Page 51 - SM Class 5 Inner.cdr

In all the above cases, we find that the prod uct is 1.

Note

When the product of two fractions is 1, we say that each of the fraction is the
reciprocal or the multiplicative inverse of the other.

1 1 3
The reciprocal of 3 is and the reciprocal of is = 3
3 3 1
5 7 7 5
The reciprocal of is and the reciprocal of is .
7 5 5 7
Division of fraction

To divide a fraction by a natural number, we multiply the fraction by the reciprocal
of the natural number. Similarly, to divide a natural numbers by a fraction, we

divide the natural number by the reciprocal of the fraction.
Dividing a fraction by a natural number Dividing by another fraction

3 1 4
Ex am ple 7 : Divide 4 ¸ 5. Ex am ple 8 : Di vide 3 by 3 .
6 7 5
3 27 1 4 22 19
Solution : 4 ¸ 5 = ¸ 5 Solution : 3 ¸ 3 = ¸
6 6 7 5 7 5
27 1 22 5
= ´ = ´
6 5 7 19
27 ´ 1 27 110
= = =
´
6 5 30 133

Properties of division of fractional numbers

1. When we divide a fractional number by 1, the quotient is always the
fractional number itself.

Let us con sider some ex am ples.

2 2 1 2 1 2
i. ¸ 1 = ¸ = ´ =
7 7 1 7 1 7

´
´
+
4 3 9 4 1 31 1 31 1 31 4
ii. 3 ¸ 1 = ¸ = ´ = = = 3
´
9 9 1 9 1 9 1 9 9
2. When we divide a fractional number by itself, the quotient is always 1.
Let us consider some examples.

´
3 3 3 17 3 17
i. ¸ = ´ = = 1
17 17 17 3 17 3
´
+
´
´
3 3 2 8 3 2 8 3 19 19
+
ii. 2 ¸ 2 = ¸ = ¸
8 8 8 8 8 8
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