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

Algebra

Again, let's have discussion on the following questions:

a) x represents the height of students in your school. What value does
x represent?

b) y represents the age of students in your school. What value does
y represent?

c) p represents the natural numbers less than 10. What number does
p represent?

The letters like x, y, z, a, b, p, q, ... do not represent a fixed or constant
number of things. We can use such letters to represent any number of
things. Therefore, these letters are called variables. The word 'variable'
means something that can vary or change.

9.3 Operation on constant and variable

Let's learn about the operations (addition, subtraction, multiplication, and
division) between constant and variables from the following illustrations.

How many marbles are there altogether in bags on each skateboard?

a) b) c)
55
x xx y yy2

5 + 5 x + x + x y+y+y+2
5 is added 2 times x is added 3 times 3 times y and 3 more
2 × 5 = 10 3 × x = 3x 3 × y + 2 = 3y + 2

Now, let's make a few more operations on constant and variables.

a) p is added to 2 = p + 2

b) 7 is subtracted from 2 times q = 2q – 7

c) The sum of x and 4 is divided by 2 = x + 4
2

In p + 2, p is a variable, 2 is a constant, and p + 2 is a variable.

In 2q – 7, q is a variable, 2 and 7 are constant, 2q is a variable, and 2q – 7
is also a variable.

In x + 4, x is a variable, 4 and 2 are constants, and x + 4 is also a variable.
2 2

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Exercise - 9.1

Section A - Classwork

1. Let's circle the variables. Then, list the constants and variables

separately. Constants Variables
4 y 3x 7 5x

10 2a 6p 6 x + 9

2. Let's tell and write whether these letters represent constant or
variable.

a) x represents the number of students in your class, x is a

b) x represents the height of students in your class, x is a

c) y represents the number of sides of a triangle, y is a

d) y represents the number of sides of polygons, y is a

e) p represents the even numbers less than 7, p is a

f) p represents the even number between 5 and 7, p is a

3. Let's fill in the blanks.

a) In 2x, constant is and variables are , .

b) In 7y, constant is and variables are , .

c) In a + 3, constant is and variables are , .

d) In 2x + 1, constant are , and variables are ,
,.

4. Let's tell and write how many letters are there altogether in bags on
each skateboard?

a) b) y y y c) x x 3

xx

e) f)
d)
p p25 x xx19
a aa4

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Algebra

Section B

Let's read these statements carefully. Then, express them in
mathematical operations with constants and variables.

5. a) x is added to 3. b) 2 times x is added to 5.

c) 4 is subtracted from y. d) 7 is subtracted from 3 times y.

e) a is increased by 6. f) b is decreased by 2.

g) 3 times the sum of x and 1. h) 5 times the difference of y and 9.

i) The sum of p and 8 is divided by 3.

j) The difference of q and 10 is divided by 7.

6. a) You are now x years old. After 2 years your age will be (x + 2) years.

b) Brother is now x years old. How old will he be after 1 year?

c) Sister is now y years old. How old will she be after 3 years?

d) Pratik has Rs x. Prabin gives him Rs 5 more. How much money does
Pratik have now?

e) Bishu aunty has Rs y. She gives Rs 10 to Devasis. How much money is left
with Bishu aunty now?

f) The cost of a pencil is Rs p. What is the cost of 6 pencils?

9.4 Algebraic term and expression

Let's study the following illustrations and learn about algebraic terms and
expressions.

Algebraic terms

x, y, 2, 3a, 5, 4ab, ... are terms. x, y, 3a, 4ab are variable terms. 2 and 5 are
constant terms.

Thus, a term can be a number, a variable, or a number and variable combined

by multiplication or division.

2x, 3p, 2x , 4xy , ... are a few more examples of terms.
6

Algebraic expressions

2x is a term but 2 + x or 2 – x or x + 2 or x – 2 are expressions.

xy is a term but x + y or x – y or y + x or y – x are expressions.

Similarly, a + b – 5, 2p – 3q + 1, ... are algebraic expressions. Thus, an
expression is a collection of terms separated by addition or subtraction
signs.

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9.5 Coefficient and base of algebraic term

Let's learn to identify the coefficient and base of algebraic terms from the

following illustrations. 4x

In 2x 2 is a constant and it is the coefficient. coefficient base
x is a variable and it is the base.

In 3ab 3 is a constant and it is the coefficient.
a and b are variable and they are base.

The coefficient of 1 in an algebraic term is usually not written.

So, 1x can be written as x, 1y is written as y, and so on.

Thus, the constant number in an algebraic term is the coefficient and the
variable (letter) is the base of the term.

Furthermore, 2x is 2 times x = 2 × x, 3y is 3 times y = 3 × y
4xy is 4 times, x times y = 4 × x × y or, 4 times xy = 4 × xy and so on.

9.6 Evaluation of terms or expressions
Let's learn about the evaluation of algebraic terms and expressions from the

following examples.

If x = 1, x + 4 = 1 + 4 = 5

If y = 2, 2y – 1 = 2 × 2 – 1 = 4 – 1 = 3

If l = 4 and b = 3, 2(l + b) = 2 (4 + 3) = 2 × 7 = 14

Thus, when we replace the variables of terms or expressions with numbers,
we find the values of the terms or expressions. It is called evaluation of
terms or expressions.

Exercise - 9.2

Section A - Classwork

51. Let's name the terms and find the number of terms. 1
a) 5x term is no. of terms

b) 3ab term is no. of terms

c) x + 7 terms are no. of terms

d) 2y – 4 terms are no. of terms

e) a + b – 6 terms are no. of terms

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Algebra

2. Let's tell and write the coefficient and base of each of the following
algebraic terms.

a) In 3x, coefficient is base is

b) In 4y, coefficient is base is

c) In p, coefficient is base is

d) In 5ab, coefficient is bases are

3. It's your time! Let's write any three algebraic terms. Then, tell and
write the coefficient and base of each term.

a) In coefficient is base is

b) In coefficient is base is

c) In coefficient is base is

4. If x = 3 and y = 2, tell and write the values of the following terms or
expressions.

a) x + 1 = b) x – 1 = c) x + y =

d) x – y = e) 2x = f) 4y =

g) xy = h) 2xy = i) xy + 2 =

Section B

5. Let's name the terms and write the number of terms in the following
expressions.

a) 3x b) 2xy c) a + b

d) a – b + 5 e) 2p + q – 1 f) x – 2y + z – 7

6. Let's write the coefficient and base of each of the following algebraic
terms.

a) 2x b) 3y c) 6a d) x e) xy f) ab g) 1 x h) 2 pq
2 3

7. If x = 2 and y = 3, find the values of the following terms or expressions:

a) x + 3 b) y + 1 c) x + y d) x – 1 e) y – 2

f) 2x g) 2y h) 5x – 2 i) 3y + 1 j) x + y – 4

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8. If a = 4, b = 1, and c = 2, find the values of the following terms or
expressions:

a) a + b + c b) a + b – c c) a – b + c d) a – b – c

e) 2ab f) 3bc g) abc h) ab + bc

9. If l = 5, b = 3, and h = 2, find the value of

a) l × b b) 4 l c) 2 (l + b) d) 2h (l + b)

10. If x = 2, find the length of the following line segments.

a) A 2x cm 2 cm B AB = 2x cm + 2 cm = 2 × 2 cm + 2 cm
= 4 cm + 2 cm = 6 cm

b) P x cm 3 cm Q c) X 4 cm 2x cm Y

d) A 3x cm 1 cm B e) C (x + 1) cm 6 cm D

11. Perimeter of each plane shape = total sum of the lengths of all sides. If

a = 3, find the perimeter of the following shapes.

C 4 cm R 2a cm H a cm G

a) b) c)
a cm 6 cm
a cm
5 cm

A (a + 2) cm B P (a + 1) cm Q E 3a cm F

9.7 Like and unlike terms Plate A

Let's study these illustrations and investigate the idea about
like and unlike algebraic terms.

There are 2 apples in plate A and 3 apples in plate B. Both
the plates have the same (like) things.

Suppose, x represents an apple. Then, plate A has 2x and B Plate B
has 3x. So, 2x nd 3x are like terms.

Plate A There are 2 apples in plate A and 2 cakes in plate B. These
plates do not have same things. They have different (unlike)
things. Suppose x represents an apple and y represents a
cake. Then, plate A has 2x and plate B has 3y. So, 2x and 3y
are unlike terms.

Plate B Now, look at the bases of these terms and investigate the
rule to identify like and unlike terms.

