Vedanta Excel in Mathematics Book 5 Final (2078) NEW

Properties of Whole Numbers

c) Possible factors of 12
Possible factors of 18

In this way, the possible factors of 12 are 1, 2 , 3, 4 , 6, and 12. The possible
factors of 18 are 1, 2, 3, 6, and 18. Here, 2, 3, and 6 are the common factors of
12 and 18.
2. Let's say and write the ϐirst 10 multiples of each pair of numbers. Then
circle the common multiples.

a) 2 o

3o

b) 4 o

6o

c) 8 o

10 o

Thus, the irst ten multiples of 8 are 8, 16, 24, …, 80. The irst ten
multiples of 10 are 10, 20, 30,…, 100. Here, 40 and 80 are the common
multiples of 8 and 10.

3.7 Highest Common Factor (H.C.F)

Classwork - Exercise

1. Let's say and write the answer of these questions.

a) What are the all possible factors of 12 ?

b) What are the all possible factors of 18 ?

c) What are the common factors of 12 and 18 ?
d) Which one is the Highest Common Factor of 12 and 18 ?
Thus, the Highest Common Factor (H.C.F) of 12 and 18 is 6.
2. a) What is the H.C.F. of 2 and 4 ?

b) What is the H.C.F of 3 and 6 ?

c) What is the H.C.F. of 4 and 8 ?

49Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers 6

3.8 Lowest Common Multiple (L.C.M.)

Classwork - Exercise

1. a) Let's say and write the irst 10 multiples of 2 and 3.
2
3

b) What are the common multiples of 2 and 3 ?
c) Which one is the Lowest Common Multiple of 2 and 3 ?
d) Thus, the Lowest Common Multiple (L.C.M.) of 2 and 3 is

2. a) What is the L.C.M. of 2 and 4 ?
b) What is the L.C.M. of 3 and 4 ?
c) What is the L.C.M. of 5 and 10 ?

3.9 Process of finding H.C.F.

Let's study the example and learn the process of inding H.C.F. of the given
numbers.

Example 1: Find the H.C.F. of 18 and 24.

Solution All possible factors of 18 and 24 are:
18 o 1, 2, 3, 6, 9, 18
2 18 2 24 24 o 1, 2, 3, 4, 6, 8, 12, 24

39 2 12 H.C.F. of 18 and 24 = 6
3 2
6 And, 6 is the product of common prime factors
18 = 2 × 3 × 3 3 2 and 3.

24 = 2 × 2 × 2 × 3 So, H.C.F. = product of common prime
? H.C.F. = 2 × 3 = 6 factors

3.10 Process of finding L.C.M.

Now, let's learn the process of inding L.C.M. of the given numbers from the
following example.

Example 2 : Find the L.C.M. of 8 and 10.

vedanta Excel in Mathematics - Book 5 50 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Properties of Whole Numbers

Solution 2 10 A few multiples of 8 and 10 are :
5 8 o 8, 16, 24, 32, 40, …, 80, …
28 10 o 10, 20, 30, 40, …, 80, …
24 L.C.M. of 8 and 10 = 40

2

8 =2×2×2 And, 40 is the product of common prime factor
10 = 2 × 5 2 and the remaining prime factors 2, 2 and 5.

? L.C.M. = 2 × 2 × 2 × 5 = 40
Alternative process (Division method)

2 8, 10 8 and 10 are divided by their common factor 2.

4, 5
? L.C.M. = 2 × 4 × 5 = 40

Example 3: Find the greatest number that divides 12 and 20 without
leaving remainder.

Solution

Here, the required greatest number is the H.C.F. of 12 and 20.

2 12 2 20 Only the common factors 2 and 4 of 12 and
20 can divide them exactly. Between 2 and
26 2 10 4, 4 is the Greatest one. So, 4 is the H.C.F. of
3 5 12 and 20.

12 = 2 × 2 × 3

20 = 2 × 2 × 5

? H.C.F. = 2 × 2 = 4

Hence, the required greatest number is 4.

Example 4 : Find the smallest number which is exactly divisible by 12 and
16.

Solution

Here, the required smallest number is the L.C.M. of 12 and 16.

2 12, 16 Only the common multiples of 12 and 16
2 6, 8 are exactly divisible by 12 and 16. And, the
smallest multiple is the L.C.M. of 12 and 16.
3, 4

L.C.M. = 2 × 2 × 3 × 4 = 48
Hence, the required smallest number is 48.

51Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

EXERCISE 3.3
Section A - Class work

1. Let's say and write the possible factors of each pair of numbers. Circle the
Highest common factor (H.C.F.).

a) 2 o and 4 o

b) 3 o and 6 o

c) 4 o and 8 o

d) 6 o and 8 o

2. Let's say and write the ϐirst 10 multiples of each pair of numbers. Then,
circle the Lowest Common Multiple (L.C.M.).

a) 2 o

4o

b) 2 o

3o

c) 3 o

6o

d) 4 o

8o

3. Let's investigate the fact from the given illustrations. Then, say and write
the H.C.F. of each pair of numbers.

4 is a factor of 8. So, H.C.F. of 4 and 8 is 4.

5 is a factor of 15. So, H.C.F. of 5 and 15 is 5.

a) H.C.F. of 2 and 4 is b) H.C.F. of 2 and 4 is

c) H.C.F. of 4 and 12 is d) H.C.F. of 6 and 24 is

4. Let's investigate the facts from the given illustrations. Then, say and write
the L.C.M. of each pair of numbers.

(i) 4 is a multiple of 2. So L.C.M. of 2 and 4 is 4.

21 is a multiple of 7. So, L.C.M. of 7 and 21 is 21.

vedanta Excel in Mathematics - Book 5 52 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Properties of Whole Numbers

a) L.C.M. of 3 and 6 is b) L.C.M. of 4 and 8 is

c) L.C.M. of 5 and 20 is d) L.C.M. of 6 and 18 is

(ii) 2 and 3 are prime numbers. So, L.C.M. of 2 and 3 = 2 × 3 = 6

a) L.C.M. of 2 and 5 is b) L.C.M. of 3 and 5 is

c) L.C.M. of 2 and 7 is d) L.C.M. of 5 and 7 is

Group B

5. Let's write the possible factors of each pair of numbers. Circle the
common factors and select the H.C.F.

a) 4, 6 b) 6, 9 c) 8, 12 d) 12, 18 e) 15, 20 f) 14, 21

6. Let's write the ϐirst ten multiples of each number of the pairs. Circle the
common multiples and select the L.C.M.

a) 2, 6 b) 4, 6 c) 3, 9 d) 6, 8 e) 5, 10 f) 4, 5

7. Let's ϐind the prime factors of each number of the pairs. Then, ϐind their
H.C.F.

a) 8, 12 b) 6, 12 c) 10, 15 d) 12, 16 e) 10, 20

f) 12, 18 g) 16, 24 h) 18, 27 i) 15, 30 j) 24, 32

8. Let's ϐind the prime factors of each number of the pairs. Then, ϐind their
L.C.M.

a) 4, 6 b) 6, 8 c) 4, 8 d) 6, 9 e) 8, 10

f) 9, 12 g) 10, 15 h) 10, 20 i) 12, 16 j) 18, 24

9. Let's ϐind the L.C.M. of these pairs of numbers by division method.

a) 6, 12 b) 8, 12 c) 4, 10 d) 9, 15 e) 12, 18

f) 14, 21 g) 15, 20 h) 16, 24 i) 18, 27 j) 20, 30

10. a) Find the greatest number that divides 12 and 18 without leaving remainder.

b) Find the greatest number that exactly divide 16 and 24.

c) Find the greatest number that divide 20 and 30 without leaving remainder.
11. a) Find the smallest number which is exactly divisible by 6 and 8.

b) Find the least number that can be divided by 9 and 12 without leaving
remainder.

c) Find the smallest number which is exactly divisible by 10 and 15.

53Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

It's your time - Project Work !

12. Let's play a game of ϐinding H.C.F. of any two numbers.

H. C. F. of 4 and 8 Equal number of
circles in both sides.
4 is less than 8. So,
remove 4 circles from 8.

48 48

So, H. C. F. is 4.

H. C. F. of 6 and 9 3 is less than 6. So, remove Equal number of
3 circles from 6. circles in both sides.
6 is less than 9. So,
remove 6 circles from 9. 69 69

69 So, H. C. F. is 3.

Now, let's ind the H.C.F. of these numbers by playing the games.
a) 2 and 4 b) 3 and 6 c) 6 and 8 d) 6 and 7 e) 10 and 5

13. Let's play a game of inding L.C.M. of any two numbers from 2 to 10. Make
number cards of the irst ten multiples of the numbers 2 to 10. Arrange the
multiple cards of each number separately in order.

Now, Let's play to ind the L.C.M. of 4 and 6.

At irst, pull the multiple card of 4 4 then 6 6

Again, pull the multiple card of 4 8 then 6
4 8 6 12

12

12
Again, pull the multiple card of 4 now stop !

Here, 12 is the L.C.M. of 4 and 6.

