Vedanta C. Math - 4 Re-print Final (2078)

Fraction

a) 1 of 6 beads = beads b) 1 of 6 beads = beads
2 3

c) 1 of 8 beads = beads d) 1 of 8 beads= beads
2 4

e) 1 of 12 beads = beads f) 1 of 12 beads= beads
3 4

3. Let's tell and write the values as quickly as possible.

a) 12 of 8 children = children b) 1 of Rs 10 = Rs
2

c) 1 of 12 eggs = eggs d) 1 of 15 kg = kg
3 3 girls

e) 1 of 16 l = l f) 1 of 30 girls =
4 5

Section B
4. How many times is each shaded part? Then find the product.

a) 2 times 14 b) c) d)

= 2 × 1 = 21 = 1
4 42 2

e) f) g) h) i)

5. The given marbles are equally divided by the dotted lines into the
fractions of the number of marbles. Let's find the values of fractions of
the number of marbles.

a) 1 of 6 marbles b) c) d)
3

= 1 × 62 = 2 marbles
3
1

e) f) g) h) i)

99Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Fraction

6. Let's multiply and find the products.

a) 2 × 1 b) 2 × 3 c) 2 × 2 d) 3 × 1 e) 3 × 92 f) 4 × 34
4 4 5 9

3

1 13 h) 1 2 1 3 1 53 k) 3 65 l) 5 5
2 2 3 3 4 4 4 12
g) × × i) × j) × × ×

7. Let's find the values of the fractions of the numbers.

a) 21 of Rs 12 b) 1 of 9 kg c) 2 of Rs 15 d) 1 of 20 boys
3 3 4

e) 3 of 28 students f) 1 of 30 l g) 4 of 25 km h) 3 of Rs 500
4 5 5 10

Let's read these problems carefully and solve them.

8. a) You save 1 of your pocket money everyday. What fraction of your pocket
4

money do you save in 6 days?

b) Workers construct 1 part of a road everyday. What fraction of the road
10

do they construct in a week?

c) What is the fraction of a half part of the half of a whole bread?

d) What is the fraction of one-third part of the half of a whole pizza?

9. a) 2 of 30 students in a class are girls. How many girls are there in the
5

class?

b) A vegetable shopkeeper sells 3 of 40 kg of vegetables in each day. How
4

much vegetables does she/he sell everyday?

c) Mother and father earn Rs 800 in a day. They ssppeenndde38veorfytdhaeyir? earning
to run their family. How many rupees do they

d) The distance from Dhangadi to Dadeldhura is 140 km. Mr. Joshi travelled
4
7 part of the distance by a taxi and the remaining distance by a bus.

(i) How many kilometres does he travel by taxi?

(ii) How many kilometres does he travel by bus?

e) There are 450 students in a school and 3 of them are girls.
5

(i) Find the number of girls. ? (ii) Find the number of boys.

vedanta Excel in Mathematics - Book 4 100 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Unit Decimal and Percent

6

6.1 Tenths and hundredths - Looking back
Classwork - Exercise

1. Let's tell and write the answer as quickly as possible.
a) How many cubes are there in the block?
b) What is the fraction of blue coloured cube?

c) Write this fraction in decimal.
d) What is the fraction of red coloured cubes?
e) Write this fraction in decimal.

f) What is the fraction of green coloured cubes?
g) Write this fraction in decimal.

It is one-tenth = 1 of the block of 10 cubes.
10
1
We write 10 = 0.1 and read it 'zero point one' or 'decimal one'.

It is two-tenths = 2 = 0.2 ('zero point two' or 'decimal two')
10

It is three-tenths = 3 = 0.3 ('zero point three' or 'decimal three')
10

It is a block of 100 cubes. So, each cube is

one-hundredth = 1 of the block. Here, blue
100

cube is one-hundredth of the block. Red cubes are

three-hundredths of the block. Green cubes are
twelve-hundredths of the block.

101Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

2. Let's learn from the given exaDmeplcesi.mThaeln, tell and write the fractions,

decimals, and decimal names.

a) One-hundredths = 1 = 0.01 Zero point zero one.
100

b) Three-hundredths = 3 = 0.03 Zero point zero three.
100

c) Two-hundredths = =

d) Five-hundredths = =

e) Twelve-hundredths = =

f) Fifteen-hundredths = =

6.2 Thousandths

It is a block of 1000 cubes. So, each cube

is one-thousandth = 1 of the block.
1000
1
One-thousandth = 1000 = 0.001.

We read 0.001 as 'zero point zero zero one'.

Four-thousandths = 4 = 0.004 is zero point zero zero four.
1000
25
Twenty-five -thousandths = 1000 = 0.025 is zero point zero two five.

One hundred seven-thousandths = 107 = 0.107 is zero point one zero
seven, and so on. 1000

6.3 Mixed number and decimal
Classwork - Exercise

1. Let's learn from the given illustrations. Then, tell and write the mixed
numbers in decimals.

a) b) c)

1120 = 1.2 2150 = =
d) 4130 = e) 5140
= f) 10190 =
102
vedanta Excel in Mathematics - Book 4 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

2. a) 11600 = 1.06 b) 61800 = c) 814020 =
3. a) 210500 = 2.005 b) 7103060 = c) 51208040 =

6.4 Place and place value of decimal numbers

Let's learn about the places and places values of decimal numbers from the
following examples.

whole number 3.432 tenths = 140 = 0.4
hundredths = 1300 = 0.03
2
thousandths = 1000 = 0.002

Similarly, let's learn the places and place values of a few more decimal

numbers from the table given below:

Decimal Place and place value
numbers
Tenths Hundredths Thousandths
0.567
5 = 0.5 6 = 0.06 7 = 0.007
0.198 10 100 1000

0.243 1 = 0.1 9 = 0.09 8 = 0.008
10 100 1000

2 = 0.2 4 = 0.04 3 = 0.003
10 100 1000

6.5 Comparison of decimal numbers

The whole number parts of decimal numbers are compared like that of
whole numbers. To compare the decimal parts, at first, we should compare
the tenths place. If the tenths place digits are equal, we compare the

hundredths place and then thousandths place.

Let's learn the comparison of decimal number from the examples given
below:

a) 0.397 0.512 b) 0.483 0.469 c) 0.584 0.587
< = =
> =
So, 0.397 < 0.512 <
So, 0.483 > 0.469
So, 0.584 < 0.587

103Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

Exercise - 6.1

Section A - Classwork

1. Let's tell and write the fractions and decimals of the shaded parts.

a) b) c)

3 = = =
10

d) e) f)



= = =

2. Let's tell and write the decimals of these fractions.

a) 7 = b) 7 = c) 10700 =
10 100

d) 25 = e) 25 = f) 436 =
100 1000 1000

3. Let's tell and write the decimals of these mixed numbers.

a) 1180 = 1.8 b) 215040 = 2.54 c) 1 3 =
10

d) 3170 = e) 21900 = f) 413030 =

4. Let's tell and write the fractions and decimals.

a) Nine-tenths = = b) Six-tenths = =

c) Five-hundredths = = d) Forty-two-hundredths= =

e) Seven-thousandths = = f) Fifteen-thousandths= =

vedanta Excel in Mathematics - Book 4 104 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

5. Let's tell and write the fraction of tenths, hundredths, or thousandths

of these decimals.

a) 0.4 = 140 b) 0.8 = c) 0.7 d) 0.03 =

e) 0.56 = f) 0.002 = g) 0.065 h) 0.352 =

6. Let's write '<' or '>' symbol in the blanks and compare the decimal
numbers.

a) 0.4 0.2 b) 0.65 0.58 c) 0.296 0.314

d) 0.05 0.5 e) 0.12 0.09 f) 0.085 0.105

7. Let's tell and write the place and place value of the digit in the decimal
number.

a) In 0.72, the place of 7 is and place value is

b) In 0.05, the place of 5 is and place value is

c) In 0.164, the place of 4 is and place value is

Section B

8. Let's write the decimal numbers of these number names.

a) zero point seven b) decimal four

c) zero point zero five d) decimal two six

e) Decimal zero zero nine f) zero point zero three eight

9. Let's write the decimal number names of these decimals numbers.

a) 0.2 b) 0.02 c) 0.57 d) 0.006 e) 0.308

10. Let's write the decimal numbers of these fractions.

a) 150 b) 1600 c) 10400 d) 13020 e) 78 f) 247
1000 1000

11. Let's write these improper fraction in mixed numbers and in decimals.

a) 27 = 2170 = 2.7 b) 316 = 311060 = 3.16 c) 2458 = 2 1405080 = 2.458
10 100 1000

d) 4150 e) 61 f) 113090 g) 510240 h) 1273 i) 2485
10 1000 1000

105Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

12. Let's write the fraction of tenths, hundredths, or thousandths of these
decimals.

a) 0.3 = 3 b) 0.07 = 1070 c) 0.025 = 25 d) 0.4 e) 0.9
10 1000

f) 0.06 g) 0.36 h) 0.009 i) 0.047 j) 0.529

13. The given ruler shows the whole numbers from 0 to 15 and their
tenths in order. The first arrow points 0.3. Which numbers do the
other arrows point to?

