NCERT Solutions For Class 6 Maths Chapter 11 Exercise 11.3
Ncert Solutions for Class 6 Maths Chapter 11 Algebra Exercise 11.3:-
Exercise 11.3 Class 6 maths NCERT solutions Chapter 11 Algebra pdf download:-
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 × 10) + 3,
3 × 100 + (2 × 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 × 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 × 5), (– 3 × 40) + 5,
8 – (7 × 2), 14 – (5 – 2),
(6 × 2) – 5, (5 × 7) – (3 × 4),
7 + (8 × 2) (5 × 7) – (3 × 4 – 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 – 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 × 3) + 5 can be
immediately evaluated as (4 × 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 × 3) + 5 = 17 as found above.
Expression How formed?
(a) y + 5 5 added to y
(b) t – 7 7 subtracted from t
(c) 10 a a multiplied by 10
(d)x3 x divided by 3
(e) – 5 q q multiplied by –5
(f) 3 x + 2 first x multiplied by 3, then 2 added to the product
(g) 2 y – 5 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 z z – 12
(b) 25 added to r r + 25
(c) p multiplied by 16 16 p
(d) y divided by 8 y/8
(e) m multiplied by –9 – 9 m
(f) y multiplied by 10 10 y + 7
and then 7 added to
the product
(g) n multiplied by 2
and 2 n – 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 – 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 – 5, y – 3, 3y, 5y, y
3, y
5, 3y + 5,
3y – 5, 5y + 3, 5y – 3
Can you make some more expressions?
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