Now, Let's play the game with a friend and ind the L.C.M. of the following
pairs of numbers. Remember, you should pull the multiple cards of the smaller
number at irst.

a) 2 and 3 b) 3 and 4 c) 5 and 6 d) 6 and 8 e) 8 and 10
54 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

14. Rolling number cubes (or dice)

You can play this game with a friend. Take turns rolling 22 1122 33 3300
two numbered cubes (or two dice). Find the LCM of 2300 55 1155 66
the two numbers rolled and circle in the square with 3300 1100 44 2200
the answer. The irst person to get 4 circles in a row is 66 11 99 1122
the winner !

3. 11 Square and square root

1 It is a square of 1 by 1 = 1 × 1 = 12 = 1 Square box
1 It is a square of 2 by 2 = 2 × 2 = 22 = 4 Square boxes

2

2

3 It is a square of 3 by 3 = 3 × 3 = 32 = 9 Square boxes

3 I got it !
When a number is multiplied
Similarly, by itself, we get the square
The square of 4 = 4 × 4 = 42 = 16 number of the given number !
The square of 5 = 5 × 5 = 52 = 25
The square of 6 = 6 × 6 = 62 = 36
and so on.

Again, let's study the following illustrations and investigate the idea about
square root of a square number.

1 Square of 1 = 12 = 1 and 1 = 1 is the square root of 1.

1

2 Square of 2 = 22 = 4 and 4 = 2 is the square root of 4.

2

3 Square of 3 = 32 = 9 and 9 = 3 is the square root of 9.

3 55 vedanta Excel in Mathematics - Book 5

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Properties of Whole Numbers

Similarly,
Square of 4 = 42 = 16 and 16 = 4 is the square root of 16

Square of 5 = 52 = 25 and 25 = 5 is the square root of 25, and so on .

In this way, when a number is multiplied by itself, the product is called the
square of the number. And, the number itself is the square root of the square

number. I got it !

We write square root of 4 as 4 = 2. 9 = 3, 36 = 6

The radical sing ( ) is the sign of square root. 49 = 7, 100 = 10

3.12 Process of finding square and square root

Let's learn about the process of inding square and square root of a given
number from the following examples.

Example 1: Find the square of a) 24 b) 50

Solution 52 = 25 Then write two zeros at the
Square of 24 = 242 = 24 × 24 = 576 end of 25.

Square of 50 = 502 = 50 × 50 = 2500

Example 2: a) Find the square root of 324
b) Find the prime factors of 8100.

Solution

a) 2 324 The same prime factors of 324
2 162 are arranged in pairs.

324 = 2 × 2 × 3 × 3 × 3 ×3

3 81 From each pair, one factor is
3 27 taken as square root and they
are multiplied.

39 ? 324 = 2 × 3 × 3 = 18

3

324 = 2 × 2 × 3 ×3 × 3 ×3

324 = 2 × 3 × 3 = 18

b) 3 81 56 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
3 27
39
3

vedanta Excel in Mathematics - Book 5

81 = 3 × 3 × 3 × 3 Properties of Whole Numbers
81 = 3 × 3 = 9
8100 = 90 We understood!
At ϔirst, we should ϔind the square root of none zero
number. So, root 81 = 9. Then, we should write half
number of zero at the end of 9. 8100 = 90 !!

Example 3: If 7 students are kept in each row of 7 rows in a school
assembly, how many students are there in the assembly?

Solution

Here, the required number of students is the
square of 7.

72 = 7 × 7

= 49

Hence, there are 49 students in the assembly.

Example 4 : 36 marbles are arranged in the same number of rows and
columns. Find the number of marbles in each row or in
column.

Solution

Here, the required number of marbles is the
square root by 36.

Now, inding the prime factors of 36.

2 36
2 18
39

3
36 = 2 × 2 × 3 × 3

∴ 36 = 2 × 3 =6

Hence, there are 6 marbles in each row or in column.

57Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

EXERCISE 3.4
Section A - Class work
1. Let's say and write the square of the given numbers.

a) 12 = b) 22 = c) 32 =

d) 42 = e) 52 = f) 62 =

g) 72 = h) 82 = i) 92 = j) 102 =

2. Let's say and write the square of the given numbers.

a) 102 = b) 202 = c) 302 =

d) 402 = e) 502 = f) 602 =

g) 702 = h) 802 = i) 902 =

3. Let's say and write the square roots of the given numbers.

a) 1 = b) 4 = c) 9 =

d) 16 = e) 25 = f) 36 =

g) 49 = h) 64 = i) 81 = j) 100 =

4. Let's investigate from the given example, how the numbers are written in
the box and in circles. Then complete the remaining sums.

a) b) c) d)
9 16 25 36

3×3 4× ×5 ×
e)
f) g) h)
64 100

7× × ×9 ×

5. Let's write the correct number under the sign of square root ( ).

a) = 3 b) = 8 c) = 5 d) =6

vedanta Excel in Mathematics - Book 5 58 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Properties of Whole Numbers

6. Insert the sign of square root ( ) to the appropriate number.

a) 16 = 4 b) 7 = 49 c) 10 = 100 d) 400 = 20

Section B
7. Let's answer the following questions ?

a) What do you mean by the square number of 5 is 25 ?

b) What do you mean by the square root of 81 is 9 ?

c) How do we ind the square number of a given natural number ?

d) What is the least natural square number ?

e) What is the greatest natural square number ?

f) What is a number which is a square and square root itself ?
8. Let's ϐind the square of the following numbers.

a) 11 b) 12 c) 13 d) 14 e) 15 f)16

g) 17 h) 18 i) 19 j) 24 k) 25 l) 36

m) 120 n) 130 o) 140 p) 150 q) 100 r) 200

9. Let's ϐind the prime factors of these square numbers. Then, ϐind their
square roots.

a) 16 b) 25 c) 36 d) 64 e) 81 f) 100

g) 144 h) 196 i) 225 j) 256 k) 324 l) 441

10. a) If 8 students are kept in each row of 8 rows in a school assembly, how many
students are there in the assembly?

b) 9 chairs are arranged in each column of 9 columns in a room. How many
chairs are there in the room ?

c) There are 10 potted lowers in each row of a garden. If there are the same
number of rows and columns, ind the total number of potted lowers in the
garden.

11. a) 64 children are arranged in the same number of rows and columns in the
ground. Find the number of children in each row or in column.

b) Class ive students collected a sum of Rs. 900 to support the 'Poor students
Helping Fund.' If every student donated the equal amount of money as their
number, ind the amount donated by each student.

59Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

c) There are 144 unit square rooms in square graph. Find the number of unit
square rooms along the length or breath of the graph.

It's your time- Project work !

12. a) Look at the pattern of square numbers.
1, 1 + 3 = 4, 4 + 5 = 9, 9 + 7 = 16, 16 + 9 = 25,

What types of numbers are 3, 5, 7, 9, ?

Let's follow the pattern and ind the square numbers upto 100.

b) Let's write the square of the numbers from 1 to 10. Investigate the fact

whether the digit at ones place of any of these square number can be 2, 3, 7,

and 8.

c) Let's investigate the interesting facts about square numbers. Then,

complete the pyramid in a chart paper.

12 1 = 1
22 1 + 2 + 1 = 4
32 1 + 2 + 3 + 2 + 1 = 9
42 =
52 =
62 =
72 =

d) Let's observe the patterns of some square numbers. Then, draw circles
(or dots) in a chart paper to show the similar patterns of the following
numbers.

22 = = 4 52 = = 25

(i) 32 (ii) 42 (iii) 62 (iv) 72 (v) 82 (vi) 92 (vii) 102

3.13 Cube and cube root

Let's study the following illustrations and learn about the cube of a given
number.

1 The cube of 1 =13 = 1 × 1 × 1 = 1
11

vedanta Excel in Mathematics - Book 5 60 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Properties of Whole Numbers

The cube of 2 = 23 = 2 × 2 × 2 = 8 A cube number
always represents
2 a cube shape!
22

The cube of 3 = 33 I got it!
When I multiply a number
3 =3×3×3 three times by itself, I get
= 27 a cube number.

3
3

Similarly,
The cube of 4 = 43 = 4 × 4 × 4 = 64
The cube of 5 = 53 = 5 × 5 × 5 = 125 and so on.

Thus, the cube of a number is the product obtained by multiplying the number
three times by itself.

Now, let's learn about cube root of a cube number.

Cube of 1 = 13 = 1 So, 1 is the cube root of 1.
Cube of 2 = 23 = 8 So, 2 is the cube root of 8.
Cube of 3 = 33 = 27 So, 3 is the cube root of 27 and so on.

In this way, we obtain a cube number by multiplying the same three numbers,
and each identical number is the cube root of the cube number.

3.14 Process of finding cube and cube root

Let's learn about the process of inding cube and cube root of a given number
from the following examples.

