NCERT Class 6 Mathematics Text book for Blind Students made Screen Readable by Professor T K Bansal.

Recall that in arithmetic we have come across expressions like (2 × 10) + 3; 3 × 100 + (2 × 10) + 4 etc. These expressions are formed from pure 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 performed 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.

The following table lists some expressions containing variables, and the situations under which they are formed.

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 :

Sarita and Anita 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, Anita comes up with (x − 3). 
Next she suggests 3x.
Sarita then immediately makes x/3.

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.

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?

In the following exercise we shall look at how few simple expressions have been formed.

EXERCISE 11.3

Q1. Make up as many expressions with numbers (no variables) as you can from three numbers 5, 7 and 8. Every number should be used not more than once. Use only addition, subtraction and multiplication.

Start of blue box

(Hint: Three possible expressions are
5 + (8 − 7),
5 − (8 − 7),
(5 × 8) + 7;
make the other expressions.)

End of blue box

Q2. Which out of the following are expressions with numbers only?
(a) y + 3
(b) (7 × 20) − 8z
(c) 5 (21 − 7) + 7 x 2
(d) 5
(e) 3x
(f) 5−5n
(g) (7 x20) − (5 x 10)−45 +p

Q3. Identify the operations (addition, subtraction, division, multiplication) in forming the following expressions and tell how the expressions have been formed.
(a) z + 1, z−l, y + 17, y−17
(b) 17y, y/17 ,5z
(c) 2y+17, 2y−17
(d) 7 m,−7 m + 3,−7 m−3

Q4. Give expressions for the following cases.
(a) 7 added to p
(b) 7 subtracted from p
(c) p multiplied by 7
(d) p divided by 7
(e) 7 subtracted from − m
(f) − p multiplied by 5
(g) − p divided by 5
(h) p multiplied by − 5

Q5. Give expressions in the following cases.
(a) 11 added to 2m
(b) 11 subtracted from 2m
(c) 5 times y to which 3 is added
(d) 5 times y from which 3 is subtracted
(e) y is multiplied by − 8
(f) y is multiplied by − 8 and then 5 is added to the result
(g) y is multiplied by 5 and the result is subtracted from 16
(h) y is multiplied by − 5 and the result is added to 16.

Q6.
(a) Form expressions using t and 4. Use not more than one number operation. Every expression must have t in it.
(b) Form expressions using y, 2 and 7. Every expression must have y in it. Use only two number operations. These should be different.