Of course, like terms have the same bases. However, unlike terms have

different bases.

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Algebra

Classwork - Exercise

1. Let's write the base of each of these terms. Tell and write whether they
are like or unlike terms.

a) The base of x is and 2x is So, x and 2x are terms.

b) The base of 3y is and 4y is So, 3y and 4y are terms.

c) The base of 5x is and 5y is So, 5x and 5y are terms.

d) The base of 2a is and 7b is So, 2a and 7b are terms.

2. Let's circle the unlike terms and list like terms separately.

a) 2a, 2b, 3a, 3y and are like terms.

b) p, q, 5p, pq and are like terms.

c) 4y, 6x, x, xy and are like terms.

3. It's your time. Let's write your own like and unlike terms.

a) and are like terms. b) and are unlike terms.

c) and are unlike terms. d) and are like terms.

9.8 Addition and subtraction of like terms
Classwork - Exercise

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

a) + +

2x + 3x = 5x

2 pencils + 3 pencils = pencils +

b) +
apples
2 apples + 2 apples = 2x + 2x = x

c) + +

4 marbles + 3 marbles = marbles 4y + 3y = y

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2. How many letters are there in each balloon? Let's find the letters

altogether.

a) x xx x b) a aaaaa c) z zzzzzz
aa z
a

+ = + = +=

3. Let's take away the letter-cards. Tell and write how many letters are
left?

a) From x x take away x = x is left.

From 2x take away x = 2x – x = x

b) From y y y take away y = y y are left

From take away = – =

c) From a a a a take away a a = a a

From take away = – =

d) From p p p p p take away p p = p p p

From take away = – =

Now, let's investigate the rule of addition and subtraction of like terms from

the examples given below. I got the rule!
a) x + 3x = (1 + 3)x = 4x
b) 2y + 5y = (2 + 5)y = 7y I should simply add or
c) 5a – 3a = (5 – 3)a = 2a subtract the coefficients

of like terms.
So, 3x + 2x = 5x

d) 8p – 5p = (8 – 5)p = 3p 7y – 3y = 4y!!

4. Let's tell and write the sum or difference as quickly as possible.

a) x + x = b) x + 2x = c) 3y + 2y =

d) 2a + 4a = e) 5p + 3p = f) 4x – x =

g) 5x – 2x = h) 7y – 4y = i) 9a – 5a =

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Algebra

9.9 Addition and subtraction of unlike terms
Let's discuss about the answers of these questions.

+ 2 pencils + 3 apples I got it!
When we add unlike
The total is pencils apples or what ? things we cannot find
the single total value!

+ 4 marbles + 2 eggs

The total is marbles eggs or what ?

Similarly, in 2x + 3y, we cannot find a single total value.
In this way, we cannot add or subtract the coefficients of unlike terms.
Now, let's learn a few more examples.

The sum of x and y = x + y
The sum of 4p and 5q = 4p + 5q
The difference of 6a and 2b = 6a – 2b
The difference of 7x and 3y = 7x – 3y, and so on.

Exercise - 9.3

Section A - Classwork

1. Let's tell and write the total number of letters in each of two balloons.

a) x xx b) y y y c) a a + aaaaaa
y y y y aa
x + xx y +

2x + 4x = + = +=

2. Let's subtract the letter-cards which are taken away. Tell and write
how many letters are left.

a) x x x x – x = 4x – x = 3x

b) y y y y y – y y y = – =

c) a a a a a a – a a = – =

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Algebra

3. How many letters are there altogether ? Let's add the coefficients of
the like terms, then tell and write the answer.

a) x + 2x = b) x + 3x = c) 4y + 2y =

d) 3x + 3x = e) 3a + 4a = f) 5p + 6p =

4. How many letters are left? Let's subtract the coefficients of the terms,
then tell and write the answer.

a) 2x – x = b) 3x – 2x = c) 6y – y =

d) 8y – 5y = e) 7a – 3a = f) 10p – 4p =

5. Let's tell and write the correct terms in the blank spaces.

a) 3x + = 5x b) + 2y = 8y c) 5a + = 11a

d) 6x – = x e) 10y – = 9y f) – 2p = 7p

6. Let's write any two appropriate like terms to match each of the given
sums or differences.

a) + = 4x b) + = 7y c) + = 8a

d) – = x e) – = 2y f) – = 3p

7. Let's fill in the missing terms to complete the sums.

5x + = 9x – 5y = 12y

+ + +– – –

+= – 2y =

= = == = =

8x + = 15x 11y – =


8. Let's tell and write the sum or difference of these unlike terms as
quickly as possible.

a) Sum of x and y = b) Sum of 2x and 3y =

c) Sum of a and 4b = d) Sum of 5p and 2q =

e) Difference of p and q = f) Difference of 3x and y =

g) Difference of 4a and 2b = h) Difference of x and 5y =

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Section B

9. Let's find the sum of the following like terms:

a) 3x + 5x b) 4x + 2x c) 6y + 3y d) 2y + 9y
h) 7p + 6p
e) 7p + 4p f) 8m + 6m g) 9x + 8x l) 9x + 6x

i) 5y + 10y j) 12q + 4q k) 10m + 7m

10. Let's find the difference of the following like terms:

a) 8x – 3x b) 9y – 4y c) 7p – 5p d) 10x – 5x

f) 9m – 5m g) 8p – 6p g) 12x – 7x h) 13y – 4y

i) 15q – 8q j) 16x – 10x k) 17y – 9y l) 18m – 8m

11. Let's simplify:

a) x + 2x + 3x b) 7x – 3x + x c) 10y – 2y – 5y

d) 4y + y + 5y e) 3p + 6p – 4p f) 2x – 4x + 6x

g) m + 5m – 2m + 3m h) 6y – y – 3y + 2y i) 8p – 4p + 5p – 2p

12. If x = 2, let's find the length of the following line segments.

a) x cm 2x cm b) x cm 2x cm 3x cm

13. Perimeter of each plane shape = total sum of the length of all sides. If

a = 3, find the perimeter of the following shapes.

a) C b) R 3a cm Q c) 4a cm G
4a cm
4a cm H
2a cm
2a cm
2a cm
3a cm

A a cm B P E a cm F

It's your time - Project work!

Let's make a few paper flowers by cutting a chart paper as shown in the

diagrams. Write an algebraic term (x, 2x, 3x, ...) in the circle. Write a pair
of terms in each of 4 petals using '+' or '–' sign between them to get the
term in the circle. Colour the petals. You can stick your flowers on the
wall-magazine.

x + 2x
3x 4x – x

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9.10 Addition and subtraction of algebraic expressions

Now, let's investigate the process of addition and subtraction of algebraic
expressions from the examples given below.

Example 1: Add a) x + 3y and 2x + y b) 3x – 2y and 4x + 3y
Solution

a) x + 3y b) 3x – 2y Let's write the like terms in the same
vertical columns.
2x + y 4x + 3y
Then add or subtract the like terms.
3x + 4y 7x + y

Example 2: Subtract 2a + 3a from 5a + 4a.

Solution Let's write the like terms in the same vertical

5a + 4a columns.

± 2a ± 3a Change the signs of the terms which are to be
subtracted. Then add or subtract according to the

3a + a sign.