Example 1: Find the cube of a) 12 b) 30 It's easy !
Solution In 303, cube of 3 is 27. Then
a) Cube of 12 = 123 = 12 × 12 × 12 = 1728 I should write three zeros
b) Cube of 30 = 303 = 30 × 30 × 30 at the end of 27 !!

= 900 × 30 = 27000 a) 216 b) 64000
Example 2: Find the cube root of

Solution

a) Finding the prime factors of 216,

61Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

2 216 The same three prime factors of 216
2 108 are grouped.
2 54
3 27 216 = 2 × 2 × 2 × 3 × 3 × 3
39
From each group , one factor is taken
3 as cube root and they are multiplied.

So, cube root of 216 = 2 × 3 = 6

216 = 2 × 2 × 2 × 3 × 3 × 3

? Cube root of 216 = 2 × 3 = 6

b) Finding the prime factors of 64,

2 64 I got it !
2 32 At ϔirst, I should ϔind the cube root
2 16 of none zero number. So, cube
28 root of 64 is 4. Then I should write
24 one-third number of zero at the end
of 4. So, cube root of 64000 = 40 !!
2

64 = 2 × 2 × 2 × 2 × 2 × 2

Cube root of 64 = 2 × 2 = 4

? Cube root of 64000 = 40

Example 3: The length, breath, and height of a small wooden cubical block
is 3 cm each. Find its volume in cubic centimetres (cm3).

Solution

Length = breath = height of the cubical block = 3 cm 3 cm 3 cm
Volume of the block = (3 cm)3 3 cm

= 3 cm × 3 cm × 3 cm
= 27 cubic centimetres (cm3)

Hence, the volume of the wooden cubical block is 27 cm3.

Example 4 : If the volume of a cubical die is 125 cm3, ϔind the length of the
die.

Solution

The length (or breath or height) of the cubical die is the cube root of 125 cm3.

vedanta Excel in Mathematics - Book 5 62 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Properties of Whole Numbers

Finding the prime factors of 125, V=125cm3 l
l l
5 125
5 25

5

125 = 5 × 5 × 5
? Cube root of 125 = 5
Hence, the length of the cubical die is 5 cm.

EXERCISE 3.5
Section A - Class work

1. Let's say and write the square numbers and cube numbers separately.

1 36 25 27 8 Square numbers Cube numbers

16 64 49 9 125

2. Let's say and write the cube of each of these numbers.

a) 13 = b) 23 = c) 33 = d) 43 =

e) 53 = f) 103 = g) 203 = h) 303 =

3. Let's say and write the cube root of each of these cube numbers.

a) cube root of 1 = cube root of 1000 =

b) cube root of 8 = cube root of 8000 =

c) cube root of 27 = cube root of 27000 =

d) cube root of 64 = cube root of 64000 =

4. Each of the following blocks is made up of unit cubical block. Write the
cube number represented by each block.

a) b) c) d)

63Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Properties of Whole Numbers

Section B
5. Let's answer the following questions.

a) What do you mean by the cube of 3 is 27 ?
b) What do you mean by the cube root of 8 is 2 ?
c) How do we find the cube of a given natural number ?
d) What is the least natural cube number ?
e) What is the greatest natural cube number ?
f) What is a number which is a square, square root, cube and cube root itself ?
6. Let's find the cube of each of the following numbers.

a) 5 b) 6 c) 7 d) 8 e) 9 f) 11

g) 12 h) 15 i) 30 j) 40 k) 60 l) 100

7. Let's find the prime factors of these cube numbers. Then, find their cube
roots.

a) 8 b) 27 c) 64 d) 125
e) 216 f) 343 g) 512 h) 729
i) 2744 j) 8000 k) 27000 l) 125000

8. Let's simplify.

a) 2 + 22 + 23 b) 33 – 32 – 3 c) 32 + 22 – 23
d) 42 – 22 + 32 e) 43 – 23 – 33 f) 52 + 23 – 42

g) 33 – 52 + 22 h) 53 – 52 – 102 i) 92 – 43 – 23

9. a) The length, breath and height of a small wooden cubical block is 2 cm each.
Find its volume in cubic centimetres (cm3).

b) A small metallic cubical block is 4 cm long. Find its volume in cubic
centimetres (cm3).

c) A solid block is in the shape of a cube. If it is 10 cm high, find its volume in
cubic centimetres (cm3).

d) The length, breath, and height of the given cube is 4 cm
each. How many cubes of 1 cm length can be made from
this cube ?

10. a) If the volume of a cubical die is 64 cm3, find the length of the die.
b) The volume of a solid wooden block is 216 cm3. Find the height of the block.
c) If the product of three identical numbers is 125, find the number.

vedanta Excel in Mathematics - Book 5 64 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Unit Fraction

4

4.1 Equivalent Fractions - Looking back

Classwork - Exercise

Let's fold a rectangular sheet of paper into halves and shade one-half part.
Again fold it into halves two times.

First folding Second folding Third folding

1. Now, let's say and write the answer of the following questions.

a) What is the fraction of the shaded part in the irst folding ?

b) What is the fraction of the shaded part in the second folding ?

c) What is the fraction of the shaded part in the third folding ?

d) Are the shaded parts of the three folding equal ?

Here, 12, 42, and 4 are the equivalent fractions.
8

However, the numerators and denominators of these equivalent fractions are

not equal, the shaded parts of these fractions cover the same region. Therefore,

they are called the equivalent fractions.

2. Let's say and write the fractions of the shaded parts. Are they 'equivalent'
or 'none equivalent' fractions ?

a) b)

and are and are
65Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
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Fraction

4.2 Process of finding equivalent fractions

Classwork - Exercise

3. Let's multiply the numerator and denominator of the fraction by the same
natural number to get equivalent fractions.

a) 1
2

1 = 1 × = 2
2 2 × 4

1 = 1 × = 3
2 2 × 6

b) 1 = 1 × = 2 , 1× = 3 , 1 = 1 × = 4
3 3 × 6 3× 9 3 3 × 12

So, 1 , 2 , 3 , 142, … are equivalent fractions.
3 6 9

Let's divide the numerator and denominator of the fraction by the same natural
number to get equivalent fractions.

c) 6 = 6 ÷ = 3 , 9 = 9÷ = 3 , 12 = 12 ÷ = 3
8 8 ÷ 4 12 12 ÷ 4 16 16 ÷ 4

So, 86, 192, 1162, … are the fractions equivalent to 43.

In this way, when we multiply or divide the numerator and denominator of a
fraction by the same natural number, we get its equivalent fractions.

4.3 Reducing fractions to their lowest terms

Let's study the following examples and learn the process of reducing a fraction

to its lowest terms.

Example 1: Reduce the fractions a) 8 b) 15 to their lowest terms.
12 20
Solution
In 8 , the H. C. F. of 8 and 12 is 4.
8 12
a) 12 = 82 = 2 8÷4
123 3 So, 12 ÷ 4 = 2
3

b) 15 = 153 = 3 In 15 , the H. C. F. of 15 and 20 is 5.
20 204 4 20
15 ÷ 5
So, 20 ÷ 5 = 3
4

vedanta Excel in Mathematics - Book 5 66 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

Example 2: Reduce the fractions a) 60 b) 1400 to their lowest terms.
90 2100

Solution In 6 , the H.C.F. of 6
9
and 9 is 3.
a) 60 = 60 = 62 = 2
90 90 93 3 So, 6 ÷ 3 = 2
9 ÷ 3 3

b) 2100 = 2100 = 213 = 3 In 2218, the H.C.F. of
2800 2800 28 4 4 21 and 28 is 7.

So, 21 ÷ 7 = 3
28 ÷ 7 4

EXERCISE 4.1
Section A - Class work

1. Let's shade the parts of each pair of diagrams to show the equivalent
fractions.

3 2
a) 4 b) 6

6 4
8 12

2. Let's write the fractions of the shaded parts. Then, list the equivalent
fractions separately.

a) , and are equivalent fractions.

b) , and are equivalent fractions.

3. Let's test whether each pair of fractions are equivalent or not.

Multiply the numerator of one fraction by the denominator of
another fraction in each pair of fractions. If the product are equal the fractions
are equivalent.

1 3 1 × 6 = 2 × 3. So, 1 and 3 are equivalent fractions.
2 6 26
6=6

67Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

a) 1 and 4 are fractions.
2 8 fractions.

b) 1 and 4 are
3 9

c) 2 and 4 are fractions.
5 10

4. Let's say and write the lowest terms of these fractions.

a) 3 = b) 3 = c) 2 = d) 4 =
6 9 8 12

e) 10 = f) 20 = g) 300 = h) 300 =
30 50 700 4000

Section B

5. Let's answer these questions.

a) What is a fraction?

b) What does the numerator of a fraction show ?

c) What does the denominator of a fraction show ?

d) A bread is divided into 5 equal slices and you ate 2 slices. How do you express
it in a fraction ?

e) why are 1 and 2 called equivalent fractions ?
2 4

6. Let's multiply the numerator and denominator of each fraction by 2, 3,
and 4 respectively. Then, ϐind their three equivalent fractions.