0.3 a b cd ef g h

0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5

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

14. Let's rewrite the decimal numbers. Then, write the places and place
values of each digit.

0.216 = 0.2 a) 0.15 b) 0.76 c) 0.28
tenths d) 0.369 e) 0.555 f) 0.819

hund redths = 0.01

thousandths = 0.006

15. Let's compare these decimal numbers using '<' or '>' symbol.

a) 0.3 and 0.5 b) 0.3 and 0.05 c) 0.7 and 0.4

d) 0.07 and 0.4 e) 0.26 and 0.28 f) 0.26 and 0.026

g) 0.539 and 0.486 h) 0.134 and 0.162 i) 0.357 and 0.355

16. Let's arrange the decimal numbers in ascending order.

a) 0.01, 0.1, 0.001 b) 0.25, 0.08, 0.095

17. Let's arrange the decimal numbers in descending order.

a) 0.005, 0.2, 0.07 b) 0.135, 0.069, 0.203

vedanta Excel in Mathematics - Book 4 106 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

18. It's your time - Project work!

a) Let's draw a decimal-tree of tenths in a chart paper as shown in the given
model.

0.1 0.1 0.1 0.1

0.2 0.1 0.1 0.1 0.1 0.2

0.3 0.1 0.1 0.1 0.1 0.1 0.1 0.3

0.4 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.4

0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.5

0.6 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.6

0.7 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.7

0.8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.8

0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.9
1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1

10 cm 10 cm

b) Let's compare the shaded parts of tenths and hundredths. Then discuss
with your friends and answer the questions .

0.5
0.1

0.50
0.10


(i) Is 0.1 (one-tenth) same as to 0.10 (ten-hundredths)?
(ii) Is 0.2 (two-tenths) same as to 0.20 (twenty-hundredths)?
(iii) Is 0.5 (five-tenths) same as to 0.50 (fifty-hundredths)?
c) Can we say 0.3 = 0.30 = 0.300? Discuss with your teacher.
d) Can we say 0.4 = 0.40 = 0.400? Discuss with your teacher.

107Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

6.6 Conversion of a decimal number into a fraction
Classwork - Exercise

Let's tell and write the fractions of the tenths and hundredths of these

decimals. Then, reduce the fractions to their lowest terms.

1. a) 0.2 = 21 = 1 0.2 = two-tenths = 2 In 0.2, there is one digit
105 5 10 after decimal. So, write
10 in the denominator!

b) 0.3 = c) 0.4 = = d) 0.5 = =

e) 0.6 = = f) 0.7 = = g) 0.8 = =

2. a) 0.05 = 51 = 1 0.05 = five-hundredths = 5 In 0.05, there are two digits
10020 20 100 after decimal. So, write
100 in the denominator!

b) 0.02 = c) 0.03 = = d) 0.04 = =

e) 0.06 = = f) 0.25 = = g) 0.75 = =
=
3. a) 1.4 = 1 42 = 1 2 1.4 = 1 whole number and four-tenths
105 5

b) 1.2 = = c) 1.3 = = d) 1.4 =

e) 1.5 = = f) 1.6 = = g) 1.7 = =

In this way, to convert a decimal number into a fraction, we write the decimal
number in the fraction of tenths, hundredths, or thousandths. Then, the
fraction is reduced to the lowest terms.

6.7 Conversion of a fraction into a decimal number
Classwork - Exercise

Let's convert these fractions into equivalent fractions with the
denominator 10 or 100. Then, write the decimals of tenths or hundredths.

1. a) 1 = 1 × 5 = 5 = 0.5 Numerator and denominator of 1 are multiplied by 5
2 2 × 5 10 2
to get its equivalent fraction with the denominator 10.

b) 1 1 = 151 × 2 = 1120 = 1.2
5 × 2

vedanta Excel in Mathematics - Book 4 108 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

c) 51 = 1 × = = d) 2 = 2 × = =
5 × 5 5 ×

e) 1 1 = 121 × = = f) 2 4 = 245 × = =
2 × 5 ×

2. a) 41 = 1 × 25 = 25 = 0.25 Numerator and denominator of 1 are multiplied by 25
4 × 25 100 4
to get its equivalent fraction with the denominator 100.

b) 2230 = 2230××55 = 211050 = 2.15

c) 34 = 3 × = = 0.75 d) 7 = 7× = =
4 × 20 20 ×

e) 1245 =1425×× = = f) 2590 = 2590×× = =

In this way, to convert a fraction into a decimal, we should write the fraction
in tenths, hundredths, or thousandths by making the denominator 10, 100,
or 1000.

6.8 Addition and subtraction of decimal numbers

Let's learn about the addition and subtraction of decimal numbers from the
given illustrations.

It is a block of 10 small cubes.
1
0.1 0.1 0.1 0.1 0.1 0 .1 0.1 0.1 0.1 0.1 Each cube is 10 = 0.1 of the block.

0.2 2 cubes of the block of 10 cubes 0.1 0.1

+ 0.3 3 cubes of the block of 10 cubes 0.1 0.10.1

0.5 5 cubes of the block of 10 cubes

0.1 0.1 0.1 0.1 0.1

Let's subtract 0.5 – 0.2

0.1 0.1 0.10.1 0.1 from 0.5 take away 0.2 0.1 0.1 0.1 0.1 0.1 = 0.1 0.1 0.1
0.5
0.5 – 0.2 0.3

0.5 from 5 cubes of the block of 10 cubes

– 0.2 take away 2 cubes

0.3 3 cubes are left

109Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

Let's learn more about addition and subtraction of decimal numbers from
the following examples:

Example 1: Add a) 0.7 + 0.5 b) 0.4 + 0.35

Solution

a) 0.7 7 cubes + 5 cubes

+ 0.5 1 = 12 cubes
1.2 = 1 block of 10 cubes and 2 more cubes
= 1.2

0.2

b) 0.4 0.40 Total of 75 parts
out of 100 parts
+ 0.35 + 0.35 = 0.75
0.75

Example 2: Subtract a) 1.4 – 0.6 b) 0.9 – 0.54

Solution

a) 1.4 from 14 cubes
1.4

– 0.6 – 0.6 take away 6 cubes

0.8 0.8 cubes are left

b) 0.90 0.9 from 9 tenths = 90 hundredths
0.9 – 0.54 take away 54 hundredths
– 0.54 0.36 36 hundredths are left
– 0.54 0.36


Exercise - 6.2

Section A - Classwork

1. Let's tell and write the fractions of these decimal numbers as quickly
as possible.

a) 0.3 = b) 0.7 = c) 0.9 = d) 1.1 =

e) 0.03 = f) 0.07 = g) 0.09 = h) 0.13 =

vedanta Excel in Mathematics - Book 4 110 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

2. Let's tell and write the decimal numbers of these fractions.

a) 130 = b) 7 = c) 1110 = d) 2190 =
10

e) 3 = f) 7 = g) 11900 = h) 211030 =
100 100

3. Let's tell and write the sums as quickly as possible.

a) 0.4 + 0.2 = b) 0.5 + 0.3 = c) 0.4 + 0.3 =

d) 1.2 + 0.2 = e) 1.6 + 0.1 = f) 2.5 + 1.2 =

g) 0.03 + 0.02 = h) 0.05 + 0.04 = i) 1.06 + 0.02 =

4. Let's tell and write the differences as quickly as possible.

a) 0.6 – 0.2 = b) 0.8 – 0.3 = c) 0.7 – 0.4 =

d) 1.4 – 0.2 = e) 1.4 – 1.2 = f) 3.9 – 1.5 =

g) 0.05 – 0.03 = h) 0.09 – 0.05 = i) 1.08 – 0.06 =

5. Let's tell and write the missing decimal numbers as quickly as possible.

a) 0.2 + = 0.5 b) 0.4 + = 0.6 c) 0.3 + = 0.8

d) 0.05 + = 0.07 e) 0.06 + = 0.09 f) 0.04 + = 0.06

g) 0.4 – = 0.1 h) 0.7 – = 0.3 i) 0.9 – = 0.4

j) 0.05 – = 0.03 k) 0.06 – = 0.02 l) 0.08 – = 0.05

6. Let's fill in the missing decimal numbers to complete the sums.

0.3 + = 0.8 – 0.2 = 0.7

+++ –––

+ = 0.4 0.6 – =

= == = ==

0.5 + = – = 0.2


111Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

Section B

7. Let's convert these decimals into the fractions of their lowest terms.

a) 0.2 b) 0.02 c) 0.4 d) 0.04 e) 0.5

f) 0.05 g) 0.6 h) 0.06 i) 0.8 j) 0.08

k) 1.2 l) 1.5 m) 2.5 n) 0.25 o) 0.36

8. Let's convert these fractions into the decimal numbers.

a) 21 b) 1 c) 2 d) 3 e) 4 f) 1 1
5 5 5 5 2

g) 2 1 h) 3 2 i) 1 3 j) 2 4 k) 1 l) 3
5 5 5 5 4 4

m) 270 n) 290 o) 245 p) 590 q) 1235 r) 2570

9. Each cube represents 0.1. Let's write decimal numbers represented by
each pair of cubes. Then, find the sum of the decimal numbers.