Exercise - 9.4

Section A - Classwork

1. Let's add, then tell and write the sums as quickly as possible.

a) x + 1 and x + 2 = 2 + 3 b) x + 2 and x + 3 =

c) 2y + 1 and y + 4 = d) x + y and x + y =

e) 2a + 3b and a + b = f) a + 4 and a – 1 =

g) 2x + 5 and x – 3 = h) 3y + 6 and 2y – 4 =

2. Let's subtract, then tell and write the difference as quickly as possible.
+ 2 2x – x and 3 – 1
a) From 2x + 3 subtract x + 1 =

b) From 3x + 4 subtract x + 2 = 3x – x and 4 – 2

c) From 4y + 7 subtract 2y + 3 = 4y – 2y and 7 – 3

d) From 6a + 5 subtract 3a + 4 = 6a – 3a and 5 – 4

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Algebra

3. Let's study each diagram until you investigate how it works. Then
complete the empty circles.

23 x4 xx 3
7 x+8
3x + 3

3 2x 2x 4

y 5 aa 7 xx 9



4. Let's play a game! In each game below, the players start with 5 points and

move one board at a time. Follow each board from 'START' to 'FINISH' to
find the total score.
S F
T win I
A3 win lose +win lose N 11 3
R x2
T 2x 1 I
S
H

S F
T win I
Ax win lose win lose N
R 2 3x
T x 5I
S
H

S F
T win I
A2 win lose win lose N
R 3y y
T 3 2y I
S
H

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Section B

5. Let's add the following algebraic expressions.

a) x + 3 b) 2x + 1 c) 3y + 4 d) a + b
a+ b
x+4 x+2 2y + 2
h) 2x – 4y
e) 2x + y f) 4a + 3b g) 3a + 5b 5x + 3y
4a – 2b
x + 3y 2a – b

i) 3x + 6 and x + 3 j) 4y – 7 and y + 4
k) 2a + 5a and 2a + 2b l) 6x – 5y and 3x + 4y

6. Let's subtract the following algebraic expressions.

a) 2x + 5 b) 3x + 6 c) 5y + 7 d) 4a + 5b

± x ±2 ± x ±3 ± 2y ± 3 ± 3a ± 4b

e) 5a + 6b f) 7x + 4y g) 6x + 3y h) 8a – 2b

3a + 3b 4x + 2y 2x – 2y a – 6b

i) From 4x + 9, subtract 2x + 4. j) From 5y + 6, subtract 3y – 1.

k) From 8a + 10b, subtract 5a – 3b. l) From 9x – 4y, subtract 4x – 7y.

9.11 Open mathematical sentence

'The sun rises from the east'. (It is a sentence.)

'The earth has seven continents'. (It is a sentence.)

'3 added to 4 is 7'. (It is a mathematical sentence.)

'2 subtracted from 5 is 3'. (It is a mathematical sentence.)

Thus, a mathematical sentence contains mathematical operations.

Again,

3 added to 4 is 7 3 + 4 = 7 (It is true.)

2 subtracted from 5 is 3 5 – 2 = 3 (It is true.)

Such true mathematical sentences are called closed sentences.

On the other hand,

x is added to 4 is 7 x + 4 = 7 (We cannot say true or false)

y is subtracted from 5 is 3 5 – y = 3 (We cannot say true or false)

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Such mathematical sentences for which we cannot say whether they are true
or false are called open mathematical sentences. We get open sentences
when we use variables in mathematical sentences.

9.12 Equation

x + 2 = 5 is an open mathematical sentences and it is an equation.

x – 3 = 6 is an open mathematical sentence and it is an equation.

2 × y = 8 is an open mathematical sentence and it is an equation.

y = 4 is an open mathematical sentence and it is an equation.
2

Thus, an equation is an open mathematical sentences that has two equal
sides separated by an equal (=) sign.

In an equation, the left side of (=) sign is called L. H. S. (Left Hand Side) and
the right side is called R. H. S. (Right Hand Side).

We can compare an equation to a pan balance, where the equal sign as the
balance point.

9=9 8+1 = 9 x+1 = 9

Classwork - Exercise

1. Let's tell and write which one is the 'closed' or 'open' mathematical
sentence.

a) 2 added to 7 is 9 b) x added to 5 is 8

c) 3 times y is 12 d) difference of 5 and 2 is 3

e) 4 times 5 is 20 f) 6 subtracted from x is 4

2. Let's make open mathematical sentences.

a) x added to 3 is 7.
b) The difference of y and 5 is 6.

c) 2 times p is 10.

d) x divided by 3 is 5. vedanta Excel in Mathematics - Book 4
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Algebra

3. Let's list out the equations separately.

x + 2, x + 2 = 5, x – 3, 4x Equations are

x – 3 = 7, 4x = 20, x , x = 6
2 2

9.13 Solving equation

Classwork - Exercise

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

a) What should be added to 1 to get 3? + 1 = 3 x + 1 = 3 then, x =

b) What should be added to 2 to get 5? + 2 = 5 x + 2 = 5 then, x =

c) From what is 1 subtracted to get 2? – 1 = 2 x – 1 = 2 then, x =

d) What should be multiplied by 2 to get 6? 2 × = 6 2x = 6 then, x =

e) What should be divided by 2 to get 4? 2 = 4 x = 4 then, x =
2

In this way, finding the value of letter (variable x, y, ...) in an equation is called
solving equation. The value of variable is called to solution to the equation.

9.14 Process of solving equation

Let's investigate the processes of solving equations from the following
illustrations:

a) x x
x

x+2=5 x+2–2=5–2 x=3

Fact 1: We can subtract equal number from both sides of an equation.

b) x x x

x–2=4 x – 2 + 2= 4 + 2 x=6

Fact 2: We can add equal number to both sides of an equation.

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c) x x xx x

2x = 6 2x = 6 x =3
2 2

Fact 3: We can divide both sides of an equation by an equal number.

d) x xx x
2 22

x = 3 2 × x = 2 × 3 x=6
2 2

Fact 4: We can multiply both sides of an equation by an equal number.

Now, let's discuss about the above illustrations in the following examples.

Example 1: Solve a) x + 3 = 7 b) x – 3 = 7

Solution x
a) x + 3
=7

or, x + 3 – 3 = 7 – 3 3 is subtracted from x+3–3=7–3
both sides.

or, x = 4

Short-cut process I got it!
x + 3 = 7
or, x = 7 – 3 If x + 4 = 9, then
x = 9 – 4 = 5

or, x = 4

b) x – 3 = 7 3 is added to both x–3
or, x – 3 + 3 = 7 + 3 sides. x–3+3=7+3
or, x = 10

Short-cut process I also understood!
x – 3 = 7
or, x = 7 + 3 If x – 4 = 6, then
x = 6 + 4 = 10

or, x = 10

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Example 2: Solve a) 3x = 12 b) x = 2
3
Solution

a) 3x = 12 xxx

or, 13x = 12 4 Both sides are 3x = 12
31 31 divided by 3. 3 3

or, x = 4

Short-cut process Now, its easier!

3x = 12 If 4x = 20, then
20 5
x = 41 = 5

or, x = 124
31

or, x = 4

b) 3x = 2 xxx
or, 3 × 3x = 3 × 2 333

Both sides are
multiplied by 3.

or, x = 6 3 × x = 3 × 2
3
Short-cut process

3x = 2 I can also find the solution!
x
or, x = 3 × 2 If 4 = 6, then 24
=4×6=
x

or, x = 6

Now, let's learn to check whether the solution of the given equation is
right or wrong.

Example 3: Solve a) 2x + 1 = 9 and check the solution.
Solution

a) 2x + 1 = 9

or, 2x + 1 – 1 = 9 – 1 Checking the solution
2x + 1 = 9
or, 2x = 8 or, 2 × 4 + 1 = 9
or, or, 8 + 1 = 9
or, 12x = 84 or, 9 = 9
21 21 So, 4 is the right solution.

x = 4

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Exercise - 9.5

Section A - Classwork

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

a) What should be added to both sides of x – 1 = 4 to get the
value of x?

b) What should be subtracted from both sides of x + 5 = 7 to get the
value of x?

c) By what should both side of 4x = 12 be divided to get the
value of x?

d) By what should both sides of x = 3 be multiplied to get the
value of x? 4

2. Let's write the correct number inside the each shape. Then find the
value of letters.

a) + 1 = 3 x + 1 = 3 So, x =

b) – 1 = 3 y – 1 = 3 So, y =

c) 2 × = 4 2 × a = 4 So, a =

d) = 2 x = 2 So, x =
3 3

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

a) x + 1 = 2, x = b) y – 1 = 2, y = c) a + 2 = 3, a =

d) p – 2, p = e) 2x = 2, x = f) y = 1, y =
g) 2x = 4, x = 3
a
h) 3 = 2, a = i) 3x = 9, x =

4. Let's write the equations below each pan balance. Then, find the value

of x.

a) x xx

+ 1 = 3 or, or,

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Algebra x–1 x

b)
x–1

c) 2x or, or,
xx x

d) or, or,
x
x xx
2 22

or, or,

Section B

5. Let's solve these questions.

a) x + 1 = 2 b) x + 2 = 4 c) x + 3 = 7 d) y + 5 = 12
e) y + 4 = 9 f) a + 6 = 13 g) a + 7 = 10 h) x + 10 = 15
6. a) x – 1 = 2 b) x – 2 = 3 c) x – 3 = 4 d) y – 4 = 5
e) y – 5 = 5 f) a – 6 = 2 g) a – 7 = 1 h) x – 10 = 6

7. a) 2x = 2 b) 2x = 4 c) 3x = 6 d) 3y = 15
e) 4y = 12 f) 5a = 10 g) 6a = 24 h) 7x = 49