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

f) 3 g) 4 h) 2 i) 3 j) 5
5 5 7 7 6

7. Let's divide the numerator and denominator of each fraction by the same
natural number. Then, ϐind a fraction equivalent to the given fraction.

a) 2 b) 4 c) 3 d) 4 e) 6
4 8 9 6 8

f) 8 g) 6 h) 8 i) 10 j) 12
10 10 12 15 18

vedanta Excel in Mathematics - Book 5 68 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

8. Let's reduce these fractions to their lowest terms.

a) 4 b) 6 c) 2 d) 6 e) 4
6 8 8 9 10

f) 8 g) 9 h) 12 i) 14 j) 16
12 12 15 21 24

9. Let's cancel the equal number of zeros from numerator and denominator
of each fraction. Then, reduce them to the lowest terms.

a) 20 b) 30 c) 20 d) 40 e) 80
30 40 60 60 100

f) 90 g) 60 h) 100 i) 500 j) 600
120 80 120 1000 900

It's your time - Project work !

10. a) Let's write any three pairs of equivalent fractions.

Draw three pairs of rectangles of the same size. Divide each pair of rectangles
into as many equal parts as your fractions. Then, shade the parts to show
your each pair of equivalent fractions.

b) Let's take three rectangular sheets of paper. Fold each of them to show an

equivalent fraction of each of 1 , 13, and 14.
2

4.4 Like and unlike fractions

A Rectangles A and B are divided into the same (like) number
B
of equal parts. So, the fractions of the shaded parts 1 and 2 are
like fractions. 3 3

Like fractions always have the same denominators. 1 , 2 , 3 are also the like
fractions. 4 4 4

Rectangles P and Q are divided into the different (unlike) P
Q
number of parts. So, the fractions of the shaded parts 1 and
4
1
5 are unlike fractions.

Unlike fractions have different denominators. 1 , 31, 25, 2 are also the unlike
fractions. 2 7

69Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

4.5 Conversion of unlike fractions into like fractions

1 and 1 are unlike fractions. In the 1 3
2 3 2 6
o
1 3 1 2
diagram 2 is converted into 6 and 3 6

is converted into 2 . Now, 3 and 2 are 1 o
6 6 6 3
26,
like fractions. Here, in 3 and 6 is the
6

lowest common denominator of the like fractions. 6 is also the L.C.M. of the

denominators 2 and 3 of the unlike fractions 1 and 13.
2
3 2
Example 1 : Convert 4 and 5 into like fractions.

Solution

L.C.M. of the denominators 4 and 5 = 4 × 5 = 20

Now, 3 = 3 × 5 = 15 and 2 = 2 × 4 = 8
4 4 × 5 20 5 5 × 4 20

So, 15 and 8 are like fractions.
20 20

4.6 Proper and improper fractions

A circle is divided into 2 equal parts and 1 part is shaded. The fraction
of the shaded part is 12.

A circle is divided into 2 equal parts and 2 parts are shaded. The

fraction of the shaded part is 2 = 1 (whole circle)
2

A circle is divided into 2 equal parts and 3 parts are shaded. Is it possible ?

It is possible when 2 parts of one circle and 1 part of

another circle are taken. Now, the fraction of the shaded

parts is 23. So, the fraction 3 has one whole and one-half. one whole and one-half
2

Here, 1 is only a fraction and it is called a proper fraction.
2

But, 3 has a whole and a fraction. It is called an improper fraction.
2

Similarly, 1 , 35, 4 , … are proper fractions and 34, 52, 47, … are improper fractions.
4 7

In a proper fraction, numerator is always less than denominator.
In an improper fraction, numerator is always greater than denominator.

vedanta Excel in Mathematics - Book 5 70 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

4.7 Mixed number
Let's study the following illustrations and learn about the mixed numbers.

5 o o 2 + 1 = 212 is a mixed number.
2 2

8 o o 2 + 2 = 232 is a mixed number.
3 3

Thus, a fraction made up of a whole number and a proper fraction is called a
mixed number ( or mixed fraction). We read 221 as 'one whole and half'.

In 5 or 5 ÷ 2 , the quotient is 2 and remainder is 1. So, 5 = 221
2 2

In 8 or 8 ÷ 3, the quotient is 2 and remainder is 2. So 8 = 232
3 3
Thus, improper fraction = quotientdreenmomaiinndaetorr

Again,

112 o o 1 time 2 parts o 1 × 2 + 1 = 2 + 1 = 3
and 1 more part 2 2 2

232 o o 2 times 3 parts o 2 × 3 + 2 = 6 + 2 = 8
and 2 more parts 3 3 3

Thus, mixed number = whole number × denominator + numerator
denominator

EXERCISE 4.2
Section A - Class work

1. Let's say and write the fractions of the shaded parts in each pair of
diagrams are 'like' or 'unlike' fractions.

a) and are fractions.

b) and are fractions.

c) and are fractions.
71Approved by Curriculum Development Centre, Sanothimi, Bhaktapur
vedanta Excel in Mathematics - Book 5

Fraction

2. Let's list the like and unlike fractions separately.

a) 3 , 3 , 5 , 2 Like fractions Unlike fractions
8 4 8 5 a)

b) 2 , 2 , 1 , 6 b)
7367

3. Let's compare the numerators. Then, compare each pair of like fractions

using the symbol '<' or '>'.

a) 3 2 b) 4 5 c) 7 5 d) 7 9
5 6 6 8 8 10 10
5

4. Let's say and write the fractions of the shaded parts are 'proper' or
'improper' fractions.

a) b)

is fractions. is fractions.

c) d)

is fractions. is fractions.

5. Let's say and write the improper fractions and the mixed numbers
represented by these shaded diagrams.

a) b) c)

5 = 114 = =
4

Section B

6. Let's answer the following questions.

a) Why are 2 and 3 like fractions ?
5 5

b) Why are 1 and 1 unlike fractions ?
4 6

c) Why is 2 a proper fraction ?
3

vedanta Excel in Mathematics - Book 5 72 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

d) Why is 3 an improper fraction ?
2

e) Can we convert a proper fraction into a mixed number ?

f) Why is 113 called a mixed number ?
g) How can we get ive- quarters pieces of apples from 2 apples ?

h) Mother divided 3 pizzas into 6 equal pieces and she gave you 5 pieces.
Express it in an improper fraction and a mixed number.

7. Let's arrange these fractions in ascending and descending orders.

a) 4 , 2 , 3 , 1 b) 3 , 7 , 5 , 2 c) 7 , 3 , 9 , 6
8 8 8 8 10 10 10 10
5555

8. Let's convert these unlike fractions to the like fractions.

a) 1 and 1 b) 1 and 1 c) 3 and 3 d) 1 and 2
2 4 3 6 4 8 2 3

e) 1 and 3 f) 2 and 1 g) 1 and 1 h) 1 and 2
2 5 3 4
46 69
9. Let's convert these fractions to the like fractions. Then compare each pair

of fractions using '<' or '>' symbol.

a) 1 and 2 b) 1 and 2 c) 3 and 5 d) 3 and 7
2 3 2 5 4 8 5 10

10. Let's convert these improper fractions to mixed numbers.

a) 5 b) 7 c) 5 d) 8 e) 9 f) 19
3 3 2 5 4 6

11. Let's convert these mixed numbers to improper fractions.

a) 131 b) 214 c) 321 d) 2 2 e) 343 f) 275
5

It's your time - Project work !

12. a) Let's draw each pair of these shaded rectangles in sheets of paper. Then
draw dotted line to convert unlike fractions into the like fractions. The irst
one is done for you.

(i) (ii)

1 = 4 1 = 3 1 = 1 =
3 12 4 12 2 3

73Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction (iv)

(iii)

1 = 1 = 1 = 1 =
2 4 2 5

b) Let's write three improper fractions of your own. Show them by shading the
parts in rectangles. Then, express each fraction in the mixed numbers.

c) Let's draw rectangular or circular diagrams to show any three mixed
numbers that you have written yourself.

4.8 Addition and subtraction of like fractions - Looking back.

Classwork - Exercise

1. Let's ϐind the total of the fractions of the green and pink shaded parts.

a) b)

+ = 1 + 2 = += =
5
total of numerators
In this way, the sum of like fractions = the same denominator

2. Let's subtract the fraction of the crossed parts from the fraction of the

shaded parts.

a) ××× ××× b) ×× ×× ××
×× ×× ××
××× ××× ×× ×× ××
××× ××× ×× ×× ××
××× ×××

– = 4–2 = –= =
6
difference of numerators
Thus, the difference of like fractions = the same denominator

Example 1 : Add or subtract . a) 115 + 225 b) 234 – 114
Solution 115 +
Another process 252
a) 151 + 225 + 353
115 + 252
6 12 1 2
= 5 + 5 = (1 + 2) + 5 + 5

= 6 + 12 =3+ 1+2
5 5
= 353
= 18 = 335
5

vedanta Excel in Mathematics - Book 5 74 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

b) 243 – 11 Another Process Fraction
4
234 – 114 243 – 141 = 124 = 112
= 11 – 5
4 4 ××××××
3 1
= 11 – 5 = (2 – 1) + 4 – 4
4
=1+ 3–1
= 6 4
4
= 142 = 1 1
= 124 = 112 2

EXERCISE 4.3
Section A - Class work

1. Let's say and write the answer of these questions.

a) Mother cut a pizza into 8 equal pieces. She gave 2 pieces to brother and 3
pieces to sister.