a) + b) + c) +

d) + e) + f) +

10. Each cube represents 0.01. Let's write decimal numbers represented
by each pair of cubes. Then, find the sum of the decimal numbers.

a) + b) + c) +

d) + e) + f) +

11. Let's add these decimal numbers.

a) 0.2 + 0.02 b) 0.3 + 0.03 c) 0.4 + 0.04
f) 1.3 + 1.05
d) 0.13 + 0.05 e) 0.26 + 0.07 i) 7.32 + 5.23

g) 2.5 + 3.07 h) 6.24 + 4.3 c) 0.7 – 0.07
f) 0.9 – 056
12. Let's subtract these decimal numbers. i) 10.23 – 7.64

a) 0.5 – 0.05 b) 0.6 – 0.06

d) 0.48 – 0.23 e) 0.72 – 0.35

g) 4.2 – 1.08 h) 7.5 – 3.45

13. Let's add or subtract the decimal numbers.
a) 0.58 b) 0.362 c) 0.54 d) 2.142

+ 0.35 + 0.498 + 0.275 + 3.468

vedanta Excel in Mathematics - Book 4 112 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

e) 28.76 f) 36.693 g) 0.67 h) 0.842

+ 24.89 + 45.548 – 0.42 – 0.556

i) 5.7 j) 9.45 k) 24.251 l) 58.042

– 2.32 – 6.635 – 12.463 – 38.725

Let's read the problems carefully and solve them.
14. a) The cost of a pen is Rs 32.25 and the cost of an exercise book is Rs 28.40.

Find the total cost of these two items.

b) Pathari is 28.350 km east from Itahari and Damak is 14.865 km east
from Pathari. Find the distance between Itahari and Damak.

c) Bijaya Lama bought an ice-cream for Rs 80.75 and a chocolate for
Rs 20.50. How much money did he spend altogether?

15. a) The cost of 1 litre of mustard oil is Rs 225.60 and the cost of 1 litre
of sunflower oil is Rs 185.80. Which oil is more expensive and by how
much?

b) 1 US dollar is equal to Rs 110.78 and 1 Australian dollar is equal to
Rs 81.80. Which one is the expensive currency and by how much?

c) Laxmi Pariyar's weight is 36.456 Kg and Neeta Shrestha's weight is
35.825 Kg. Who has got more weight and by how much?

16. It's your time - Project work

Let's play the card matching game of sums or difference of decimal numbers.

Each of 2 students in a group should prepare at least 10 rectangular flash
cards of equal size from a chart paper. Each student of the group should
write sums of addition and subtraction of decimal numbers in 5 cards. They
should write the answer of each sum in other 5 cards as shown below:

0.02+0.05 0.7 + 0.02 0.3 + 0.4 0.8 – 0.3 0.09–0.05

0.07 0.72 0.7 0.5 0.04
0.6 + 0.1 0.5 + 0.3 0.03 + 0.5 0.7 – 0.4 0.06 – 0.02

0.7 0.8 0.35 0.3 0.04

Each student shuffles their cards well and exchanges them with each other.
Now, the student who matches the sums and answers cards first is the
winner!

113Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Decimal and Percent

6.9 Multiplication of decimal numbers

Let's learn about the multiplication of decimal numbers from the illustrations
given below:

2 times 0.2 = 2 × 0.2 = 0.2 + 0.2 = 0.4

3 times 0.3 = 3 × 0.3 = 0.3 + 0.3 + 0.3 = 0.9

4 times 0.2 = 4 × 0.2 = 0.2 + 0.2 + 0.2 + 0.2 = 0.8

Similarly,

5 × 0.2 = 0.2 + 0.2 + 0.2 + 0.2 + 0.2 = 1.0

4 × 0.3 = 0.3 + 0.3 + 0.3 + 0.3 = 1.2

Also,

2 × 0.02 = 0.02 + 0.02 = 0.04 3 × 0.02 = 0.02 + 0.02 + 0.02 = 0.06
2 × 0.03 = 0.03 + 0.03 = 0.06 3 × 0.03 = 0.03 + 0.03 + 0.03 = 0.09
Let's learn more about the multiplication of decimal numbers from the

following examples.

Example 1: Multiply a) 1.2 × 3 b) 1.8 × 6 c) 1.24 × 4 d) 2.45 × 5

Solution

a) one digit after b) 1.8 one digit after
decimal point
1 . 2 decimal point
×3 ×6
10 . 8 one digit after decimal
3 . 6 one digit after decimal
point in the product
point in the product

c) two digits after d) two digits after

1 . 24 decimal point 2 . 45 decimal point

×4 ×5
12.25 two digits after decimal
4 . 96 two digits after decimal
point in the product
point in the product

6.10 Use of decimals

We use decimal system in different types of measurements, such as the
measurements of money, length, weight, capacity, and so on. We specially
use decimal numbers in the conversion of a unit of measurement into its
higher or lower units.

vedanta Excel in Mathematics - Book 4 114 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal and Percent

Let's learn some of the uses of decimal numbers from the following examples.

Example 2: Convert a) 55 paisa (p) into rupees (Rs)

b) Rs 0.36 into paisa

Solution I got it!

1 paisa is one hundredths of Re 1.

a) 55 p = Rs 55 = Rs 0.55 So, 55 paisa is 55 of Re 1!
100 100

b) Rs 0.36 = Rs 36 I understood! 36
100 100
0.36 is 36 hundredths =

= Rs 36 × 100 P Re 1 = 100 p. So, Rs 36 = 36 × 100 p!!
100 100 100

= 36 P

Example 3: Convert a) 7 millimetre (mm) into centimetre (cm)

b) 0.65 metre (m) into cm.

Solution It's easy!

1 mm is one tenth of 1 cm.

a) 7 mm = 7 cm So, 7 mm is 7 tenths of 1cm = 7 cm !!
10 10

= 0.7 cm

I got it! 65
100
b) 0.65 m = 65 m 0.65 is 65 hundredths = × 100
100
1 m = 100 cm, So, 65 m = 65 cm!!
100 100
= 65 cm
100 × 100

= 65 cm

Example 4: Convert a) 250 gram (g) into kilogram (kg)

b) 0.375 litre (l) into millilitre (ml)

Solution

250 1 g is one thousandth of 1 kg.
1000
a) 250 g = kg So, 250 g is 250 thousandths of 1 kg = 250 kg!!
1000

= 0.250 kg or, 0.25 kg

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Decimal and Percent

b) 0.375 l = 375 l 0.375 is 375 thousandths = 375 .
1000 1000
375 375
375 So, 1 l = 1000 ml. So, 1000 l = 1000 × 1000 ml!!
1000
= × 1000 ml

= 375 ml

Exercise - 6.3

Section A - Classwork
1. Each cube represents 0.1. How many times the decimal cubes and how

many altogether? Let's tell and write the answer as quickly as possible.
a) b)

3 × 0.2 = ×=

c) d)
× = ×=

e) f)

× = ×=

2. Each cube represents 0.01. How many times the cubes and how many
altogether? Let's tell and write the answer as quickly as possible.

a) b)

2 × 0.02 = 0.04 ×=

c) × d) ×=
=

3. Let's tell and write the product as quickly as possible.

a) 2 × 0.2 = b) 3 × 0.2 = c) 4 × 0.2 =

d) 2 × 0.3 = e) 3 × 0.3 = f) 2 × 0.4 =

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g) 2 × 0.02 = h) 3 × 0.02 = Decimal and Percent

i) 4 × 0.02 =

j) 2 × 0.03 = k) 3 × 0.03 = l) 2 × 0.04 =

m) 4 × 0.3 = n) 5 × 0.3 = o) 6 × 0.4 =

Section B

Let's multiply and find the products.