8. a) 2x = 1 b) x = 2 c) x = 1 d) y = 4
e) 2y = 2 2 3 3
9. a) 2x + 1 = 5 a a x
f) 3 = 5 g) 4 = 3 h) 5 = 2

b) 2y – 1 = 5 c) 2a + 3 = 7 d) 2x – 3 = 7

e) 3y + 2 = 8 f) 3x – 1 = 8 g) 4a + 3 = 15 h) 5x – 2 = 3

i) 23x = 2 j) 2y = 4 k) 3a = 6 l) 3x = 9
5 2 4

10. Let's solve the equations and check the solutions.

a) x + 5 = 9 b) 2x – 3 = 7 c) y – 4 = 3 d) 3y + 1 = 7
e) 2a = 12 f) 3x = 15
g) a = 4 h) 2x = 6
2 3

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11. Let's make equations from these balances, then solve them.

a) b) c) d)



12. The lengths of the straight line segments are given. Make equations
and solve them.

a) x cm 5 cm b) a cm a cm 6 cm
7 cm
10 cm

13. Perimeter of each plane shape = total sum of the length of all sides.

From the given perimeter of each shape, let's make equations and solve

them.

a) b) c) 3x cm

2x cm
x cm
2x cm
2x cm

4 cm
3 cm

4 cm x cm 3x cm

Perimeter = 9 cm Perimeter = 13 cm Perimeter = 20 cm

9.15 Use of equation

We use equations to find the unknown number (or number of quantity)
in word problems. We take a variable (x, y, z, a, b, c, ...) to represent the

unknown number. Then we make an equation. By solving the equation we
find the unknown number (or quantity).

Let's learn more about the use of equations from these examples.

Example 1: The sum of two numbers is 9. If one of them is 5, find the

other number. It's interesting!
The sum of two number is 9.
Solution

Let the other number is x. So, x + 5 = 9
Then, x + 5 = 9 or, x = 9 – 5 = 4
I could easily find the unknown number!!

or, x + 5 – 5 = 9 – 5

or, x = 4

Hence, the other number is 4.

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Example 2: A brother is 3 years younger than his sister. If brother is 5

years old, how old is the sister?

Solution I got it!

Let the sister's age is x year. Brother's age is 3 years
less than sister's age.

Then, x – 5 = 3 So, x – 5 = 3
or, x – 5 + 5 = 3 + 5 or, x = 3 + 5 = 8

or, x = 8

Hence, the sister is 8 years old.

Exercise - 9.6

Section A - Classwork

1. Let's tell and write the value of x as quickly as possible.

a) The sum of x and 2 is 5. x=

b) The difference of x and 3 is 4. x=

c) The product of x and 5 is 10. x=

d) The quotient of x divided by 2 is 3. x =

e) Double of x is 8. x=

f) One-third of x is 3. x=

2. Let's make equation of each of the following statements.

a) The sum of x and 4 is 7. Equation is

b) The difference of y and 5 is 4. Equation is

c) Two times x is 10. Equation is

d) Two times y added to 3 is 9. Equation is

e) x is more than 2 by 1. Equation is

f) 3 is less than y by 2. Equation is

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Section B

Let's make equations and solve them to find the unknown number or
quantity.

3. a) If the sum of x and 4 is 10, find x.
b) If the difference of y and 5 is 7, find y.
c) If the product of 3 and p is 12, find p.
d) If the quotient of x divided by 2 is 5, find x.
e) If the double of a is 16, find a.
f) If the half of b is 10, find b.
g) If x increased by 2 is 8, find x.
h) If y decreased by 3 is 7, find y.
i) If x is more than 10 by 5, find x.
j) If 5 is less than y by 4, find y.

4. a) The sum of two numbers is 17. If one of them is 9, find the other number.
b) The difference of two numbers is 10. If the smaller number is 5, find the

bigger number.

c) When a number is multiplied by 7, the product is 56. Find the number.

d) When a number is divided by 4, the quotient is 6. Find the number.

e) When a number is increased by 8 it becomes 15. Find the number.

f) When 9 is decreased from a number it becomes 7. Find the number.

g) When two times a number is added to 4, the sum is 10. Find the number.

h) When 5 is subtracted from three times a number, the difference is 7.
Find the numbers.

5. a) There are 30 students in a class. If 18 of them are girls, find the number
of boys.

b) There are 540 students in a school. If 260 of them are boys, find the
number of girls.

c) A box contains 50 kg of fruits. If it contains 30 kg of apples and the rest
is oranges, find the weight of oranges.

6. a) There are some students in a class. When 4 more new students join
the class the number becomes 30. Find the number of students before
joining the new students in the class.

b) Sunayana has some money. When she spends Rs 25, she has Rs 50 left.
How much money does she have at the beginning?

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c) Pemba Lama had a few number of marbles. When he bought 7 more
marbles, he had 35 marbles altogether. How many marbles did he have
at the beginning?

7. a) The number of girls in a class is 3 less than the number of boys. If there
are 14 girls, find the number of boys.

b) The number of girls in a class is 5 more than the number of boys. If there
are 17 girls, find the number of boys.

c) Aarshiya has Rs 10 more than Diyoshana. If Diyoshana has Rs 15, how
much money does Aarshiya have?

8. a) Anu Gupta is 4 years younger than her brother. If Anu is 8 years old, how
old is her brother?

b) Bikash Tamang is 3 years elder than his sister. If Bikash is 10 years old,
how old is his sister?

c) Mickey Mouse is 2 years younger than Bugs Bunny. If Bugs Bunny is 9
years old, how old is Mickey Mouse?

It's your time - Project work

9. a) There are x number of girls in your class. Let's count the number of boys
and the total number of students in your class. Then make an equation
and find the value of x.

b) There are y number of boys in your class. Let's count the number of girls
and the total number of students in your class. Then, make an equation
and find the value of y.

c) There are x number of male teachers in your school. Let's count the
number of female teachers and the total number of teachers in your
school. Then make an equation and find the value of x.

10. Let's cut a longer and a shorter paper strips of any lengths from a chart
paper.

a) By how many centimetres is one strip longer or shorter than another
strip? Let's use this answer and do these activities.

b) Let the length of the shorter strip is x cm. Now, make an equation and
find x. [Hint: x + .......... = longer strip]

c) Let the length of the longer strip is y cm. Now, make an equation and find
y. (Hint: y – .......... = shorter strip)

?

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10

10.1 Measurement of length - Looking back
Classwork - Exercise

1. Look at the pictures. Let's tell and write the name of the non-standard
units of length.



2. Let's use your finger-width, hand-span, cubit, and foot-length to
measure these lengths.

a) Length of a pencil in finger-width finger-widths.

b) Length of a book in hand-span hand-spans.

c) Length of your desk or table in cubit cubits.

d) Width of a door in foot-length foot-lengths.

e) Why are finger-width, hand-span, cubit, and foot-length called
non-standard units? Discuss with your friends.

10.2 Standard units of length

Classwork - Exercise

1. Look at the standard instruments. Let's tell and tick the appropriate
instrument and unit to measure the given lengths.

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a) Length of a playground is measured by a (ruler/measuring-tape/
milometre) in (cm/m/km)

b) Length of a pencil is measured by a (ruler/measuring-tape/milometre)
in (cm/m/km)

c) Height of a room is measured by a (ruler/measuring-tape/milometre) in
(cm/m/km).

d) Distance between two towns is measured by a (ruler/measuring tape/
milometre) in (cm/m/km).

Ruler (centimetre-scale or metre-scale), measuring tape and milometre
are the standard instruments to measure the lengths. Centimetre (cm),
metre (m) and kilometre (km) are the standard units of measurement of
length (or distance).

2. Let's learn about centimetre (cm) and millimetre (mm) in the given
centimetre-scale. Then tell and write the lengths of different objects.

1cm=10mm 5.4 cm 8.2 cm 12.8 cm

3 cm 5 mm = 3.5 cm

a)

Length of eraser cm

b)

Length of pencil cm

10.3 Conversion of units of length

Let's remember the relation between millimetre (mm), centimtre (cm),
metre (m) and kilometre (km).