(i) What fraction of pizza did brother get ?

(ii) What fraction of pizza did sister get ?

(iii) What fraction of pizza did they get altogether ?

(iv) What fraction of pizza was left with mother ?

b) Father cut a bread into 10 equal slices and he gave you 7 slices.

(i) What fraction of bread did you get ?

(ii) If you gave 3 slices to your friend, what
fraction of bread did your friend get ?

(iii) What fraction of the bread was left with you ?

c) What is the numerator of the sum of 2 + 3 ?
7 7

d) What is the denominator of the difference of 7 – 5 ?
9 9

2. Let's ϐind the total of the fractions of different coloured parts.

a) b)

+= = ++ = =

75Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

3. Let's subtract the faction of the crossed parts from the fraction of the
shaded parts.

a) b)

–= = –= =

4. Let's say and write the sums or difference of these fractions quickly.

a) 1 + 1 = b) 1 + 2 = c) 3 + 1 = d) 2 + 3 =
4 4 6 6
33 55

e) 2 _ 1 = f) 4 _ 2 = g) 7 _ 4 = h) 8 _ 1 =
7 7 8 8 10 10
33

5. Let's add or subtract any two like fractions to get the given sums or

differences.

a) + = 4 b) + = 5 c) + = 7
5 7 9

d) – =1 e) – = 2 f) – = 3
6 10
Section B 3

6. Let's write the mixed numbers for the shaded parts, then add.

a) + b) +

7. Let's write the mixed numbers then subtract.

a) b)

8. Let's add or subtract these fractions. Write the answer in the mixed
number or in the lowest terms wherever necessary.

a) 2 + 1 b) 3 + 2 c) 141 + 141 d) 292 + 294
8 8
55

e) 5 – 3 f) 7 – 4 g) 2 5 – 161 h) 453 – 252
7 7 10 10 6

9. Let's simplify. Write the answer in the mixed number or in the lowest
terms wherever necessary.

a) 3 + 1 – 2 b) 4 – 1 + 2 c) 5 + 1 – 3
5 5 5 7 7 7 8 8 8

vedanta Excel in Mathematics - Book 5 76 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

d) 365 – 161 – 161 e) 494 – 191 – 292 f) 3130 – 2110 + 1170

10. a) Dakshata cut her birthday cake into 9 equal pieces. She gave 3 pieces to her
brother and 2 pieces to her mother. What fraction of the cake did she give
them altogether ?

b) A teacher asked you to fold a rectangular sheet of paper into 8 equal folding.
Then, she asked you to colour 2 parts with red and 3 parts with green.
What fraction of the sheet of paper did you colour ?

c) A painter mixed 2 litre of blue paint and 3 litre of yellow paint to get a
7 7
green paint. Find the amount of green paint.

11. a) Sunayana cuts a pizza into 6 equal pieces and she gives 2 pieces to Sayad.
What fraction of the pizza is left with her ?

b) Bishwant cut a bread into 10 equal slices and he gave 6 slices to Pratik. If
Pratik ate 2 slices and he gave remaining slices to Debashis, what fraction
of the bread did Debashis get ?

c) A pole is 425 m high is standing on the ground. The length of the pole under
the ground is 4 m. Find the length of the pole above the ground.
5

It's your time - Project work !

12. a) Let's take three rectangular sheets of paper. Fold them separately into
quarters, sixths, and eights. Then, colour the parts to represents the
following sums.

(i) 1 + 2 (ii) 2 + 3 (iii) 3 + 4
4 4 6 6 8 8

b) Let's write three pairs of proper like fractions. Then, ind their sums and
differences.

4.9 Addition and subtraction of unlike fractions

We can add or subtract unlike fractions by converting them to the like fractions.
Let's learn the processes from the following examples.

Example 1 : Add or subtract a) 2 + 1 b) 221 - 131
3 4

Solution

a)L.C.M. of 3 and 4 = 3 × 4 = 12

77Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

So, 2 = 2×4 = 8 +
3 3×4 12
21
And, 1 = 1×3 = 3 34
4 4×3 12
+
Now, 8 + 3 = 8+3
12 12 12 83
12 12
11
= 12

Now, we can do this process directly in the following ways .

2 + 1 = 4 × 2+3 × 1
3 4 12
L. C. M. of 3 and 4 = 3 × 4 = 12
= 8+3 12 ÷ 3 = 4 and 4 × 2 = 8
12 12 ÷ 4 = 3 and 3 × 1 = 3

= 11 So, 2 + 1 = 4 × 2+3 × 1 = 8+3 = 11
12 3 4 12 12 12

b) 221 – 131 = 5 – 4
2 3

L.C.M. of 2 and 3 = 2 × 3 = 6

So, 5 = 5×3 = 15 2 1 = 5
2 2×3 6 2 2

And, 4 = 4×2 = 8 3 15
3 3×2 6 6 6
2 =
8
Now, 15 – 6 = 15 - 8
6 6

= 7 = 161 2 3 – 1 2 = 1 1
6 6 6 6

Direct process Another process

221 – 113 221 – 1 1
3
5 4 = (2 – 1) + (12 – 31)
= 2 – 3

= 3×5–2×4 = 1 + (3 – 2)
6 6

= 15 – 8 = 7 = 161 = 1+ 1 = 1 1
6 6 6 6

vedanta Excel in Mathematics - Book 5 78 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

EXERCISE 4.4
Section A - Classwork

1. Let's write fractions of the shaded parts. Then add the unlike fractions.

a) b) + = +
+ =+

1 + 1 = 2 + 1 = 3 +=+=
3 6 6 6 6 d) + = +

c) + = +

+=+= +=+=

2. Let's shade the parts and add the mixed numbers.

a) b)
+ +

112 + 131 = 112 + 114 =

c) + d) +

113 + 161 = 113 + 114 =

3. Let's convert unlike fractions to like fractions. Then add or subtract.

a) 1 + 1 = 1× + 1× = + = =
2 3 2×3 3×2 = + = =
= – = =
b) 1 + 1 = 1 × 2 + 1 = – = =
5 10 5 × 10

c) 1 – 1 = 1× 4 – 1 × 3
3 4 3× 4 ×

d) 1 – 1 = 1× 3 – 1 × 2
4 6 4× 6 ×

4. Let's investigate the quick process. Then tell and write the sums or
differences quickly.

1 + 1 = 3 m 2+1 1 – 3 = 2 m 5–3
2 2 2 5 5 2

Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 79 vedanta Excel in Mathematics - Book 5

Fraction

a) 1 + 1 = b) 1 + 1 = c) 1 + 2 =
3 = 4 3
=
d) 1 + 3 = e) 1 + 2 = f) 1 + 5 =
4 5 6

g) 1 – 2 h) 1 – 3 = i) 1 – 3 =
3 4 5

j) 1 – 5 k) 1 – 4 = l) 1 – 7 =
8 9 10
Section B

5. Let's add these fractions and write the answer in the mixed number or in

the lowest terms wherever necessary. 1
3 3 1 3
a) 1 + 1 b) 1 + 4 c) + 4 d) 2 + 4
24 2 3

e) 1 + 2 f) 2 + 3 g) 3 + 1 h) 5 + 3
2 5 3 5 4 6 6 8

i) 131 + 1 j) 21 + 181 k) 243 + 232 l) 265 + 294
6 4
6. Let's subtract these fractions and write the answer in the mixed number

or in the lowest terms wherever necessary. 1
1 4
a) 1 – 1 b) 2 – 1 c) 3 – 2 d) 1 –
2 3 3 4 5 2

e) 3 – 1 f) 5 – 2 g) 5 – 3 h) 3 – 1
4 2 6 3 6 4 8 6

i) 121 – 5 j) 232 – 192 k) 331 – 252 l) 21 – 251
6 4

7. Let's simplify and write the answer in the mixed number or in the lowest
terms wherever necessary .

a) 1 + 1 + 1 b) 1 + 1 – 1 c) 3 – 2 + 1
2 3 4 2 3 4 4 3 6

d) 121 + 131 – 141 e) 21 – 141 – 1110 f) 22 – 152 – 1110
2 3

g) 1 + 171 – 1134 h) 4 – 243 + 183 i) 361 – 281 – 1

8. a) Sayam drank 2 of a cup of milk at breakfast, and 3 of a cup of milk at dinner.
3 4
In total, how many cups of milk did Sayam drink today ?

b) Mrs. Pandey has a loriculture farming. She has cultivated 3 of the farm with
3 5

rose lowers and 10 of the farm with marigold lowers. Find the total fraction

of the farm covered by these two types of lowers.

vedanta Excel in Mathematics - Book 5 80 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

c) A room is 721 m long and 543 m broad. Find its perimeter.
9. a) The capacity of Diyoshana's water bottle is
4 litre of water and the capacity
5
2
of Aarshiya's water bottle is 3 litre of water. By how much does Diyoshana's

water bottle have more capacity than Aarshiya's?

b) You have a block of cheese. If you eat 7 of cheese in 7 days, how much
8

cheese is left with you ?

c) 2 of the number of students in a class are boys. What fraction of the number
5

are girls ?