4. a) 0 . 2 b) 0 . 02 c) 0 . 3 d) 0 . 03 e) 0 . 4

×7 ×7 ×6 ×6 ×8

f) 0 . 05 g) 0 . 6 h) 0 . 07 i) 0 . 8 j) 0 . 09

×9 ×8 ×9 ×5 ×8

5. a) 1 . 2 b) 1 . 3 c) 1 . 4 d) 1 . 5 e) 1 . 8
×4 × 6 × 7 × 5 × 8

f) 1 . 0 2 g) 1 . 0 4 h) 2 . 0 3 i) 3 . 0 5 j) 4 . 0 6

×6 ×7 ×5 ×3 ×8

6. Let's convert tenths and hundredths into fractions. Then, multiply and
find the products.

a) 0.1 × 10 = 1 × 10 = 1 b) 0.02 × 100 = 2 × 100 = 2
10 100

c) 0.2 × 10 d) 0.3 × 10 e) 0.03 × 100 f) 0.4 × 10

g) 0.04 × 100 h) 0.5 × 10 i) 0.05 × 100 j) 0.7 × 10

k) 0.07 × 100 l) 1.2 × 10 m) 1.15 × 100 n) 2.6 × 10

7. Re 1 = 100 p , 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000g,
1 l = 100 ml. Use these relations to convert the units as indicated.

a) 45 p (in Rs) b) 80 p (in Rs) c) Rs 0.56 (in paisa)

d) Rs 0.95 (in paisa) e) 5 mm (in cm) f) 8 mm (in cm)

g) 0.4 cm (in mm) h) 0.9 cm (in mm) i) 36 cm (in m)

j) 75 cm (in m) k) 0.25 m (in cm) l) 0.82 m (in cm)

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m) 118 m (in km) n) 250 m (in km) o) 0.148 km (in m)
p) 0.376 km (in m) q) 225 g (in kg) r) 460 g (in kg)
s) 0.185 kg (in g) t) 0.734 kg (in g) u) 327 ml (in l)
v) 567 ml (in l) w) 0.275 l (in ml) x) 0.690 l (in ml)

8. It's your time - Project work!

Let's visit to the available website such as www.google.com and find the
exchange rate of the following currencies with our Nepali currency.

a) US Dollar ($) b) Indian Rupee ( ) c) U. K. ( )

d) Chinese Yuan (Y) e) Saudi Arabian Riyal f) Thai Baht

6.11 Percent - How many out of 100?

Let's count the number of square rooms in a
row and in a column of the square grid.

There are 100 square rooms in the grid.

5 rooms out of 100 are pink.

5 percent rooms of the grid are pink.

We write 5 percent as 5%.

For the word 'percent', we use a symbol %.

Similarly, 10% rooms of the grid are blue and

7% rooms are green.

Here, 5% = 5 out of 100 = 5 , 10% = 10 out of 100 = 10 ,
100 100

7% = 7 out of 100 = 7 , and so on.
100

6.12 Conversion of fraction into percent

Let's investigate the rule to convert a fraction into percent from the given

examples.

Example 1: Convert a) 53 b) 9 into percent.
Solution 10

a) 53 = 3 × 20 = 60 = 60% It is another process:
5 × 20 100
3 = 3 × 100
9 9 × 10 5 5 100
10 10 × 10
b) = = 90% = 3 × 20 % = 3 × 20% = 60%
5
100

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Rule 1: To convert a fraction into percent, find the equivalent fraction of the

given fraction with denominator 100. 100
100
Rule 2: Another process is to multiply the given fraction by , where

100 is 100%. So, we can directly multiply the given fraction by
100

100% to convert into percent.

6.13 Conversion of percent into fraction

Again, let's investigate the rule to convert a percent into fraction from the
following examples.

Example 2: Convert a) 13% b) 30% c) 45% into fractions.

Solution

a) 13% = 13 b) 30% = 30 = 3 I got it!
100 100 10
13 % is 13 hundredths,
45 9 9 30 % is 30 hundredths
10020 20 45% is 45 hundredths.

b) 45% = =

So, to convert a percent into fraction, we write the given percent into

hundredths. Then, we should reduce the fraction to its lowest terms if it is

necessary.

6.14 To find the value of the given percent of a quantity

Now, let's learn the process of finding the value of the given percent of a
quantity from these examples.

Example 3: Find a) 10% of 40 children b) 25% of Rs 80.
Solution

a) 10% of 40 children = 10 × 40 I got it!
100 I should multiply the given
quantity by the given percent!!
= 4 children Then, I should convert the percent
into the fraction and simplify!
b) 25% of Rs 80 = 25 5 4
100
× Rs 80

2

= Rs 20

In this way, to find the value of the given percent of a quantity, we multiply
the quantity by the percent. Then, we convert the percent into fraction and

simplify it.

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Decimal and Percent

Exercise - 6.4

Section A - Classwork
1. There are 100 square rooms in the following square grids. Let's count

and write the fractions and percents of the different coloured rooms.

==

= =
=
=



2. Let's count and write how many percent are.

a) 60 girls out of 100 students are girls.

b) 40 boys out of 100 students are boys.

c) 25 apples out of 100 fruits are apples.

d) 98 marks out of 100 full marks marks.

3. The marks obtained by Anita Tamang out of 100 full marks in 5 subjects
are given in her progress report. Tell and write her marks in percents.

First Terminal Examination

Progress Report

Name: Anita Tamang Class: 4 Roll No. 7

Subject Full Marks Marks Obtained Marks in Percent

English 100 87

Nepali 100 82

Mathematics 100 96

Science 100 75

Social Science 100 64

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4. Let's tell and write the fractions of these percents as quickly as possible.

a) 3% = b) 7% = c) 9% =

d) 33% = e) 51% = f) 99% =

Section B

5. Let's convert these fractions into percent.

a) 21 b) 41 c) 3 d) 51 e) 25 f) 3
4 5

g) 54 h) 110 i) 130 j) 170 k) 190 l) 1
20

m) 230 n) 270 o) 290 p) 215 q) 285 r) 9
50

6. Let's convert these percent into fraction of their lowest terms.
a) 2% b) 4% c) 5% d) 6% e) 8% f) 10%
g) 15% h) 20% i) 25% j) 30% k) 35% l) 40%
m) 45% n) 50% o) 60% p) 75% q) 80% r) 90%

7. Let's find the value of the given percent of quantity.

a) 10% of Rs 50 b) 20% of Rs 80 c) 25% of 40 students

d) 30% of 70 people e) 40% of 60 km f) 50 % of 90 kg

g) 60% of 100 boys h) 70% of 20 girls i) 80% of 50 eggs

Let's read these problems carefully and solve them.

8. a) On the occasion of 'Children's Day', 100 children are participating in
different activities. Among them, 55 are girls and 45 are boys. How many
percent of children are girls and boys?

b) There are 30 men, 45 women and 25 children in a wedding party.

(i) How many people are there in the party?

(ii) How many percent of people are men, women, and children in the
party?

9. a) If you got 18 marks in maths in a monthly test, how many percent of
20

marks did you get?

b) Bhurashi obtained 20 marks in science in a monthly test. How many
25

percent of marks did she obtain?

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Decimal and Percentage

c) In a school, 35 of the number of teachers are female. How many percent
50

of the teachers are female?

10. a) There are 30 students in class 4. 60% of them are girls. Find the number
of girls.

b) In a terminal test, Pankaj Chaudhari got 80% of 50 full marks in English.
How many marks did he get in English?

c) Mother spends 40% of Rs 500 to buy a book for you.

(i) How much money does she spend?
(ii) How much money is left with her?

d) There are 400 students in a school. 70% of them are boys. How many
girls are there in the school?

It's your time - Project work!

11. a) How many students are there in your class?
b) How many percent of them are girls?
c) How many percent of them are boys?

12. a) How many teachers are there in your school?
b) How many percent of them are male teachers?
c) How many percent of them are female teachers?
13. Let's make 3 sets of flowers by cutting a chart paper as shown in the

diagrams. Write a percent (10%, 20%, 40%, 50%, 60%, and 80%) in the
circle. Then, write fractions and decimals equal to the percent in the 4
petals. Colour the petals. You can stick, your flowers on the wall-magazine.

20
100

0.2 20% 2
10

1
5

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Unit Unitary Method, Buying, Selling and Billing

7

7.1 Unitary Method - Unit number, unit value, more number, more value
Classwork - Exercise

1. Let's read the price tag of a pencil. Then, tell and write the price of
more number of pencils.

a) What is the price of 1 pencil? Rs 10
b) The price of 2 pencils = 2 ×
=

c) The price of 3 pencils = 3 × = ??

d) The price of 4 pencils = × = ??
e) The price of 5 pencils = × =

2. Let's read the price tags of the given number of different things. Then,
tell and write the unit price of unit number of thing.

a) What is the price of 2 pencils? Rs 20
What is the price of 1 pencil? Rs 20 ÷ 2 =

b) What is the price of 3 sweets? Rs 15
What is the price of 1 sweet?
÷ =

c) What is the price of 5 biscuits? ÷ = Rs 100
What is the price of 1 biscuit?

In this way, a method of finding more values by multiplication and unit values
by division is known as unitary method.

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Let's learn to solve more problems by using unitary method from the
following examples.

Example 1: There are 12 pencils in 1 packet. How many pencils are there

in 6 packets?

Solution I got it!

The number of pencils in 1 packet = 12 I find more value just
The number of pencils in 6 packets = 6 × 12 by multiplication!!

= 72

Hence, there are 72 pencils in 6 packets.

Example 2: The cost of 5 packets of noodle is Rs 125. Find the cost of

a) 1 packet and b) 2 packets of noodle.

Solution

We understood!

a) Cost of 5 packets of noodles = Rs 125 We find unit value by division.

So, cost of 1 packet of noodle
125
Cost of 1 packet of noodle = Rs 125 = Rs 125 ÷ 5 = Rs 5
5

= Rs 25

Hence, the cost of 1 packet of noodle is Rs 25.

b) Cost of 1 packet of noodle = Rs 25

Cost of 2 packets of noodle = 2 × Rs 25

= Rs 50

Hence, the cost of 2 packets of noodle is Rs 50.

Example 3: The bus fare of 8 people is Rs 320. How much is the fare of 10

people?

