## Ncert Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.3:-

**Exercise 11.3**Ā Class 6 maths NCERT solutions Chapter 11 Algebra pdf download:-

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### Ncert Solution for Class 6 Maths Chapter 11 Algebra Exercise 11.3 Tips:-

**Expressions with Variables**

Recall that in arithmetic we have come across expressions like (2 Ć 10) + 3,

3 Ć 100 + (2 Ć 10) + 4 etc. These expressions are formed from numbers like 2,

3, 4, 10, 100 and so on. To form expressions we use all the four number

operations of addition, subtraction, multiplication and division. For example,

to form (2 Ć 10) + 3, we have multiplied 2 by 10 and then added 3 to the

product. Examples of some of the other arithmetic expressions are :

3 + (4 Ć 5), (ā 3 Ć 40) + 5,

8 ā (7 Ć 2), 14 ā (5 ā 2),

(6 Ć 2) ā 5, (5 Ć 7) ā (3 Ć 4),

7 + (8 Ć 2) (5 Ć 7) ā (3 Ć 4 ā 7) etc.

Expressions can be formed from variables too. In fact, we already have

seen expressions with variables, for example, 2n, 5m, x + 10, x ā 3 etc. These

expressions with variables are obtained by operations of addition, subtraction,

multiplication and division on variables. For example, the expression 2n is

formed by multiplying the variable n by 2; the expression (x + 10) is formed

by adding 10 to the variable x and so on.

We know that variables can take different values; they have no fixed

value. But they are numbers. That is why as in the case of numbers,

operations of addition, subtraction, multiplication and division can be

done on them.

One important point must be noted regarding the expressions

containing variables. A number expression like (4 Ć 3) + 5 can be

immediately evaluated as (4 Ć 3) + 5 = 12 + 5 = 17

But an expression like (4x + 5), which contains the variable x, cannot

be evaluated. Only if x is given some value, an expression like (4x + 5) can

be evaluated. For example,

when x = 3, 4x + 5 = (4 Ć 3) + 5 = 17 as found above.

ExpressionĀ Ā Ā Ā Ā Ā Ā Ā How formed?

(a) y + 5Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā 5 added to y

(b) t ā 7Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā 7 subtracted from t

(c) 10 aĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā a multiplied by 10

(d)x3Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā x divided by 3

(e) ā 5 qĀ Ā Ā Ā Ā Ā Ā Ā Ā Ā q multiplied by ā5

(f) 3 x + 2Ā Ā Ā Ā Ā Ā Ā Ā Ā first x multiplied by 3, then 2 added to the product

(g) 2 y ā 5Ā Ā Ā Ā Ā Ā Ā Ā Ā first y multiplied by 2, then 5 subtracted from the product

Write 10 other such simple expressions and tell how they have been formed.

We should also be able to write an expression through given instruction

about how to form it. Look at the following example :

Give expressions for the following :

(a) 12 subtracted from zĀ Ā z ā 12

(b) 25 added to rĀ Ā Ā Ā Ā Ā Ā Ā r + 25

(c) p multiplied by 16Ā Ā Ā Ā 16 p

(d) y divided by 8Ā Ā Ā Ā Ā Ā Ā y/8

(e) m multiplied by ā9Ā Ā Ā ā 9 m

(f) y multiplied by 10Ā Ā Ā Ā 10 y + 7

and then 7 added to

the product

(g) n multiplied by 2

andĀ 2 n ā 11

subtracted from the product

Sarita and Ameena decide to play a game of

expressions. They take the variable x and the number

3 and see how many expressions they can make. The

condition is that they should use not more than one

out of the four number operations and every

expression must have x in it. Can you help them?

Sarita thinks of (x + 3).

Then, Ameena comes up with (x ā 3).

Is (3x + 5) allowed?

Is (3x + 3) allowed?

Next, she suggests 3x. Sarita then immediately makes x3

Are these the only four expressions that they can get under the given

condition?

Next, they try combinations of y, 3 and 5. The condition is that they should

use not more than one operation of addition or subtraction and one operation

of multiplication or division. Every expression must have y in it. Check, if

their answers are right.

In the following exercise we shall look at how few simple expressions

have been formed.

y + 5, y + 3, y ā 5, y ā 3, 3y, 5y, y

3, y

5, 3y + 5,

3y ā 5, 5y + 3, 5y ā 3

Can you make some more expressions?