It's your time - Project work !

10. a) Let's take a few rectangular sheets of paper. Fold them separately into

halves, thirds, quarters and sixths. Then colour 1 , 1 , 41, and 61. Draw dotted
2 3

lines in each sheet of paper to show the following sums.

(i) 1 + 1 (ii) 1 + 1 (iii) 1 + 1 (iv) 1 + 1
2 3 2 4 4 6 2 6

b) Let's write three pairs of proper unlike fractions. Then, ind their sums and
differences.

c) Let's draw rectangles in chart papers. Divide each rectangle into equal

parts and colour the parts to show each of the following mixed numbers.

Then draw dotted lines and ind the sums.

(i) 121 + 131 (ii) 121 + 1 1 (iii) 113 + 161
4

4. 10 Multiplication of fractions by whole numbers
Let's study the following illustrations. Then, investigate the rule of

multiplication of fractions by whole numbers.

3 × 1 o + + o =3
2 2

2 × 1 o + o = 2
4 4

Thus, whole number × fraction = whole number × numerator
denominator

81Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

4.11 Multiplication of fractions by fractions

Half of a half circle o o = 1 × 1 = 1× 1 = 1
2 2 2× 2 4

Two-thirds of a quarter rectangle o o = 2 × 1 = 2× 1 = 2
3 4 3× 4 12

Thus, fraction × fraction = numerator × numerator
denominator × denominator

Example 1 : Multiply a) 12 × 2 b) 3 × 14
Solution 9 7 15

a) 12 × 2 = 4 ×92 3 Numerator 12 and denominator 9 are
9 divided by 3 12 ÷ 3 = 4 and 9 ÷ 3 = 3
12

= 4 × 2 = 8 = 223 Numerator 3 and denominator 15 are
3 3 divided by 3 3 ÷ 3 = 1 and 15 ÷ 3 = 5

b) 3 × 14 = 31 × 14 2 Numerator 14 and denominator 7 are
7 15 71 15 5 divided by 7 14 ÷ 7 = 2 and 7 ÷ 7 = 1

= 1 × 2
1 × 5

= 2
5

4.12 Finding the value of fraction of number in a collection.
Let's investigate the rule of inding the value of fraction of a number in a

collection of objects.

Half of 6 pencils Two-third of 6 pencils
1
= 1 of 6 = 21 × 63 = 2 of 6 = 2 × 62
2 3 31

= 3 pencils = 2 × 2 = 4 pencils

Thus, the value of the given fraction of a number = fraction × number

EXERCISE 4.5
Section A - Class work

1. Let's complete multiplication from the given shaded diagrams.

a) + + + = =24 × 1 = 2
21

vedanta Excel in Mathematics - Book 5 82 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

b) + + + + = Fraction

=×=

c) =×=
+++=

d) =×=
++++=

2. Let's shade the parts of each diagram. Then, complete the multiplication.

a) + + = = 3 × 1 =
2

b) + + + = = 4 × 1 =
3

c) + + = = 3 × 1 =
4

3. Let's complete multiplication from the given shaded diagrams.

a) 1 of 1 = 1 × 1 =
= 2 2 2 2

b) of = × =
=

c) of = × =
=

4. Let's say and write the product as quickly as possible.

a) 2× 1 = b) 2 × 1 = c) 2 × 1 = d) 3 × 1 =
2 4 6 3

e) 3 × 1 = f) 1 × 1 = g) 1 × 1 = h) 1 × 1 =
6 2 2 2 3 3 4

5. Let's draw dotted lines to divide the circles into the given fractions of the
number of circles. Then, ϐind the values of the fractions.

83Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

a) 1 of 6 circles = circles b) 1 of 8 circles= circles
3 4

c) 1 of 12 circles = circles d) 1 of 15 circles= circles
2 5

6. Let's say and write the values as quickly as possible.

a) 1 of 20 students = students b) 1 of 15 eggs = eggs
2 boys 3 kg

c) 1 of 12 boys = d) 1 of 30 kg =
4 5

e) 1 of 35 l =l f) 1 of 90 km = km
7 10

Section B

Let's multiply and ϐind the products in the lowest terms or in mixed
numbers wherever necessary.

7. a) 2 × 1 b) 3 × 1 c) 4 × 1 d) 5 × 1 e) 10 × 1
2 3 4 5 10

f) 3 × 2 g) 4 × 3 h) 1 × 8 i) 2 × 15 j) 5 × 21
3 4 2 5 7

8. a) 1 × 1 b) 1 × 2 c) 2 × 3 d) 2 × 9 e) 3 × 8
2 3 2 3 3 4 3 10 4 9

f) 3 × 10 g) 9 × 132 h) 17 × 252 i) 15 × 175 j) 33 × 2112
5 21 16 8 9 5

9. Let's ϐind the values:
1 2 1
a) 1 of Rs 24 b) 3 of 18 kg c) 3 of 30 km d) 4 of 28 l
2

e) 3 of Rs 36 f) 2 of 50 girls g) 3 of 75 boys h) 3 of 200 students
4 5 5 10

10. a) Mrs. Tharu saves 3 of her income in a month. What fraction of her income
4

does she save in 6 months ?

b) Bamboo is one of the fastest-growing plants in the world. It can grow 9 m
10
in a day. How many metres can it grow in 15 days ?

12
c) Teacher asked you to colour 2 of 3 parts of a rectangle. What fraction of the

rectangle did you colour ?

vedanta Excel in Mathematics - Book 5 84 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

d) If the cost of 1 kg of potatoes is Rs 2021 , ind the cost of 221 kg of potatoes.
e) What is the fraction of a half part of the half of a whole apple ?

f) what is the fraction of two-third part of the half of a whole bread ?

11. a) There are 30 students in a class and 2 of them are girls.
3

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

b) There are 35 teachers in a school and 3 of them are male teachers.
5

(i) Find the number of male teachers (ii) Find the number of female teachers.

c) The capacity of a water bottle is 750 ml and you drank 2 parts of water when
it was full of water. 5

(i) How much water did you drink ?
(ii) How much water was left in the bottle ?

d) The capacity of a water tank is 1000 litres. If 3 parts of water is used up,
10

how many litres of water is left in the tank ?

e) The road distance between two villages is 56 km. If 4 parts of the road is
7

blacktopped and the rest is gravelled, how many kilometres of the road is

gravelled ?

It's your time - Project work !

12. Let's collect 50 marbles or maize grains (or gram, pea, etc.). Arrange equal

number of grains in rows or in columns to ind 1 , 1 , 3 , 2 , … of different
numbers of grains. 2 3 4 5

or or 1 of 12 = 1 × 12 = 6
2 2

a) Let's draw rectangles of the same size. Divide each rectangle into halves and
colour the parts to show the following fractions.

2 - halves = 1 rectangle, 3 - halves = 1 and a half rectangles, etc.

4 - halves = 2 rectangles, 5 - halves = 2 and a half rectangles, etc.

85Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Fraction

Let's repeat the similar activities with other rectangles dividing and

colouring them into thirds and quarters separately. 11
(v) 3 of 4
b) Let's show (i) 1 of 1 (ii) 1 of 1 (iii) 1 of 1 (iv) 1 of 1
2 2 2 3 2 4 3 3

by folding and colouring rectangular sheets of paper separately.

4.13 Division of a whole number by a fraction

Classwork - Exercise

1. Let's discuss about these questions and answer them.

a) How many halves are there in 1 rectangle ?

There are halves.

b) How many halves are there in 2 rectangles ?

There are halves.

c) how many thirds are there in 3 rectangles ?

There are thirds.

d) How many quarters are there in 3 rectangles ?