Solution Now, it's easy to me! Rs 320
8
The fare of 8 people = Rs 320 Fare of 1 person =

The fare of 1 person = Rs 320 And fare of 10 people = Rs 320 × 10
8 8

= Rs 40 = Rs 400

The fare of 10 people = 10 × Rs 40

= Rs 400

Hence, the bus fare of 10 people is Rs 400.

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7.2 Rate of cost

Classwork - Exercise

Let's study the given example. Then, tell and write the rate of cost of
different items.

Mother buys 1 kg of fruits for Rs 80. We got it!
The rate of cost of fruit is Rs 80 per kg. Rate of cost means
cost of unit quantity!

a) Dipak buys 1 kg of vegetables for Rs 60.

The rate of cost of vegetables is

b) Deepa buys 1 litre of sunflower oil for Rs 190.
The rate of cost of oil is

c) Dhurmus buys 2 pencils for Rs 20. per pencil.
The rate of cost of pencil = Rs 20 ÷ 2 =
I understood!
d) Suntali buys 3 erasers for Rs 15. = Rate of cost of eraser
The rate of cost of eraser = is the cost of 1 eraser!!

e) Pinky buys 5 sweets for Rs 25. =
The rate of cost of sweet =

Exercise - 7.1
Section A - Classwork
1. Let's tell and write more values of more number of things.
a) Cost of 1 eraser is Rs 5, cost of 4 erasers is

b) Cost of 1 pencils is Rs 7, cost of 6 pencils is

c) 1 jar can hold 10 litres of water, 8 jars hold

d) In 1 m there are 100 cm, in 10 m there are

e) In 1 hour there are 60 minutes, in 5 hours there are

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2. Let's tell and write unit value of unit number of things.

a) Cost of 3 chocolates is Rs 30, cost of 1 chocolate is

b) Cost of 5 packets of noodle is Rs 100, cost of 1 packet is

c) 6 bottles contain 12 litres of cold drink, 1 bottle contains

d) In 4 cm there are 40 mm, in 1 cm there are

e) In 7 weeks there are 49 days, in 1 week there are

3. Let's tell and write the rate of cost.

a) The cost of 2 pencils is Rs 20.

What is the cost of 1 pencil? ÷ =

What is the rate of cost of pencil? per pencil.

b) The cost of 3 kg of mangoes is Rs 240.

What is the cost of 1 kg of mangoes? ÷ =

What is the rate of cost of mangoes? per kg.

Section B
Let's read these problems carefully and solve them.

4. a) The cost of 1 packet of milk is Rs 40. Find the cost of 8 packets of milk.
b) The cost of 8 packets of milk is Rs 320. Find the cost of 1 packet of milk.
c) The cost of 1 kg of grapes is Rs 120. Find the cost of 5 kg of grapes.
d) The cost of 5 kg of grapes is Rs 600. Find the cost of 1 kg of grapes.
e) A gas cylinder holds 15 l of gas. How much gas do 12 cylinders hold?
f) 12 gas cylinders hold 180 l of gas. How much gas does 1 cylinder hold?

5. a) The cost of 2 chocolates is Rs 40 and the cost of 3 biscuits is Rs 45.
Which one is more expensive?

b) The cost of 4 crayons is Rs 48 and the cost of 5 pencils is Rs 50. Which
one is cheaper?

6. a) The cost of 2 kg of vegetables is Rs 50.
(i) Find the cost of 1 kg of vegetables.
(ii) Find the cost of 3 kg of vegetables.

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b) There are 90 eggs in 3 crates of eggs.
(i) How many eggs are there in 1 crate?
(ii) How many eggs are there in 5 crates?
7. a) The cost of 4 exercise books is Rs 120. Find the cost of 6 exercise books.

b) There are 180 children in 9 equal rows. How many children are there in
7 rows?

c) In 5 km, there are 5000 m. How many metres are there in 8 km?

d) There are 6000 g in 6 kg. How many grams are there in 12 kg?

It's your time - Project work!

8. Let's collect the information about the rate of cost of the following items in
your locality.

Items Rice Sugar Cooking oil
Rate of cost per kg per kg per litre

a) Estimate the quantity of rice consumed by your family in 1 month and
in 1 year.

b) Estimate the expenditure on rice in 1 month and in 1 year.

c) Estimate the quantity of sugar consumed by your family in 1 month and
in 1 year.

d) Estimate the expenditure on sugar in 1 month and in 1 year.

e) Estimate the quantity of cooking oil consumed by your family in 1
month and in 1 year.

f) Estimate the expenditure on oil in 1 month and in year.

g) How much is the total expenditure on these items in 1 month and in 1
year?

7.3 Buying and selling

When we buy something from a shop, we
should pay money to the shopkeeper. This
money is buying or purchasing price. The
buying price is also called cost price.

A shopkeeper takes money from the vedanta Excel in Mathematics - Book 4
customers when she sells things. This
money is the selling price of the things.

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7.4 Profit and loss

Ram buys a pen for Rs 20. So, cost price of the pen is Rs 20. He sells the pen
to Sita for Rs 25. So, selling price of the pen is Rs 25.

Does Ram make profit or loss?
Of course, Ram makes profit because his selling price is more than the cost price.
His profit = Rs 5 = Rs 25 – Rs 20 = selling price – cost price

Again, let's take another example.
Hari buys a sweet for Rs 10 and sells it to Laxmi for Rs 8.
So, the cost price of the sweet is Rs 10 and selling price is Rs 8.
Here, Hari makes loss because his selling price is less than cost price.
His loss = Rs 2 = Rs 10 – Rs 8 = cost price – selling price
Let's learn more about profit and loss from the examples given below.

Example 1: The cost price of a book is Rs 200 and its selling price is

Rs 220. Find profit. When selling price is
more than cost price,
Solution there is profit!

Cost price of the book = Rs 200

Selling price of the book = Rs 220
Profit = selling price – cost price = Rs 220 – Rs 200 = Rs 20

Example 2: The cost price of 1 kg of vegetable is Rs 75 and the selling

price is Rs 65. Find loss. When selling price is
less than cost price,
Solution there is loss!
Cost price of vegetable = Rs 75

Selling price of vegetable = Rs 65

Loss = cost price – selling price = Rs 75 – Rs 65 = Rs 10

Exercise - 7.2
Section A - Classwork
1. Let's tell and write the answer as quickly as possible.
a) A shopkeeper buys a packet of sweets for Rs 100 and sells it for Rs 120.

(i) What is the cost price of the sweets?

(ii) What is the selling price of the sweets?
(iii) Does the shopkeeper make profit or loss?

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b) A fruit-seller buys some fruits for Rs 800 and sells them for Rs 750.
(i) What is the cost price of the fruits?
(ii) What is the selling price of the fruits?
(iii) Does the fruit-seller make profit or loss?
2. Let's tell and write profit or loss as quickly as possible.
a) Cost price is Rs 10 and selling price is Rs 14, profit =
b) Cost price is Rs 20 and selling price is Rs 18, loss =
c) CostpriceisRs100andsellingpriceisRs125,profit=
d) Cost price is Rs 150 and selling price is Rs 140, loss =

Section B

3. Let's find profit or loss.
a) Cost price is Rs 45 and selling price is Rs 60. Find profit.
b) Cost price is Rs 80 and selling price is Rs 75. Find loss.
c) Cost price is Rs 120 and selling price is Rs 110. Find loss.
d) Cost price is Rs 160 and selling price is Rs 200. Find profit.

4. Let's decide whether there is profit or loss. Then find profit or loss.

a) Cost price is Rs 30 and selling price is Rs 40. Find profit or loss.
b) Selling price is Rs 90 and cost price is Rs 60. Find profit or loss.
c) Selling price is Rs 100 and cost price is Rs 115. Find profit or loss.
d) Cost price is Rs 300 and selling price is Rs 250. Find profit or loss.

5. Let's read the problems carefully and solve them.
a) The cost price of a pen is Rs 40 and its selling price is Rs 48. Find profit

or loss.

b) Pratik Shrestha buys a doll of Mickey Mouse for Rs 250. He sells it to
Bishu Rai for Rs 300. Find his profit or loss.

c) A fruit-seller buys some apples for Rs 740. She/he sells these apples for
Rs 710. How much profit or loss does fruit-seller make?

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Unitary Method, Buying, Selling and Billing

7.5 Billing

Have you ever got a piece of paper from
a shopkeeper when you buy goods?
This piece of paper is a bill. Have you
ever read a bill?

In a bill, a shopkeeper writes the
customer's name and address, quantity,
rate of cost, and total cost of goods that
we buy from the shop.

Exercise - 7.3

Section A - Classwork

1. Let's read the given bill. Tell and write the answer of the following

questions as quickly as possible.



Vedanta Stationery Traders

Budha Subba chowk, Rajabas - 9

Bill No. 0345 Date: 7 Shrawan, 2077

Customer's Name: Badri Rai Address: Prakashpur

S. No. Particulars Quantity Rate (Rs) Amount
(Rs)

1 Crayons 6 20.00 120.00

2 Instrument box 1 115.00 115.00

3 Drawing books 3 60 180.00

Sold by: Anamol Grand Total 415.00

a) What is the name of the shop?
b) What is the name of the customer?

