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2. Associative property: We know that the numbers hold the associative property of addition
and of multiplication. We have,

2 + (3 + 5) = 2 + 8 = 10 Or (2 + 3) + 5 = 5 + 5 = 10
⇒ 2 + (3 + 5) = (2 + 3) + 5 = 10 (Associative property of addition)
Also, 2 × (3 × 5) = 2 × 15 = 30

Or (2 × 3) × 5 = 6 × 5 = 30
⇒ 2 × (3 × 5) = (2 × 3) × 5 = 60 (Associative property of multiplication)

Similarly, variables also hold the associative property of addition and multiplication.
Let x, y and z be three variables which represent three unknown quantities.

Therefore, x + (y + z) = (x + y) + z and x × (y × z) = (x × y) × z or x(yz) = (xy)z
3. Distributive Property: We know that the numbers hold distributive property over addition
and subtraction.

Suppose, 7 × 39 = 273
Or 7 × 39 = 7 × (30 + 9) = 7 × 30 + 7 × 9 = 210 + 63 = 273
\ 7 × 39 = 7 × (30 + 9) = 7 × 30 + 7 × 9 (Distributive property over addition)

Similarly, 7 × 39 = 273
Or 7 × 39 = 7× (40 – 1) = 7 × 40 – 7 × 1 = 280 – 7 = 273

\ 7 × 39 = 7 × (40 – 1) = 7 × 40 – 7 × 1 (Distributive property over subtraction)
Similarly, variables also hold the distributive property over addition and subtraction.

Let x, y and z be three variables which represent three unknown quantities.
Therefore, x × (y + z) = x × y + x × z and x × (y – z) = x × y – x × z

Constant and Variables

Every numeral has a specific value such value is same everywhere in all situations that are
unchanged. These numerals are called constants.

1
For example: 5, –7, , etc. are constants.
2
On the other hand, laterals which represent unknown quantities may have different values in
different situations, that is, the values of laterals are not fixed. So, these are called variables.

For example: x, y, z, a, b, c, u, etc. are variables.

Example 6: Identify the constants and variables in the following:
(a) 8 (b) –9 (c) z (d) x
1
(e) a (f) (g) xy (h) 0
2
lm 1
(i) (j) –
n 2

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