Thus, number of halves in 1 rectangle = 1 ÷ 1 = 1 × 2 = 2 halves
2 1 = 4 halves
= 9 thirds
Number of halves in 2 rectangles = 2 ÷ 1 = 2 × 2
Number of thirds in 3 rectangles 2 1

= 3 ÷ 1 = 3 × 3
3 1

Number of quarters in 3 rectangles = 3 ÷ 1 = 3 × 4 = 12 quarters
4 1
2 1
Here, 1 ( or simply 2) is called the reciprocal of 2

3 (or simply 3) is called the reciprocal of 1 .
1 3

4 ( or 4 ) is called the reciprocal of 1 .
1 4

So, whole number ÷ fraction = whole number × reciprocal of fraction

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Fraction

4.14 Division of a fraction by a whole number

Again, let's discuss the answers of these questions.

a) Divide a half into 2 equal parts . ×× ×× ×× ××

1 ÷ 2 = 1 × 1 = 1 = ×× ×× ×× ××
2 2 2 4 ×× ××
×× ×× ×× ××
b) Divide a half into 3 equal parts. ×× ×× ×× ××
×××
1 ÷ 3 = 1 × 1 = 1 ×××
2 2 3 6
= ×× ××××
×× ×× ××
×× ×× ××
×××

c) Divide two-thirds into 4 equal parts.

2 ÷ 4 = 2 × 1 = 2 or 1 = or =
3 3 4 12 6

4.15 Division of a fraction by a fraction.

a) How many quarters are there in a half ? =

1 ÷ 1 = 1 × 4 = 2 (quarters) =
2 4 2 1

b) How many halves are there in tow-thirds ? 4 1 half 1
3
2 ÷ 1 = 2 × 2 = 4 3
3 2 3 1 3

In this way, in the case of division of fraction, the dividend is multiplied
by the reciprocal of the devisor.

EXERCISE 4.6
Section A - Class work

1. Let's say and write the answer as quickly as possible.

a) How many halves are there in 3 circles ?

There are halves in 3 circles.

b) How many thirds are there in 4 circles ?

There are thirds in 4 circles.

c) How many quarters are there in 2 circles ?

There are quarters in 2 circles.

d) How many quarters are there in a half of a circle ?

There are quarters in a half of a circle.

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Fraction

e) Divide half of a rectangle in 4 equal parts. ×× ××
×× ××
Each part is of the rectangle. ×× ××
×× ××
××

f) Divide a third of a rectangle in 2 equal parts. × ××
× ××
×× ×× ××
×× ×× ××
×× ×× ××
Each part is of the rectangle. × ××

2. Let's say and write the reciprocal of

a) 2 is b) 3 is c) 4 is d) 10 is

e) 1 is f) 1 is g) 2 is h) 3 is
5 6 3 4

3. Let's say and write the answer as quickly as possible.
1 1 1 1
a) 2 ÷ 2 = b) 3 ÷ 2 = c) 2 ÷ 3 = d) 4 ÷ 3 =

e) 1 ÷ 2 = f) 1 ÷ 3 = g) 1 ÷ 2 = h) 1 ÷ 4 =
2 2 3 3

i) 1 ÷ 1 = j) 1 ÷ 1 = k) 1 ÷ 1 = l) 1 ÷ 1 =
2 3 3 2 4 5 5 4

4. Let's say and write the answer quickly.

a) How many half litres are there in 3 litres ?

b) How many one third kilograms are there in 4 kg ?

c) How many quarter metres are there in 5 m ?

d) How many one- ifth rupees are there in Rs 10 ?

Section B

5. Let's answer these questions.

a) What do you mean by 2 ÷ 1 ?
2
1
b) What do you mean by 2 ÷ 2 ?

c) Can we say how many thirds are there in 3 ÷ 1 ?
3
1
d) Can we say how many threes are there in 3 ÷ 3 ?

e) What do you mean by the reciprocal of a number or of a fraction ? Write

with any two examples .

Let's divide and ϐind the answers in the lowest terms or in mixed numbers

wherever necessary.

6. a) 2 ÷ 1 b) 3 ÷ 1 c) 4 ÷ 1 d) 2 ÷ 1 e) 3 ÷ 1
3 2 2 4 5

vedanta Excel in Mathematics - Book 5 88 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Fraction

f) 5 ÷ 1 g) 2 ÷ 2 h) 3 ÷ 3 i) 4 ÷ 2 j) 5 ÷ 10
3 3 4 5 11

7. a) 1 ÷ 3 b) 1 ÷ 2 c) 1 ÷ 2 d) 1 ÷ 3 e) 2 ÷ 2
2 3 4 5 3

f) 3 ÷ 3 g) 4 ÷ 2 h) 2 ÷ 4 i) 3 ÷ 6 j) 3 ÷9
4 5 5 4 5

8. a) 1 ÷ 1 b) 1 ÷ 1 c) 1 ÷ 2 d) 1 ÷ 1 e) 1 ÷ 1
2 3 3 2 3 3 4 2 2 4

f) 1 ÷ 1 g) 3 ÷ 1 h) 5 ÷ 5 i) 5 ÷ 5 j) 8 ÷ 16
5 10 10 5 6 12 12 6 9 27

9. a) Teacher takes 3 breads and cuts each bread into halves and shares all pieces

between some students equally. How many students will get half piece of

the bread ?

b) The capacity of a vessel is 5 litres. How many half litre jars can ill the vessel
completely ?

c) Mickey Mouse has 2 bars of chocolate. He eats only a quarter piece of
chocolate everyday. In how many days will he inish the two bars of
chocolate?

10. a) Mother cut a half cake into 2 equal pieces and gave to her 2 children. What
fraction of the whole cake did each child get ?

b) Priyasha Shrestha divided a quarter piece of bread into 3 equal parts and

gave her 3 friends. What fraction of the whole bread did each friend get ?

11. a) How many quarter pieces of chocolate can you get from a half piece of the

chocolate bar ?

b) A string is 4 m long. How many pieces of string each of 1 m length can be
5 5

cut from the string ?

c) The capacity of a vessel is 9 litre. How many jars each of the capacity 3
10 10

litre are needed to ill the vessel completely ?

It's your time - Project work !

12. a) Let's fold different sheets of paper into halves, thirds and quarters. Then,
ind separately the number of halves, thirds, and quarters in 1, 2, 3, 4, and 5
sheets of paper. Also, show these numbers dividing the whole numbers by
fractions.

b) Let's fold a sheet of paper into halves. Then, colour the half of a half folding.

c) Let's fold a sheet of paper into halves. Then, colour the quarter a half folding.

"

89Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Unit Decimal

5

5.1 Tenths, hundredths, and thousandths - looking back

Classwork - Exercise

1. Let's say and write the fractions and decimals of the different coloured
blocks.

Colours Fractions Decimals Colours Fractions Decimals
Red Blue

Green Red

Colours Fractions Decimals
Green
Red
Blue

Colours Fractions Decimals
Green
Red
Blue

2. Let's say and write these fractions in decimals and also write the name of
the decimal numbers.

a) 3 =
10

b) 5 =
100

c) 64 =
100

d) 7 = 0.007 Zero point zero zero seven
100

vedanta Excel in Mathematics - Book 5 90 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal

e) 36 =
1000

f) 479 =
1000

3. Let's say and write these decimals in fractions and also write the fractions
in words.

a) 0.9 = 9 nine- tenths b) 0.7 =
10

c) 0.03 = d) 0.56 =

e) 0.001 = f) 0.09 =

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

Fractions Decimals

ive- tenths
ive- hundredths
ive- thousandths
forty-seven-hundredths
forty-seven-thousandths
three hundred twelve- thousandths

5. Let's say and write the mixed numbers shown by the shaded diagrams.
Then express them in decimals.

a) b) c)

1130 = 1.3 = =

5.2 Place and place value of decimal numbers

Let's study the following example and learn about the places and place values
of decimal numbers.

91Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Decimal

whole number 5.746 tenths = 7 = 0.7
10
4
hundredths = 100 = 0.04

thousandths = 6 = 0.006
1000

Now, let's learn the places and place values of a few more decimal numbers
from the table given below.

Decimal numbers Tenths Place and place value
0.165 Hundredths Thousandths
0.397
0.824 1 = 0.1 6 = 0.06 5 = 0.005
10 100 1000

3 = 0.3 9 = 0.09 7 = 0.007
10 100 1000

8 = 0.8 2 = 0.02 4 = 0.004
10 100 1000

5.3 Comparison of decimal numbers

While comparing decimal numbers, we should start to compare the digits at
tenths places, then hundredths and thousandths places.

a) 0. 6 0.08 b) 0.539 0.57 c) 0.495 0.493

> ==
<=
>

So, 0.6 > 0.08 So, 0.539 < 0.57 So, 0.495 > 0.493

If decimal numbers also have whole number parts, we should irst compare

the whole numbers. For example :

2.5 < 3.5, 48.16 > 36.75 , 580.054 < 585.9, and so on.

5.4 Conversion of a decimal number into a fraction

To covert a decimal number into a fraction, we write it in the fraction of tenths,
hundredths or thousandths. Then, the fraction is reduced to the lowest terms
wherever necessary.

Example 1: Convert a) 0.4 b) 2.5 c) 0.75 into fraction.

Solution 0.4
a) 0.4 = 42 10
105 0.4 is 4 tenths one zero for one digit
of decimal part.