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Measurement

1 cm = 10 mm 10 mm = 1 cm
2 cm = 2 × 10 mm = 20 mm
3 cm = 3 × 10 mm = 30 mm 1 mm = 1 cm = 0.1 cm
And so on... 10
cm × 10 mm
2 mm = 2 cm = 0.2 cm
10

And so on...

mm ÷ 10 cm

1 m = 100 cm 100 cm = 1 m
2 m = 2 × 100 cm = 200 cm
3 m = 3 × 100 cm = 300 cm 1 cm = 1 m = 0.01 m
And so on... 100
m × 100 cm
25 cm = 25 m = 0.25 m
100

And so on...

cm ÷ 100 m

1 km = 1000 m 1000 m = 1 km
2 km = 2 × 1000 m = 2000 m
3 km = 3 × 1000 m = 3000 m 1 m = 1 km = 0.01 km
4 km = 4 × 1000 m = 4000 m 1000
And so on...
km × 1000 m 86 m = 86 km = 0.086 km
1000

345 m = 345 km = 0.345 km
1000

And so on...

m ÷ 1000 km

Now, let's learn about the conversion of lengths from the following examples.

Example 1: Covert a) 2 cm 4 mm into mm b) 5 cm 6 mm into cm

Solution 1 cm = 10 mm b) 5 cm 6 mm 1 mm = 10 cm
a) 2 cm 4 mm 6
2 cm = 2 × 10 mm = 5 cm + 6 cm 6 mm = 10 cm
= 2 × 10 mm + 4 mm 10
= 20 mm = 0.6 cm
= 20 mm + 4 mm
= 5 cm + 0.6 cm

= 24 mm = 5.6 cm

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Example 2: Covert a) 3 m 25 cm into cm b) 4 m 82 cm into m

Solution 1 m = 100 cm b) 4 m 82 cm 100 cm = 1 m
a) 3 m 25 cm 82
= 3 × 100 cm + 25 cm 3 m = 3 × 100 cm = 4 m + 82 m 82 cm = 100 cm
100
= 300 cm = 0.82 cm

= 300 cm + 25 cm = 4 m + 0.82 m

= 325 cm = 4.82 m

Example 3: Convert 4 km 560 m into km. 1000 m = 1 km
Solution

4 km 560 m = 4 km + 560 km 560 m = 560 km
1000 1000
= 0.560 km
= 4 km + 0.560 km
= 0.56 km
= 4.560 km

= 4.56 km 4.560 is the same as 4.56

Exercise - 10.1

Section A - Classwork
1. Let's tell and write the correct answer in the blank spaces.
a) Any three standard instruments to measure the lengths are

b) Any three standard units of measurements of lengths are



c) In a centimetre-scale, 1 cm is divided into equal parts and
each part is called

d) Each part of 100 equal parts of a metre-scale is equal to

e) There are metres in 1 km.

2. Let's tell and write the correct measurements in the boxes.

cm

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3. Let's measure the lengths of these line segments using ruler. Tell and
write the lengths in the blanks spaces.

a) A B b) P Q
AB = PQ =

c) X Y d) C D
XY = CD =

4. Let's covert higher to lower or lower to higher units.

a) 1 cm = mm, 5 cm = × mm = mm

b) 1 m = cm, 4 m = × cm = cm

c) 1 km = m, 2 km = × m = m
d) 10 mm = = cm
e) 100 cm = cm, 5 mm = 5 cm m
10 m =

m, 75 cm =

f) 1000 m = km, 432 m = km = km

5. Let's convert into the decimal of higher units of length.
4 cm 6 mm = 4.6 cm, 2 m 36 cm = 2.36 m, 3 km 215 m = 3.215 km

a) 7 cm 3 mm = cm b) 5 cm 8 mm = cm

c) 1 m 25 cm = m d) 4 m 64 cm = m

e) 1 km 148 m = km f) 2 km 788 m = km

Section B

6. Let's convert the units of length as indicated.

a) 2 cm 5 mm (into mm) b) 6 cm 7 mm (into mm)

c) 4 cm 2 mm (into cm) d) 8 cm 4 mm (into cm)

e) 1 m 20 cm (into cm) f) 2 m 46 cm (into cm)

g) 3 m 55 cm (into m) h) 5m 80 cm (into m)

i) 1 km 150 m (into m) j) 2 km 300 m (into m)

k) 4 km 218 m (into km) l) 7 km 945 m (into km)

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7. a) The thickness of a book is 1 cm 4 mm. Express this thickness in
centimetres.

b) The length of a finger nail is 0.7 cm. Express this length in millimetres.

c) The length of a bridge is 30 m 54 cm. Express this length in metres.

d) The distance between two places is 3 km 527 m. Express this distance in
kilometres.

e) A tunnel is 0.916 km long. Express this length in metres.

8. Let's draw the line segments of the following lengths.

a) 4 cm b) 4.5 cm c) 5.6 cm d) 6.8 cm e) 7.2 cm

It's your time - Project work!

9. Let's use a 15 cm - ruler and find

a) thickness of your math book in mm. b) length of your pencil in cm.

c) length of your longest finger in cm.

10. Let's use a measuring tape and find

a) Your waist in cm b) length of trousers in m and cm

c) length and breadth of your classroom in metres.

11. Let's ask your parents or teachers and estimate,

a) distance between your house and school in km,

b) a place which is about 3 km away from your school,

c) distance between your house and the nearest hospital or health post.

10.4 Addition and subtraction of lengths

Classwork - Exercise

1. Let's add and regroup into the higher units. 14 mm = 10 mm + 4 mm
= 1 cm 4 mm
6 mm + 8 mm = 14 mm = 1 cm 4 mm 120 cm = 100 cm + 20 cm
70 cm + 50 cm = 120 cm = 1 m 20 cm = 1 m 20 cm
580 m + 940 m = 1520 m = 1 km 520 m

a) 4 mm + 9 mm = =

b) 7 mm + 8 mm = =

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c) 60 cm + 80 cm = =

d) 90 cm + 45 cm = =

e) 500 m + 700 m = =

f) 650 m + 860 m = =

2. Let's convert the higher units into the lower units, then subtract.

1 cm – 6 mm = 10 mm – 6 mm = 4 mm I've remembered!
1 cm = 10 mm
1 m – 25 cm = 100 cm – 25 cm = 75 cm 1 m = 100 cm
1 km – 540 m = 1000 m – 540 = 460 m 1 km = 1000 m!!

a) 1 cm – 4 mm = =

b) 1 m – 60 cm = =

c) 1 km – 200 m = =

Now, let's learn more about addition and subtraction of length from the
following examples.

Example 1: Add a) 12 cm 6 mm + 10 cm 8 mm

b) 25 m 40 cm + 14 m 75 cm

Solution

a) 121 cm 6 mm I got it!
+ 10 cm 8 mm 6 mm + 8 mm = 14 mm and
14 mm = 1 cm 4 mm
So, 1 cm is carried over to cm!!

22 cm 14 mm

= 23 cm 4 mm

Let's learn this addition converting into the decimals.

12 cm 6 mm = 12 . 6 cm 12 cm 6 mm = 12 cm + 6 cm
10 cm 8 mm = + 10 . 8 cm 10
23 . 4 cm
= 12.6 cm

10 cm 8 mm = 10 cm + 8 cm
10
= 10.8 cm

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Measurement

b) 251 m 40 cm I understood!
+ 14 m 75 cm 40 cm + 75 cm = 115 cm = 1 m 15 cm
39 m 115 cm So, 1 m is carried over to metre columns!!

= 40 m 15 cm

Again, let's learn this addition converting into the decimals.