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c) How many crayons are purchased?

d) What is the rate of cost of crayons?

e) What is the amount of the crayons?

f) What amount is paid for instrument box?

g) How much is the cost of 1 drawing book?

h) What is the total amount of the bill?

Section B

2. Let's prepare the similar format of bill as given in Q. No. 1. Then,
workout these problems.

a) Kopila purchased 4 exercise books at Rs 35 each, 2 pens at Rs 25 each,
and 6 colour pencils at Rs 10 each. Prepare a bill given to her by the
shopkeeper.

b) The price list of different food items Rice: Rs 80.00 per kg
displayed by a provision shop is given. Flour: Rs 45.00 per kg
Prepare bills given to the customers by Pulses: Rs 120.00 per kg
the shopkeeper. Sugar: Rs 75.00 per kg
Tea: Rs 250.00 per kg
(i) Bill of 5 kg of rice, 2 kg of flour, 3 kg Cooking oil: Rs 160 per litre
of sugar

(ii) Bill of 4 kg flour, 2 litres cooking oil,
1 kg of tea

(iii) Bill of 3 kg of pulses, 4 kg of rice, 1 litre cooking oil.

3. It's your time - Project work!

a) Let's make groups of your friends. Visit a few number of shops in your
locality and collect the sample of some bills. Discuss about these bills in
your class.

b) Let's ask to your family members whether they have any types of bills
given by shopkeeper. Then, study about the bills.

? vedanta Excel in Mathematics - Book 4

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Unit Time and Money

8

8.1 Telling time - Looking back
Classwork - Exercise

1. Let's tell and write the time using a. m. or p. m.
a) At what time do you wake up usually in the morning?
b) At what time do you usually go to your school?
c) What is your school's assembly time?
d) At what time does your maths class start?
e) At what time is your school over?
f) At what time do you usually arrive home from your school?
g) What is your usual dinner time?
h) At what time do you go to bed usually?
Now, can you make your timetable?

2. Let's tell and write the time using a. m. or p. m. shown in the clocks.

a) b) c) d)

Morning Afternoon Evening Morning
6:05 a.m.

3. Let's tell and write the time in words mentioning morning, afternoon
or evening.

a) 7 : 45 a. m. Quarter to 8 in the morning

b) 8 : 05 a. m.

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Time and Money

c) 12 : 00 noon
d) 3 : 30 p. m.
e) 9 : 15 p. m.

8.2 24-hour clock system

From 12: 01 in the morning to 11:59 in the morning we
tell and write time using a. m. (Ante Meridiem).

From 12:01 afternoon to 11:59 at night we tell and write
time using p. m. (Post Meridiem).

In 12-hour clock system, we tell and write the hours
using the numbers 1 to 12. In 24-hour clock system, we tell and write the
hours using number 1 to 24.

The given clock shows the hours 1:00 a. m. in the morning to 12:00 noon in
the mid-day. Then, it shows 13:00 in the afternoon to 24:00 at mid-night.

Classwork - Exercise

1. Now, let's tell and write the p. m. time in 24-hour clock system.
Trick!

1:10 p.m. = 13:10 1 : 10 p. m. = (1 + 12) : 10 = 13 : 10

a) 1 : 20 p. m. = b) 2 : 30 p. m. =

c) 4 : 00 p. m. = d) 7 : 40 p. m. =

e) 9 : 45 p. m. = f) 12 : 50 a. m. = 00 : 50

2. Let's tell and write the time in 12-hour clock system using a. m. or p. m.

00 : 00 = 24 – 12 = 12 : 00 mid-night 00:30 = (24 – 12):30 = 12:30 a.m.

02 : 10 = 2 : 10 a. m. 15 : 25 = (15 – 12) : 25 = 3 : 25 p. m.

a) 00.15 = b) 03 : 05 =

c) 13 : 40 = d) 16 : 20 =

e) 18 : 55 = f) 23 : 30 =

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Time and Money

3. Let's calculate how many hours.
How many hours are there between 10 : 00 a. m. and 4 : 00 p. m.?
Here, 4 : 00 p. m. = 12 + 4 = 16 hours. So, 16 – 10 = 6 hours

a) How many hours are there between 9 : 00 a. m. and 1 : 00 p. m.?
(12 + 1) : 00 – 9 00 a. m. =

b) How many hours are there between 11:00 a. m. to 2 : 00 p. m. ?



c) How many hours are there between 7 : 00 a. m. to 7 : 00 p. m.?



8.3 The calendar - Days, weeks, months, and year
Classwork - Exercise

1. Let's study Nepali and English Calendars. Then tell and write the
answer of the given questions as quickly as possible.

a}zfv @)&* h7] @)&* c;f/ @)&*

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@# @$ @% @^ @& @* @( @( #) @& @* @( #)

vedanta Excel in Mathematics - Book 4 134 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

January 2021 SAT February 2021 SAT March 2021 SAT

SUN MON TUE WED THU FRI 2 SUN MON TUE WED THU FRI 6 SUN MON TUE WED THU FRI 6
9 13 13
31 1 16 1 2 34 5 20 1 2 34 5 20
3 4 5 67 8 23 7 8 9 10 11 12 27 7 8 9 10 11 12 27
10 11 12 13 14 15 30 14 15 16 17 18 19 14 15 16 17 18 19
17 18 19 20 21 22 21 22 23 24 25 26 21 22 23 24 25 26
24 25 26 27 28 29 28 28 29 30 31

April 2021 May 2021 SAT June 2021 SAT

SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI 1 SUN MON TUE WED THU FRI 5
8 12
12 3 30 31 15 1 23 4 19
4 5 6 7 8 9 10 2 3 4 56 7 22 6 7 8 9 10 11 26
11 12 13 14 15 16 17 9 10 11 12 13 14 29 13 14 15 16 17 18
18 19 20 21 22 23 24 16 17 18 19 20 21 20 21 22 23 24 25
25 26 27 28 29 30 23 24 25 26 27 28 27 28 29 30

July 2021 August 2021 SAT September 2021 SAT

SUN MON TUE WED THU FRI SAT SUN MON TUE WED THU FRI 7 SUN MON TUE WED THU FRI 4
14 11
12 3 1 2 3 45 6 21 12 3 18
4 5 6 7 8 9 10 8 9 10 11 12 13 28 5 6 7 8 9 10 25
11 12 13 14 15 16 17 15 16 17 18 19 20 12 13 14 15 16 17
18 19 20 21 22 23 24 22 23 24 25 26 27 19 20 21 22 23 24
25 26 27 28 29 30 31 29 30 31 26 27 28 29 30

October 2021 SAT November 2021 SAT December 2021 SAT

SUN MON TUE WED THU FRI 2 SUN MON TUE WED THU FRI 6 SUN MON TUE WED THU FRI 4
9 13 11
31 1 16 1 2 34 5 20 12 3 18
3 4 5 67 8 23 7 8 9 10 11 12 27 5 6 7 8 9 10 25
10 11 12 13 14 15 30 14 15 16 17 18 19 12 13 14 15 16 17
17 18 19 20 21 22 21 22 23 24 25 26 19 20 21 22 23 24
24 25 26 27 28 29 28 29 30 26 27 28 29 30 31

a) Which is the new year month in Nepali calendar?

b) Which is the new year month in English calendar?

c) How many months are there in a year?

d) How many days are there in a week?

e) How many weeks are there in a year?

f) How many days are there in a year?

g) Which day is the 17th Mangsir 2078?

h) Which day is the 1st May 2021?

i) Write the month, date, and day of your birthday in Nepali and in English
calendars.

Nepali calendar:

English calendar:

135Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Time and Money

8.4 Conversion of units of time
Let's remember the relation between different units of time.

1 hour (h) = 60 minutes (min) Now, I can convert the units!
1 minute (min) = 60 seconds (s) 2 h = 2 × 60 min = 120 minutes
3 m = 3 × 60 s = 180 seconds

1 week = 7 days I can also convert the units!
1 month = 30 days 4 weeks = 4 × 7 days = 28 days
1 year = 12 months 3 months = 3 × 30 days = 90 days
1 year = 52 weeks 2 years = 2 × 12 months = 24 months
1 year = 365 days


Now, let's learn to convert the units of time from the following examples.

Example 1: Convert 2 h 30 min into minutes.

Solution It's easy!

2 h 30 min = 2 × 60 min + 30 min 1 h = 60 min
So, 2h = 2 × 60 min = 120 min

= 120 min + 30 min

= 150 minutes

Example 2: Convert 90 minutes into hour and minutes. × 60
Solution Minute

90 min = (90 ÷ 60) h Hour ÷ 60
= 1 quotient and 30 remainder

= 1 h 30 min

Another process I've remembered!
90 min = 60 min + 30 min 60 minutes = 1 hour!!
= 1 h + 30 min
= 1 h 30 min

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Time and Money

Example 3: Convert 2 years 6 months into months. × 12
Solution Month

2 years 6 months = 2 × 12 months + 6 months ÷ 12

= 24 months + 6 months Year

= 30 months

Example 4: Convert 45 days into weeks and days.

