squares =

Area = sqaure cm.

Number of unit squares =

Area = sqaure cm.

Number of unit squares =

Area = sqaure cm.

6. Complete the unit squares (taking 1cm long side) for the following
and find the area.

5 cm

2 cm Number of unit squares =

Area = square cm.

4 cm 8 cm Number of unit
Approved by CDC squares =
250 Area =
square cm.

Mathematics 3