25 m 40 cm = 25 . 40 m 25 m 40 cm = 25 m + 40 cm
100
14 m 75 cm = + 14 . 75 m
40.15 m = 25.40 m

14 m 75 cm = 14 m + 75 m
100

= 14.75 m

Example 2: Subtract 9 km 420 m – 5 km 600 m

Solution

1 km = 1000 m Subtraction by converting into decimal

8 1420 9 km 420 m = 9.420 km

9 km 420 m 5 km 600 m = – 5.600 km
– 5 km 600 mm 3.820 km
3 km 820 m

Exercise - 10.2

Section A - Classwork

1. Let's add and regroup into the higher units.

a) 3 mm + 7 mm = mm = cm
m
b) 20 cm + 80 cm = cm = km
cm
c) 400 m + 600 m = m = m
km
d) 6 mm + 9 mm = mm = mm
cm
e) 50 cm + 70 cm = cm =
m
f) 500 m + 800 m = m =

2. Let's convert into the lower units, then subtract.

a) 1 cm – 5 mm = mm – 5 mm = mm
b) 1 m – 60 cm =
c) 1 km – 800 m = cm – 60 cm = cm

vedanta Excel in Mathematics - Book 4 m – 800 m = m

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Section B Measurement

3. Let's add. 3 mm b) 7 cm 5 mm c) 10 m 60 cm
a) 6 cm 5 mm + 8 cm 9 mm + 9 m 50 cm
+ 4 cm
e) 12 km 327 m f) 20 km 640 m
d) 30 m 75 cm + 18 km 473 m + 54 km 895 m
+ 24 m 55 cm
b) 15 cm 3 mm c) 17 m 40 cm
4. Let's subtract. – 10 cm 5 mm – 12 m 25 cm
a) 8 cm 7 mm
– 3 cm 4 mm e) 7 km 670 m f) 25 km 345 m
– 4 km 480 m – 14 km 560 m
d) 40 m 35 cm
– 24 m 60 cm

5. Let's convert into the decimal of higher units, then add or subtract.

a) 7 cm 5 mm + 5 cm + 8 mm b) 10 cm 6 mm + 14 cm 9 mm

c) 8 m 65 cm + 11 m 76 cm d) 36 m 80 cm + 23 m 75 cm

e) 4 km 570 m + 5 km 590 m f) 16 km 750 m + 20 km 880 m

g) 9 cm 4 mm – 6 cm 5 mm h) 13 cm 6 mm – 7 cm 8 mm

i) 8 m 32 cm – 4 m 40 cm j) 45 m 50 cm – 15 m 90 cm

k) 10 km 300 m – 5 km 500 m l) 54 km 460 m – 28 km 750 m

Let's read these problems carefully and solve them.

6. a) Bamboo is known as one of the fastest growing plants. A bamboo plant
is 3 m 400 cm high on a day. If it grows by 85 cm in one day, what is the
new height of the plant next day?

b) A rubber is 10 cm 6 mm long. If you stretch it by 4 cm 7 mm, what is the
length of the stretched rubber?

c) A book is 1.8 cm thick and another book is 1.4 cm thick. When these
two books are placed one above another, find the total thickness of two
books.

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d) The height of a cupboard inside a room is 2.75 m. The ceiling of the room
is 1.86 m above the top of the cupboard. Find the height of the room.

e) Of the total road distance between two villages, 3 km 570 m is blacktop
and the remaining 2 km 685 m is gravelled road. Find the distance
between these two villages.

7. a) The total length of a small fish is 15 cm 3 mm and it's tail is 2 cm 4 mm.
Find the length of the fish excluding the length of its tail.

b) In the long-jump event on a Sport Day, Sahayata jumped 1 m 90 cm and
Sayad jumped 2 m 10 cm. By how much did Sayad win to Sahayata?

c) When a rubber is stretched by 8.6 cm, it's length becomes 20.4 cm. Find
the original length of the rubber.

d) The whole height of an electric pole is 12.35 m. The length of its
underground part is 1.5 m. Find the height of the pole above the ground.

e) A road between two villages is 36 km 280 m long. The part of
20 km 500 m of the road is constructed by the Local Government and
the remaining part is by the Public effort. Find the distance of the road
constructed by the public.

It's your time - Project work!

8. a) Let's measure the length and breadth of your mathematics book by using
a 30 cm - scale. Find by how much is the length longer than the breadth.

b) Lets measure the thickness of your mathematics and English book by
using a ruler.

(i) Find which book is thicker and by how much?

(ii) If you place one book above the another, what is the total thickness?

c) Let's measure the length and breadth of your desk (or table)by using a
measuring tape.

(i) Find the total of the length and breadth.

(ii) Find the difference of the length and breadth.

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10.5 Map and distance

Exercise - 10.3

Section A - Classwork
1. Let's read the map of our country Nepal. Tell and write the directions of

different places as quickly as possible.

North

West East

Jumla South

Dhangadhi Jomsom

Nepalgunj Pokhara

Butwal Kathmandu Charikot
Bhaktapur

Birgunj Ilam
Kalaiya
Janakpur Dharan
Damak
Biratnagar


North, south, east, west, north-east, north-west, south-east, south-west

a) In which direction is Nepalganj from Kathmandu? It is in south-west.

b) In which direction is Dharan from Pokhara? It is in

c) In which direction is Jomsom from Birganj? It is in

d) What is the direction of Dhangadhi from Jumla? It is in

e) What is the direction of Ilam from Biratnagar? It is in

f) In which direction is your home from your school? It is in

2. a) Which place is nearest from Janakpur? Butwal or Damak?

b) Which place is farther from Bhaktapur? Charikot or Kalaiya?

c) Which one is nearer from your home, your school or health post?

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Measurement

Section B

3. Let's read the given road-map distance between different places of far

western provinces of Nepal. Then calculate the distance between the places.

Dadeldhura Surkhet

Bhimdatta (Karnali)
135.18 km

Chisapani
98.43 km
47.54 km Attariya 69.85 km 75.78 km Kohalpur

19.32 km
13.67 km

Dhangadhi Nepalganj

a) Calculate the road distance between Bhimdatta to Dhangadhi.

b) Find the road distance between Dadeldhura and Chisapani.

c) How far is Kohalpur from Attariya?

d) Calculate the road distance from Chisapani to Surkhet.

e) Calculate the road distance from Surkhet to Nepalganj.

4. a) Itahari is 86.46 km west from Chandragadhi and Lahan is 103.68 km
west from Itahari. Find the distance between Chandragadhi and Lahan.

b) Dhulikhel is 105.15 km north-west from Sindhuli and Kathmandu is
32.47 km north-west from Dhulikhel. Calculate the distance between
Sindhuli to Kathmandu.

c) Bhratpur is 162.35 km east from Lumbini and Hetauda is 76.74 km east
from Bharatpur. How far is Hetauda from Lumbini?

5. It's your time - Project work!

a) Let's draw a map of Nepal in a chart paper and show 7 provinces with
different colours.

b) (i) Let's locate one of the famous places or cities in each province. (You
can get help from the original map or google map, etc.)

(ii) Let's visit to the available website (such as www.google.com) and
search the distance between those places or cities. Mention your
findings in the same chart paper.

(iii) In which directions are those places or cities from your place? Which
one is the nearest place to you?

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10.6 Measurement of weight Measurement
Classwork - Exercise
50 grams
1. Let's choose and circle the better estimate. 500 grams

a) b) c)

2 kilograms 3 kilograms

200 grams 30 grams

d) e) f) 10 kilogram
40 kilograms 1 kilograms 1000 grams
400 grams 10 grams

2. Let's tell and write any three pairs of objects, one is heavier and another
is lighter.

a) is heavier and is lighter.

b) is heavier and is lighter.

c) is heavier and is lighter.

3. Let's tell and write which one is a pan balance, spring balance, or a dial
balance.


A balance A
balance A balance

A heavier object has more weight than a lighter
object. We use kilogram (kg) unit to measure
the weight of heavy objects. We use gram (g)
unit to measure the weight of lighter objects.

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10.7 Conversion of units of weight

Let's remember the following relationship between kilogram (kg) and
gram (g).

1 kg = 1000 g 1000 g = 1 kg
2 kg = 2 × 1000 g = 2000 g
3 kg = 3 × 1000 g = 3000 g 1 g = 1 g = 0.001 kg
And so on... 1000

kg × 1000 g 48 g = 48 g = 0.048 kg
1000

250 g = 250 g = 0.250 kg
1000

And so on... = 0.25 kg

g ÷ 1000 kg

Let's learn more about the conversion of units of weight from the following
examples:

Example 1: Convert a) 2 kg 340 g into grams (g)

b) 3 kg 575 into kilograms (kg)

Solution I got it!

a) 2 kg 340 g = 2 × 1000 g + 340 g 1 kg = 1000 g

So, 2 kg = 2 × 1000 g = 2000 g !!

= 2000 g +340 g

= 2340 g I also understood it!

575 1g = (1 ÷ 1000) kg or 1 kg
1000 1000
b) 3 kg 575 g = 3 kg + kg 575
So, 575 g = 1000 kg = 0.575 kg !!

= 3 kg + 0.575 kg

= 3.575 kg

Example 2: Convert 1750 into kg and g I have remembered!
Solution 1000 g = 1 kg!!