Solution I got it!

45 days = (45 ÷ 7) weeks 7 days = 1 week

= 6 quotients and 3 remainder So, 45 days = (45 ÷ 7) weeks

= 6 weeks 3 days

Exercise - 8.1
Section A - Classwork
1. Let's tell and write the answer in the blank spaces.
a) Using a. m. and p. m., quarter past 8 in the morning is written as

b) Using a. m. or p. m. 10 minutes to 9 at the night is written as

c) In 24 - hour clock system, 2 : 00 p. m. is

d) In 12 - hour clock system, 18 : 00

e) Number of hours between 11 : 00 a. m. and 1 : 00 p. m. is

2. Let's tell and write the correct answers as quickly as possible.

a) 1 h = min, 2 h = min, 180 min = h

b) 65 min = h min, 70 min = h min

c) 1 min = s, 2 min = s, 180 s = min

d) 1 week = days, 2 weeks = days, 21 days = weeks

e) 1 year = months, 2 years = months, 36 months = year

f) 1 month = days, 2 months = days, 90 days = months

137Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Time and Money

Section B
3. Let's write the time in 24 - hour clock or in 12 - hour clock.

a) 1 : 30 p. m. b) 2 : 05 p. m. c) 6 : 45 p. m. d) 10 : 15 p. m.
e) 13 : 10 f) 15 : 40
g) 20 : 20 h) 23 : 50

4. Let's convert into as indicated.

a) 1 h 10 min (minutes) b) 1 h 15 min (minutes) c) 2 h 20 min (minutes)

d) 1 min 20 s (seconds) e) 1 min 30 s (seconds) f) 2 min 5 s (seconds)

g) 65 min (hours and minutes) h) 80 min (hours and minute)

i) 125 min (hours and minutes) j) 90 s (minutes and seconds)

5. Let's convert into as indicated. b) 2 years 7 months (months)
a) 1 year 4 months (months)

c) 18 months (years and months) d) 39 months (years and months)

e) 2 weeks 5 days (days) f) 4 weeks 2 days (days)

g) 18 days (weeks and days) h) 38 days (weeks and days)

i) 2 months 10 days (days) j) 80 days (months and days)

k) 2 years (weeks) l) 2 years (days)

6. Let's calculate how many hours and minutes are there?

a) between 8:00 a. m. and 12:00 noon b) between 9:15 p. m. and 11:15 p. m.

c) between 10:00 a. m. and 2:00 p. m. d) between 11:10 a. m. and 4:30 p. m.

It's your time - Project work!

7. a) Let's make your timetable including your regular tasks: wake up time,

breakfast time, morning study time, morning meal time, school time,
tiffin time, evening playing time, evening study time, dinner time, bed
time.

Show your timetable to your friends and compare with them. You can
stick your timetable in your bed-room. Are you always following your
timetable?

b) Let's make Nepali and English calendars of the month of your birthday.
You can use the format of the calendars given in the book. Circle the date
and day of your birthday on it.

vedanta Excel in Mathematics - Book 4 138 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

8.5 Addition and subtraction of time
Classwork - Exercise

1. Let's add minutes and regroup into hours and minutes.

a) 40 min + 30 min = 70 min = 60 min + 10 min = 1 h 10 min

b) 40 min + 25 min =

c) 45 min + 25 min =

d) 50 min + 15 min =

e) 50 min + 40 min =

2. Let's add and find what time it is now. (30 + 45) min = 75 min
a) 9 : 30 a. m. + 45 min = 10 : 15 a. m. 75 min = 60 min + 15 min
b) 9 : 40 a. m + 20 min =
c) 10 : 30 p. m. + 40 min = = 1 h 15 min
d) 8 : 55 a. m. + 30 min = (9 + 1) : 15 = 10 : 15 a. m.
e) 1 : 35 p. m. + 45 min =
(30 + 40) min = 70 min
70 min = 60 min + 10 min

= 1 h 10 min
(10 + 1) : 15 = 11 : 10 a. m.

3. Let's subtract as shown in the example.

60 min

a) 1 h 10 min – 20 min = (60 + 10) min – 20 min = 70 min – 20 = 50 min

60 min

b) 1 h 10 min – 30 min = 70 min – 30 min =

60 min

c) 1 h 20 min – 30 min =

d) 1 h 20 min – 40 min =

e) 1 h 30 min – 40 min =

4. Let's subtract and find what time it is now.

60 min

a) 7 : 10 a. m. – 30 min = 6 : 70 – 30 min = 6 : 40 a. m.

b) 7 : 10 a. m. – 20 min = vedanta Excel in Mathematics - Book 4
139Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

c) 9 : 10 p. m. – 40 min =

d) 11 : 20 a. m. – 50 min =

e) 1 : 30 p. m. – 40 min =

Now, let's learn more about the addition and subtraction of time from the
examples given below.

Example 1: Add or subtract a) 2 h 30 min + 3 h 40 min

b) 4 h 20 min – 2 h 30 min

Solution

a) 2 h 30 min

+ 3 h 40 min (30 + 40) min = 70 min = 1 h 10 min
5 h 70 min (1 + 2 + 3) h = 6 h
6 h 10 min 2 h 30 min + 3 h 40 min = 6 h 10 min

b) 1 h=60 min 1 h = 60 min is borrowed to 20 min.
4 h 20 min So, (60 + 20) min = 80 min

– 2 h 30 min (80 – 30) min = 50 min
1 h 50 min Also, (4 – 1) h – 2 h = 3 h – 2 h = 1h

Example 2: Maths period starts at 10 : 45 a. m. and finishes in 40

minutes. At what time is it over?

Solution 85 min = 60 min + 25 min

10 : 45 a. m. + 40 min = 10 : 85 = 11 : 25 a. m. = 1 h 25 min

So, it is over at 11 : 25 a. m.

Example 3: Dinesh started to read a story at 8 : 30 p. m. and finished it
at 10 : 00 p. m. How long did he take to finish the story?

Solution
10 : 00 p. m. – 8 : 30 p. m. = 9 : 60 p. m. – 8 : 30 p. m. = 1 h 30 min

So, he finished the story in 1 h 30 min.

Example 4: A bus started its journey from Surkhet to Nepalganj at
11 : 30 a. m. It arrived at Nepalgunj in 4 hours 40 minutes.
At what time did it arrive at Nepalganj?

vedanta Excel in Mathematics - Book 4 140 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

Solution (11 + 4) : (30 + 40)
11 : 30 a. m. + 4 h 40 min = 15 : 70 70 min = 1 h 10 min
= 16 : 10 (15 + 1) h = 16 h
= (16 – 12) : 10 As the time crosses 12 : 00
= 4 : 10 p. m. subtract 12.

So, the bus arrived at 4 : 10 p. m.

Example 5: The construction of a road was started on 18 Baisakh 2077

and completed on 25 Bhadra 2078. In how many years,

months, and days was the construction over?

Solution Y MD
18th Baisakh 2077 to 18 Baisakh 2078 = 1 year 2078 / 05 / 25

18th Baisakh 2078 to 18 Bhadra 2078 = 4 months – 2077 / 01 / 18
18th Bhadra 2078 to 25th Bhadra 2078 = 7 days 1 y 4 m 7 days

So, the construction work was over in 1 year 4 months 7 days.

Exercise - 8.2

Section A - Classwork

1. Let's add minutes and regroup into hours and minutes
a) 25 min + 40 min =

b) 50 min + 30 min =

2. Let's add seconds and regroup into minutes and seconds.
a) 40 s + 35 s =

b) 50 s + 40 s =

3. Let's add days and regroup into months and days.

a) 20 days + 15 days =

b) 25 days + 25 days =

141Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Time and Money

4. Let's add months and regroup into years and months.
a) 5 months + 9 months =
b) 7months+10months=

5. Let's convert into the lower units and subtract.

a) 1 h – 20 min = 60 min – 20 min =

b) 1 h – 15 min = =

c) 1 min – 10 s = =

d) 1 year – 5 months = =

e) 1 month – 18 days = =

Section B

6. Let's add or subtract.

a) 1 h 20 min + 1 h 45 min b) 2 h 30 min + 1 h 40 min

c) 3 h 30 min – 1 h 40 min d) 5 h 20 min – 2 h 30 min

e) 1 year 6 months + 1 year 8 months f) 5 years 4 months – 3 years 6 months

g) 3 months 20 days + 2 months 25 days h) 8 month 10 days – 4 months 20 days

7. Let's add or subtract using a. m. or p. m.

a) 6 : 30 a. m. + 1 h 45 min b) 10 : 20 a. m. + 4 h 50 min

c) 4 : 45 p. m. – 1 h 15 min d) 2 : 30 p. m. – 3 h 20 min

e) 1 : 40 p. m. – 9 : 25 a. m. f) 3 : 50 p. m. – 10 : 10 a. m.

Let's read the problems carefully, and solve them.
8. a) You started doing maths homework at 7 : 20 a. m. and finished in 40

minutes. At what time did you finish your homework?