2 1 is written for
5
= decimal point.

vedanta Excel in Mathematics - Book 5 92 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal

b) 2.5 = 255 Alternative process
102
51 1 1
= 5 = 2 1 2.5 = 2 + 0.5 = 2 + 102 = 2 + 2 = 2 2
2 2

c) 0.75 = 7515 0.75 is 75 hundredths 0.75 Two zeros for two
100 20 100 digits of decimal part.

= 153 = 3 1 is written for
204 4 decimal point.

5.5 Conversion of a fraction into a decimal

In this case, we should express the given fraction in tenths, hundredths,
thousandths, etc. by making the denominator 10, 100, 1000, …

Alternatively, to convert a fraction into a decimal, we should divided

the numerator by denominator directly. The process is important if the

denominator of a fraction cannot be converted into 10, 100, 1000, etc.

Example 2: Convert a) 1 b) 2 2 c) 3 into decimals.
2 5 4
Solution
3 3 × 25
a) 1 = 1 × 5 = 5 = 0.5 c) 4 = 4 × 25
2 2 × 5 10
75
b) 2 2 = 2 + 2 = 2 + 2 × 2 = 2 + 4 = 2 + 0.4 = 2.4 = 100 = 0.75
5 5 5 × 2 10

Example 3: Convert a) 1 b) 213 into decimals dividing numerator by
2 is divided by 2.
denominator .

Solution

a) 1 = 1 ÷ 2 2 10 0.5 is divided by 2.
2
–10
= 0.5 0 Each shares 0.5.

b) 231 = 7 3 7 2.333
3 –6
10
= 7÷3 –9
10
= 2.333 -9
0

93Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Decimal

EXERCISE 5.1

Section A - Class work
1. Let's say and write these fractions in decimals and decimals in fractions.

a) 8 = b) 0.5 = c) 9 =
10 100
7
d) 0.07 = e) 1000 = f) 0.003 =

g) 66 = h) 0.27 = i) 69 =
100 1000
2. Let's say and write these mixed numbers in decimals and decimals in

mixed numbers.

a) 1110 = b) 1.3 = c) 21060 =
d) 3.07 = e) 519090 = f) 4.27 =

3. A portion of the ruler shows the whole numbers from 0 to 6 and their

tenths in order. Let's write the value of each letter.

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

ab c d

ef g h

4. Let's say and write the place and place value of the digit in decimal number.

a) In 0.59, the place of 5 is and place value is

b) In 0.07, the place of 7 is and place value is

c) In 0.038, the place of 8 is and place value is

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

a) 0.5 0.05 b) 0.09 0.1 c) 0.364 0.372

d) 0.007 0.07 e) 0.28 0.275 f) 0.786 0.78

vedanta Excel in Mathematics - Book 5 94 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal

Section B
6. Let's answer these questions.

a) De ine the meaning of three-tenths and three- hundredths ? Express them
in fractions and decimals.

b) Which one is greater between ifteen-hundredths and ifteen-thousandths?
Express them in fractions and decimals.

c) A chocolate bar is cut into 10 equal pieces and you take 7 pieces. Express it
in tenths and in decimal.

d) There are 100 centimetres in a metre- rod. Express 45 cm in hundredths
and in decimal.

e) You cut a bread into 10 equal pieces and share between your 5 friends

equally. Express the number of pieces received by each friend in decimal.

7. Let's write the decimal numbers of these number names. Then, express
them in fractions.

a) Zero point one b) Zero point zero zero one

c) Zero point zero zero zero ive d) Zero point three eight

e) Zero point zero seven four f) Zero point four zero nine

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

a) 0.5 b) 0.05 c) 0.005 d) 0.72 e) 0.046 f) 0.308

9. Let's write the place and place value of each digit of these decimal numbers
as shown in the example.

0.472 tenths = 0.4 a) 0.36 b) 0.07
hundredths = 0.07 c) 0.195 d) 0.004
thousandths = 0.002 e) 0.281 f) 0.999

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

a) 0.8 and 0.6 b) 0.42 and 0.45 c) 0.7 and 0.68

d) 0.09 and 0.1 e) 0.03 and 0.006 f) 0.296 and 0.33

11. Let's arrange these decimal numbers in ascending and in descending
order.

a) 0.002, 0.2, 0.02, 0.12 b) 0.54, 0.5, 0.054, 0.542

12. Let's convert these decimals into fractions and reduce the fractions to the
lowest terms wherever necessary.

a) 0.1 b) 0.01 c) 0.001 d) 0.2 e) 0.02

95Approved by Curriculum Development Centre, Sanothimi, Bhaktapur vedanta Excel in Mathematics - Book 5

Decimal

f) 0.002 g) 0.3 h) 0.04 i) 0.25 j) 0.125

k) 1.5 l) 2.4 m) 4.5 n) 3.1 o) 7.5

13. Let's convert these fractions into decimal by making them tenths,
hundredths or thousandths.

a) 1 b) 1 c) 2 d) 3 e) 4 f) 121
2 5 5 5 5 l) 141
r) 2230
g) 221 h) 152 i) 254 j) 1 k) 3
4 4

m) 243 n) 1 o) 7 p) 3 q) 1215
20 25 50

14. Let's convert these fractions into decimals dividing the numerator by
denominator.

a) 1 b) 3 c) 1 d) 4 e) 3 f) 1
4 4 5 5 8 6

g) 3 h) 5 i) 1 j) 2 k) 131 l) 323
2 2 3 3

It's your time - Project work

15. a) Let's draw 9 rectangular strips each of 10 cm long in a chart paper. Divide
each strip into 10 equal parts. Colour the parts of each strip separately to
show the decimal numbers from 0.1 to 0.9.

b) Let's cut 10 separate rectangular strips of lengths 1 cm to 10 cm from a

chart paper. Stick the strips in a chart paper with glue to form a stair as

shown. 0.10.20.30.40.50.60.70.80.91

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

0.1 0.4 0.7

0.10 0.40 0.70

(i) Is 0.1 (one-tenth) same as 0.10 (ten-hundredths)?

(ii) Is 0.4 (four-tenths) same as 0.40 (forty-hundredths)?

(iii) Is 0.7 (seven-tenths) same as 0.70 (seventy-hundredths)?

vedanta Excel in Mathematics - Book 5 96 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal

5.6 Addition and subtraction of decimal numbers

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

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.

Now, let's add 0.3 and 0.4

0.3 o 3 cubes of the block of 10 cubes 0.1 0.1 0.1
+ 0.4 o 4 cubes of the block of 10 cubes
0.1 0.1 0.1 0.1
0.7 o 7 cubes of the block of 10 cubes
0.1 0.1 0.1 0.1 0.1 0.1 0.1
Again, let's add 0.6 and 0.7.
6 cubes + 7 cubes
1 = 13 cubes
= 1 block of 10 cubes
0.6 0.1 0.1 0.1 0.1 0.1 0.1
and 3 more cubes
+ 0.7 = 1.3

0.1 0.1 0.1 0.1 0.1 0.1 0.1

1.3 0.3

1

Now, let's subtract 0.3 from 0.8.

from 0.8 take 0.8 – 0.3 = 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 away 0.3
0.5
0.8

0.8 o from 8 cubes of the block of 10 cubes

– 0.3 o take away 3 cubes.

0.5 o 5 cubes are left.

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

Example 1: Add or subtract a) 0.5 + 0.27 b) 1.6 – 0.7.

Solution 50 hundredths

a) 5 tenths
0.5
0.50

+ 0.27 + 0.27 27 hundredths 27 hundredths
0.77
97 vedanta Excel in Mathematics - Book 5
Approved by Curriculum Development Centre, Sanothimi, Bhaktapur

Decimal 1.6 o from 16 cubes

b) 1.6 ×××××××
– 0.7
0.9 –0.7 o take away 7 cubes 1 .6

0.9 o 9 cubes are left.

c) 3.8 o 3.80 I got it!
In 3.8, 8 tenths = 80 hundredths
– 1.95 o – 1.95 So, 3.8 = 3.80!!
1.85

EXERCISE 5.2
Section A - Class work

1. Each cube represents 0.1. Let's say and write decimal numbers represented
by each pair of cubes. Then, ϐind the sum of the decimal numbers.

a) + b) +

+= +=

c) + d) +

+= +=

2. Each cube represents 0.01. Let's say and write decimal numbers
represented by each pair of cubes. Then, ϐind the sum of the decimal
numbers.

a) + = b) +
+ +=

c) + d) +
+= +=

3. Let's say and write the sums or differences as quickly as possible.

a) 0.2 + 0.3 = b) 0.02 + 0.03 = c) 0.2 + 0.03 =

d) 1.4 + 0.4 = e) 1.04 + 0.4 = f) 1.004 + 0.4 =

g) 0.6 – 0.2 = h) 0.6 – 0.02 = i) 0.09 – 0.03 =

j) 1.5 – 0.5 = k) 1.5 – 0.05 = l) 1.7 – 1.2 =

vedanta Excel in Mathematics - Book 5 98 Approved by Curriculum Development Centre, Sanothimi, Bhaktapur