1750 g = 1000 g + 750 g

= 1 kg +750 g

= 1 kg 750 g

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Exercise - 10.4
Section A - Classwork
1. Let's tell and write how many grams (g).

a) 1 kg = b) 4 kg = c) 5 kg =

d) 0.265 kg = e) 0.325 kg = f) 3.550 kg =

2. Let's tell and write how many kilograms (kg).

a) 1000 g = b) 3000 g = c) 6000 g =

d) 215 g = e) 478 g = f) 1236 g =

3. Let's tell and write how many kilograms (kg) and grams (g).

a) 1.276 kg = kg g b) 1.036 kg = kg g

c) 2.480 kg = kg g d) 3.5 kg = kg g

4. These are the common weights that we use in our daily lives. Let's tell
and write the answer of the following questions.

a) How many 50 g weights make 200 g?

b) How many 100 g weights make 500 g?

c) How many 500 g weights make 1 kg?

d) How many 2 kg weights make 6 kg?

e) Father said that he bought 1.5 kg of vegetables. How many kilograms

and grams vegetables did he buy? kg g

f) Mother said that she bought 2.25 kg of fruits. How many kilograms and

grams of fruits did she buy? kg g

Section B

5. Let's convert the units of weight as indicated.

a) 5 kg (into g) b) 1 kg 200 g (into g)

c) 2 kg 750 g (into g) d) 3 kg 500 g (into g)

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e) 15 g (into kg) f) 125 g (into kg)
h) 2 kg 685 g (into kg)
g) 1 kg 300 g (into kg)

6. Let's convert these grams (g) into kilograms (kg) and grams (g).

a) 1250 g b) 1300 g c) 1500 g d) 1750 g

e) 2100 g f) 2460 g g) 2550 g h) 3225 g

10.8 Addition and subtraction of weights
Classwork - Exercise

1. Let's add grams (g), and regroup into kilograms (kg) and grams (g).

a) 500 g + 600 g = 1100 g = 1 kg 100 g

b) 400 g + 800 g = =

c) 600 g + 700 g = =

d) 800 g + 900 g = =

2. Let's convert kg into g, then subtract.
a) 1 kg – 200 g = 1000 g – 200 g = 800 g

b) 1 kg – 300 g = =

c) 1 kg – 250 g = =

d) 1 kg – 500 g = =

Now, let's learn more about addition and subtraction of weights from the
following examples.

Example 1: Add 3 kg 560 g + 2 kg 780 g.

Solution I understood!
560 g + 780 g = 1340 g = 1 kg 340 g
1
So, 1 kg is carried over to kg column.
3 kg 560 g
+ 2 kg 780 g
5 kg 1340 g

= 6 kg 340 g

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Let's learn this addition converting into the decimals of kg.

3 kg 560 g = 3 . 560 kg 3 kg 560 g = 3 kg + 560 kg
1000
2 kg 780 g = + 2 . 780 kg
6 . 340 kg = 3.560 kg

2 kg 780 g = 2 kg + 780 kg
1000

= 2.780 kg

Example 2: Subtract 10 kg 250 g – 4 kg 500 g

Solution: Subtracting by converting into decimal

1 kg = 1000 g 10 kg 250 g = 10.250 kg
9 1250
4 kg 500 g = – 4.500 kg
10 kg 250 g
– 4 kg 500 g 5 . 750 kg
5 kg 750 g

Exercise - 10.5

Section A - Classwork
1. Let's tell and write the sums or differences as quickly as possible.
a) 500 g + 800 g = g = kg g

b) 400 g + 750 g = g = kg g

c) 1 kg – 300 g = g – 300 g = g

d) 1 kg – 550 g = = g

Let's read the following statements carefully. Then, tell and write the
appropriate weights in the empty circles.

2. a) Priyasha has a 5 kg weight and a 1kg weight. How does she weigh 4 kg of
fruits using her balance just one time?

Fruits Weight Weight
kg 5 kg

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b) Nirjal has 5 kg weight and a 2 kg weight. How does he weigh 3 kg of
potatoes using his balance just one time?

Potatoes Weight Weight
kg 5 kg



c) Sunayana has a 10 kg weight, 1 kg weight, and a 2 kg weight. How does
she weigh 7 kg of rice using her balance just one time?

Rice Weight Weight Weight
kg kg kg



3. a) Shreyasha has only a 500 g weight. How does she weigh 1 kg 500 g of
sugar using her balance just two times?

Sugar Weight Sugar Sugar Weight
g 500 g g 500 g 500 g

b) Bishwant has only a 1 kg weight. How does he weigh 3 kg of apples using
his balance just two times?

Apples Weight Apples Apples Weight
kg 1 kg kg kg kg

c) Deejina has a 1 kg weight and a 2 kg weight. How does she weigh 7 kg of
flour using her balance just two times?

Flour weight Weight Flour Flour Weight
kg kg kg 4 kg kg kg

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Section B
4. Let's add or subtract.
a) 5 kg 700 g b) 8 kg 650 g c) 10 kg 840 g d) 15 kg 475 g

+ 3 kg 500 g + 7 kg 750 g + 6 kg 690 g + 20 kg 580 g

e) 6 kg 200 g f) 9 kg 550 g g) 12 kg 480 g h) 25 kg 640 g
– 2 kg 300 g – 7 kg 700 g – 6 kg 820 g – 13 kg 960 g

5. Let's convert into the decimal of kilogram, then add or subtract.

a) 4 kg 360 g + 2 kg 790 g b) 7 kg 580 g + 7 kg 840 g

c) 11 kg 720 g + 8 kg 675 g d) 24 kg 900 g + 35 kg 750 g

e) 8 kg 310 g – 3 kg 750 g f) 15 kg 500 g – 8 kg 880 g

g) 20 kg 630 g – 10 kg 570 g h) 36 kg 485 g – 14 kg 655 g

Let's read these problems carefully and solve them.

6. a) Mrs. Kandel bought 2 kg 500 g of cabbage and 3 kg 750 g of potatoes.
Find the total weight of vegetables she bought.

b) Mr. Tharu sold 10 kg 250 g of mangoes yesterday and 15 kg 950 g of
mangoes today. Find the total weight of mangoes he sold in two days.

c) The weight of an empty bag is 275 g. What is the weight of the bag when
it is filled with 4 kg 975 g of potato chips?

d) In a hostel, 5 kg 400 g of rice is consumed at the lunch time and
1 kg 850 g more rice is consumed on the dinner time. How much rice is
consumed at the dinner time?

7. a) A shopkeeper sold 12 kg 600 g of vegetables in the morning and
16 kg 450 g of vegetables in the evening. How much more vegetables did
she sell in the evening?

b) A kangaroo and her joey together have a weight of 72 kg 280 g. If the
mother kangaroo has a weight of 64 kg 540 g, what is the weight of the
joey?

c) The weight of Mr. Motu is 82 kg 510 g and the weight of Mr. patlu is
30 kg 920 g less than the weight of Mr. Motu. Find the weight of Mr. Patlu.

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d) Before starting regular cycling Mr. Shrestha had 78 kg 225 g of weight.
After regular cycling for 6 months, he is able to reduce his weight by
7 kg 500 g. How much is his weight now?

It's your time - Project work!

8. a) Let's measure the weight of your empty bag using any type of balance
available in your school. Also find the weight of each of your textbook,
exercisebook, box, water bottle, etc.

(i) Find the total weight of bags and other items you carry everyday
while coming to school.

(ii) Compare this total weight to your friends' total weight of bags and
other items.

b) Let's make a group of 5 friends of your class. Measure your weights using
a dial balance or a digital balance. Find the difference of your weight
with the weights of your 4 other friends.

9. a) Let's ask your parents about the estimated quantity of rice that your
family consume in the morning meal and at the dinner. How much rice
does your family consume in (i) 1 day (ii) 7 days (iii) 30 days?

b) Do you know a cup of white rice contains about 53.5 g of carbohydrate?
How much carbohydrate do you consume (i) in 1 day (ii) in 1 month
(iii) in 1 year?

10.9 Measurement of capacity
Classwork - Exercise

1. Let's choose and circle the better estimate: how much liquid do these
vessels may hold?

a) 3 litres b) 4 litres c) 1 litre
5 liters
300 milliliters 400 milliliters

d) e) f)

100 millilitres 75 millilitres 200 litres
1 litre 750 millilitres 20 litres

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2. Let's tell and write the names of any three pairs of vessels; one holds
more liquid and another holds less liquid.

a) A holds more liquid than a

b) A holds less liquid than a

c) A holds more liquid than a

The amount of liquid that a vessel can hold
when it is filled completely is called the

capacity of the vessel.
We use litre (l) to measure the higher

capacity and millilitre (ml) to measure the
less capacity.

