Page 20 - Maths Skills - 8

18 Maths

Additive Identity
Consider the following.


3 3 3 and − 2 + =+ −  2  =− 2
00

00
7 7 7 5   5 5
As is clear from the above examples, when 0 is added to any rational number, it leaves the rational number
unaltered. Therefore, zero (0) is called the identity for addition or additive identity of rational numbers.

In general, for any rational number a, a + 0 = 0 + a = a

Additive Inverse
For every rational number a, there is a rational number – a such that

a + (– a) = – a + a = 0

p +  − p = − p + p = 0, where, a = p
or

q   q  q q q
− p p p − p
Here, is termed as the additive inverse of . Also is the additive inverse of .
q q q q
Look at the following example of additive inverse.

5 5 5 ( 5)
7 7 7 0
Multiplicative Identity
Consider the following expressions.

3 3
11

2 2 2
When 1 is multiplied by any rational number, it leaves the rational number unaltered. One (1) is the identity of
multiplication or multiplicative identity of rational numbers.

In general, for any rational number a,
a × 1 = 1 × a = a

Multiplicative Inverse
p
For a given rational number , if there exists another rational number r such that p r 1, then r is called the
s
q q s s
p r p p r
multiplicative inverse or reciprocal of . If s is the reciprocal of , then q is the reciprocal of . In other words,
s
q
q

they are both inverses or reciprocals of each other.
Here are two examples of multiplicative inverse.

9 5 2 7
1, 1
5 9 7 2