7 : 20 a. m. + 40 minutes =

vedanta Excel in Mathematics - Book 4 142 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

b) Science class test started at 11 : 30 a. m. and finished in 45 minutes. At
what time was the test over?

c) A plane takes off at 13 : 35 from Tribhuvan airport. It is landed at
Biratnagar airport in 35 minutes. At what time is it landed?

9. a) Yesterday, father started cooking dinner at 7 : 15 p. m. and finished at
8 : 30 p. m. How long did he take to cook the dinner?

8 : 30 p. m. – 7 : 15 p. m. =

b) You left your home at 9 : 05 a. m. for your school and you arrived at
school at 9 : 55 a. m. How long did you take to arrive at school?

c) A T20 cricket match started at 11 : 25 a. m. it was over at 2 : 30 p. m.
What was the duration of the match?

d) On August 1 the sun rose at 5 : 22 a. m. and set at 6 : 10 p. m. How long
was the sun above the horizon?

e) On the same day, the moon rose at 10 : 20 p. m. and set at 5 : 10 a. m. For
how long could the moon be seen?

10. a) A bus starts its journey from Birtamod to Bharatpur at 9 : 45 a. m. If it
arrives at Bharatpur in 8 h 30 min, at what time does it arrive?

b) A plane takes off from Tribhuvan International airport at 11 : 15 a. m.
for Bankok, Thailand. If it is landed at Savarnabhumi airport, Bankok at
Nepali time 2 : 45 p. m., how long was the flight?

c) The construction of a school building was started on 7 Shrawan 2077
and completed on 17 Mangsir 2078. In how many years, months, and
days was the construction over?

d) Write today's date in year, month, and day (such as 2078/03/08) and
subtract your date of birth in year, month, and day. How old are you
today?

11. It's your time - Project work

a) Let's prepare the school routine of your Sunday classes.

b) Let's calculate your school days in the first, the second and the final terminal
sessions from your school calendar. How many school days are there in this

year?

143Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Time and Money

8.6 Money

We express our currency (money) in rupees (Rs) and paisa (p). We write 1
rupee as Re 1, 5 rupees as Rs 5, and so on. We usually express rupees and
paisa together in the decimal of rupees.

Rs 10 and 20 p = Rs 10.20, Rs 25 and 50 p = Rs 25.50 and so on.

8.7 Conversion between rupees and paisa

Let's remember the relation between rupees and paisa.

Re 1 = 100 p 100 p = Re 1, So, 1 p = Rs 1 = Rs 0.01
Rs 2 = 2 ×100 p = 200 p 100
Rs 5 = 5 ×100 p = 500 p
2 p = Rs 2 = Rs 0.02
100

5 p = Rs 5 = Rs 0.05
100

Similarly, × 100

Rs 3 and 15 p = Rs 3 + Rs 15 Rupees paisa
100

= Rs 3 + Rs 0.15

= Rs 3.15 ÷ 100

8.8 Addition and subtraction of money

When money is given in the decimal of rupees, we should simply use the
rules of addition or subtraction of decimals.

Let's study the illustrations and learn about the addition and subtraction of
money.

Example 1: Add or subtract a) Rs 40.60 + Rs 35.80 b) Rs 56.45 – Rs 42.60

Solution: b) Rs 56 . 45
a) Rs 40 . 60 – Rs 42 . 60
Rs 13 . 85
+ Rs 35 . 80
Rs 76 . 40

When rupees and paisa are given separately, we should first write them in
decimals of rupees. Then, add or subtract the decimals.

vedanta Excel in Mathematics - Book 4 144 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Time and Money

Example 2: Add or subtract a) Rs 25 and 75 p + Rs 50 and 45 p

b) Rs 180 and 50 p – Rs 75 and 90 p

Solution

a) Rs 25 and 75 p = Rs 25.75 b) Rs 180 and 50 p = Rs 180.50

Rs 50 and 45 p = + Rs 50.45 Rs 75 and 90 p = – Rs 75.90

Rs 76.20 Rs 104.60

Exercise - 8.3

Section A - Classwork

1. Let's tell and write how many paisa (p).

a) Re 1 = b) Rs 3 = c) Rs 4 =

d) Rs 0.02 = e) Rs 0.05 = f) Rs 0.20 =

2. Let's tell and write how many rupees (Rs).

a) 100 p = b) 200 p = c) 600 p =

d) 5 p = e) 50 p = f) 75 p =

3. Let's tell and write in the decimals of rupees.

a) Re 1 and 5 p = b) Rs 6 and 15 p =

c) Rs 12 and 30 p = d) Rs 25 and 55 p =

4. Let's tell and write how many rupees altogether?

a) Rs 1.10 + Rs 2.05 = b) Rs 3.20 + Rs 4.15 =

c) Rs 5.30 + Rs 3.20 = d) Rs 7.50 + Rs 2.10 =

5. Let's tell and write how many rupees are left?

a) Rs 2.10 – Rs 1.05 = b) Rs 4.20 – Rs 2.10 =

c) Rs 8.40 – Rs 3.20 = d) Rs 10.80 – Rs 6.50 =

145Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Time and Money

6. Let's tell and write the answer as quickly as possible.

a) How many Rs 5 notes make a Rs 50 note?

b) How many Rs 10 notes make a Rs 100 note?

c) How many Rs 20 notes make a Rs 100 note?

d) How many Rs 50 notes make a Rs 500 note?

e) How many Rs 100 notes make a Rs 1000 note?

7. Let's read the price of each item. Tell and write the number of rupees
notes needed to buy the item.

a) Number of Rs 50 notes , number of Rs 20

notes , and number of Rs 10 notes

Rs 80

b) Number of Rs 100 notes , number of Rs 50
Section B
Rs 270 notes , and number of Rs 20 notes

8. Let's add or subtract:

a) Rs 24.30 + Rs 16.45 b) Rs 45.25 + Rs 32.60

c) Rs 318.50 + Rs 156.70 d) Rs 64.85 – Rs 27.40

e) Rs 172.25 – Rs 75.60 f) Rs 536.35 – Rs 250.75

9. Let's convert into the decimal of rupees, and add or subtract.

a) Rs 5 and 40 p + Rs 9 and 50 p b) Rs 38 and 60 p + Rs 48 and 70 p

c) Rs 80 and 75 p + Rs 65 and 55 p d) Rs 45 and 80 p – Rs 18 and 60 p

e) Rs 96 and 25 p – Rs 47 and 50 p f) Rs 215 and 10 p – Rs 120 and 85 p

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Time and Money

10. Let's read these problems carefully and solve them.

a) The cost of a packet of crayons is Rs 75.40 and the cost of a box is
Rs 90.60.

(i) Find the total cost of these two items.

(ii) If mother gives Rs 200 to the shopkeeper, what changes does the
shopkeeper return her?

b) The rate of cost of apple is Rs 140.75 per kg and the rate of cost of orange
is Rs 80.25 per kg.

(i) By how much is the rate of cost of apple more expensive than the rate
of cost of orange?

(ii) Find the total cost of 1 kg of apples and 2 kg of oranges.

c) The total cost of a mathematics book and a science book is Rs 690.80.
The cost of science book is Rs 320.50.

(i) Find the cost of mathematics book.

(ii) By how much is the cost of science book cheaper than the cost of
mathematics book?

d) The cost of a ticket of a cable car for an adult is Rs 510.50 and for a child
is Rs 225.50. Find the total cost of tickets for father, mother, and a child.

e) The monthly school fee of brother is Rs 1,250.75 and the fee of younger
sister is Rs 975.25.

(i) Find the total of their monthly fee.

(ii) Calculate their total fee in 1 year.

11. It's your time - Project work!

a) How much school fee do you pay in a month? Calculate your total fee in a
year.

b) Let's write the price of your Nepali, English, Mathematics, and Science
textbooks. Then, calculate the total price.

c) At what rate of price do you buy your exercise books? Estimate the number
of exercise books you use in a month and calculate their total price.

?

147Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 4

Unit Algebra

9

9.1 Letters and numbers - Looking back
Classwork - Exercise

1. Let's tell and write the values of letters as quickly as possible.

a) There are 'x' number of students in your class. x =

b) There are 'x' number of students in your school. x =

c) There are 'y' number of teachers in your school. y =

d) There are 'y' number of members in your family. y =

e) There are 'p' number of provinces in Nepal. p =

f) There are 'q' number of districts in Nepal. q=

2. Let's tell and write the time using a. m. or p. m. shown by the clocks.

a) There are 'a' number of pencils. a =

b) There are 'b' number of books. b =

c) There are 'x' number of balls. x =

In this way, we can use any letter to represent any number.

9.2 Constant and variable

Let's have a discussion on the following questions.

a) How many number of things does 1 always represent?
b) How many number of things does 5 always represent?
c) Does 8 sometimes represent 7, 9, or any other number of things?
Therefore, the numbers 1, 2, 3, 4, 5, ... always represent the fixed number of

things. The numbers are called constants.

vedanta Excel in Mathematics - Book 4 148 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur