44 MATHEMATICS

Reciprocal of a fraction

The number

2

1 can be obtained by interchanging the numerator and denominator of

1

2 or by inverting

1

2. Similarly,

3

1 is obtained by inverting

1

3.

Let us first see about the inverting of such numbers.

Observe these products and fill in the blanks :

7 1

7

 = 1^54

45

 = ---------

(^19)
9
 = ------^2
7
 ------- = 1
23
32
 =^23
32

 =
6
6 = 1 ------
5
9
 = 1
Multiply five more such pairs.
The non-zero numbers whose product with each other is 1, are called the
reciprocals of each other. So reciprocal of
5
9 is
9
5 and the reciprocal of
9
5 is
5
9. What
is the receiprocal of
1
9?
2
7?
You will see that the reciprocal of
2
3 is obtained by inverting it. You get
3
2.
THINK, DISCUSS AND WRITE
(i) Will the reciprocal of a proper fraction be again a proper fraction?
(ii) Will the reciprocal of an improper fraction be again an improper fraction?
Therefore, we can say that
1 
1
2 =
1 2
1
 = 1× reciprocal of^1
2.
3 
1
4 =
3 4
1
 = 3× reciprocal of^1
4.
3 
1
2
= ------ = ----------------------.
So, 2 
3
4
= 2 × reciprocal of
3
4

2 4
3
.
5 
2
9 = 5 × ------------------- = 5 × -------------