We use standard jars of different capacities to measure liquids in litres and
millilitres.

10.10 Conversion of units of capacity

Let's remember the following relationship between litre (l) and
millilitre (ml) .

1 l = 1000 ml 1000 ml = 1 l
2 l = 2 × 1000 ml = 2000 ml
3 l = 3 × 1000 ml = 3000 ml 1 ml = 1 l = 0.001 l
And so on... 1000

l × 1000 ml 55 ml = 55 l = 0.055 l
1000

750 ml = 0.750 l = 0.75 l

And so on... litre
ml ÷ 1000

Let's learn more about the conversion of units of capacity from the following
examples:

Example 1: Convert a) 1 l 250 ml into millilitres (ml) I've remembered!
1 l = 1 × 1000 ml !!
b) 2 l 180 ml into litres (l)

Solution

a) 1 l 250 ml = 1 × 1000 ml + 250 ml

= 1000 ml + 250 ml = 1250 ml

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b) 2 l 180 ml into litres (l) = 2 l + 180 l I got it!
1000
1 ml = (1 ÷ 1000) l or 1 l
1000
= 2 l + 0.180 l 180
So, 180 ml = 1000 l = 0.180 l !!

= 2.180 l = 2.18 l

Example 2: Convert 2225 ml into l and ml. I've remembered!
Solution 1000 ml = 1 l
2225 ml = 2000 ml + 225 ml 2000 ml = 2 l !!

= 2 l + 225 ml

= 2 l 225 ml

Exercise - 10.6

Section A - Classwork

1. Let's tell and write: how many millilitres (ml).

a) 1 l = b) 5 l = c) 0.180 l =

d) 0.75 l = e) 0.325 l = f) 1.240 l =

2. Let's tell and write: how many litres (l).

a) 1000 ml = b) 4000 ml = c) 325 ml =

d) 650 ml = e) 1436 ml = f) 2550 ml =

3. Let's tell and write: how many litres (l) and millilitres (ml).

a) 1.175 l = l ml I know it.
b) 2.240 l = l ml 3.5 l means 3.500 l.
c) 3.5 l = l ml It is 3 l 500 ml !!

d) 4.75 l = l ml

e) Father said that he bought 2.5 l of milk. How many liters and millilitres
of milk did he buy? l ml.

f) Science teacher said that the average adult has bout 4.85 l of blood
circulating inside their body. It is l ml.

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Section B

4. Let's convert the units of capacity as indicated.

a) 6 l (into ml) b) 1 l 300 ml (into ml)

c) 2 l 220 ml (into ml) d) 3 l 450 ml (into ml)

e) 36 ml (into l) f) 275 ml (into l)

g) 1 l 180 ml (into l) h) 4 l 625 ml (into l)

5. Let's convert millilitres (ml) into litres (l) and millilitres.

a) 1150 ml b) 1500 ml c) 1890 ml d) 2475 ml

e) 2700 ml f) 3225 ml g) 3570 ml h) 4180 ml

10.11 Addition and subtraction of capacities
Classwork - Exercise

1. Let's add millilitres (ml) and regroup into litres (l) and millilitres (ml).

a) 400 ml + 800 ml = 1200 ml = 1 l 200 ml

b) 500 ml + 600 ml = =
c) 750 ml + 700 ml = =

2. Let's convert l into ml, then subtract.

a) 1 l – 100 ml = 1000 ml – 100 ml = 900 ml

b) 1 l – 300 ml = =

c) 1 l – 600 ml = =

Now, let's learn more about addition and subtraction of capacities from the
following examples.

Example 1: Add 2 l 450 ml + 5 l 870 ml

Solution 450 ml I got it!
870 ml 450 ml + 870 ml = 1320 ml = 1 l 320 ml
1
So, 1 l is carried over to l column.
2 l

+ 5 l

7 l 1320 ml
= 8 l 320 ml

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Let's learn this addition converting into the decimals of l.

2 l 450 ml = 2 . 450 l 2 l 450 ml = 2 l + 450 l = 2.450 l
1000
5 l 870 ml = + 5 . 870 l
5 l 870 ml = 5 l + 870 l = 5.870 l
1000
8 . 320 l

Example 2: Subtract 12 l 300 ml – 7 l 650 ml
Solution:

1 l = 1000 ml Subtraction by converting into decimal
11 1300 12 l 300 ml = 12.300 l

12 l 300 ml

– 7 l 650 ml 7 l 650 ml = – 7.650 l

4 l 650 ml 4 . 650 l

Exercise - 10.7

Section A - Classwork
1. Let's tell and write sums or differences as quickly as possible.

a) 600 ml + 500 ml = ml = l ml

b) 350 ml + 850 ml = ml = l ml

c) 1 l – 200 ml = ml – 200 ml = ml

d) 1 l – 750 ml = = ml

2. Let's tell and write the capacities of these vessels.

a) A jug is a completely filled with water by a 2l and a 1l jars.

The capacity of the jug is

b) A bottle is completely filled with juice by three 500 ml of jars.
The capacity of the bottle is

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c) A bucket is completely filled with water by a 5 l, 2 l, and 500 ml
d) of jars. The capacity of the bucket is

A glass is completely filled with milk by a 200 ml and a 50 ml of
jars. The capacity of the glass is

Section B c) 12 l 580 ml d) 25 l 760 ml
+ 7 l 850 ml + 24 l 940 ml
3. Let's add or subtract.
a) 4 l 300 ml b) 3 l 450 ml

+ 2 l 800 ml + 5 l 750 ml

e) 7 l 100 ml f) 10 l 300 ml g) 14 l 250 ml h) 27 l 840 ml

– 3 l 400 ml – 5 l 500 ml – 10 l 650 ml – 11 l 390 ml

4. Let's convert into the decimal of litres, then add or subtract.

a) 3 l 420 ml + 4 l 860 ml b) 8 l 530 ml + 6 l 970 ml

c) 20 l 355 ml + 15 l 245 ml d) 32 l 675 ml + 17 l 775 ml

e) 9 l 200 ml – 2 l 600 ml f) 18 l 350 ml – 5 l 700 ml

g) 26 l 610 ml – 11 l 450 ml h) 40 l 180 ml – 14 l 360 ml

Let's read these problems carefully and solve them.

5. a) A painter mixed 2 l 500 ml of yellow and 1 l 500 ml of blue paint to make
green paint. How many litres of green paint did he make?

b) 1 l 850 ml of juice is in a jar. When 1 l 650 ml of juice is poured into it, the
jar full. Find the capacity of the jar.

c) In an average, a cow gives 5 l 380 ml of milk in the morning and 4 l 950 ml
of milk in the evening. How much milk does the cow give in a day?

d) A tea-stall owner uses 15 l of milk and 8 l 750 ml of water to make tea
everyday. What amount of tea does she make everyday?

6. a) A motorcycle tank contains 15 l 500 ml of petrol when it is full. After
driving a certain distance 6 l 840 ml of petrol is left in the tank. How
much petrol is used up in driving?

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b) In a bucket, there is 4 l 520 ml of water. If the capacity of the bucket is
9 l 500 ml, how much more water is needed to fill up the bucket?

c) Mother had 1 l 250 ml of orange juice. She gave two glasses each of
250 ml of juice to me and to my sister.

(i) How much juice did she give us altogether?

(ii) How much juice was left with mother?

d) A dairy had 90 l of milk. It sold 55 l 250 ml of milk in the morning and
25 l 750 ml of milk in the evening.

(i) How much milk did the diary sell in a day?

(ii) How much milk was left in the dairy?

e) A doctor prescribed 10 ml of medicine in the morning and 10 ml in the
evening from a 200 ml bottle of medicine to a patient.

(i) How much medicine did the patient take everyday?
(ii) For how many days is the bottle of medicine sufficient?

It's your time - Project work!
7. Let's take a water bottle of 1 l capacity.
a) Pour as many glasses of water into the bottle as to fill it completely. Now,

estimate the capacity of the glass.
b) Pour as many cups of water into the bottle as to fill it completely. Now,

estimate the capacity of the cup.

8. a) Boys and girls of ages 8 to 12 years need 2.2 l of water everyday. Estimate
how much water do you drink

(i) on 1 day (ii) in 7 days (iii) in 30 days (1 month) (iv) in 1 year?

b) Estimate how much milk do you drink

(i) on 1 day (ii) in 30 days?

c) Estimate how much milk is used in your family

(i) on 1 day (ii) in 30 days?

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