Question

Division is not associative in rational numbers explain with an example

Answer 1

Helloo!!

No, it is not!!

Eg::

(1÷2)÷3=1/2÷3=1/6,
but
1÷(2÷3)=1÷2/3=3/2.

hope it helps!!

Answer 2

To prove:

The division is not associative in rational numbers

Solution:

• The associative property is the characteristic of rational numbers in which we obtain the same result if we compute them by interchanging their order.
• But this is not true for the division of rational numbers.
• Let us take three rational numbers a, b, and c
• Let a= $\frac{1}{4}$ ,  b= $\frac{2}{4}$ ,   c= $\frac{3}{4}$ be the rational numbers
• According to the associative property:

     => a ÷ (b ÷ c) = (a ÷ b) ÷ c

     => $\frac{1}{4}$ ÷ ($\frac{2}{4}$ ÷ $\frac{3}{4}$) = ($\frac{1}{4}$ ÷ $\frac{2}{4}$ ) ÷ $\frac{3}{4}$

     => $\frac{1}{4}$ ÷ ($\frac{2}{4}$ × $\frac{4}{3}$) = ($\frac{1}{4}$ × $\frac{4}{2}$) ÷ $\frac{3}{4}$

     =>  $\frac{1}{4}$ ÷ $\frac{2}{3}$ = $\frac{1}{2}$ ÷ $\frac{3}{4}$

     => $\frac{1}{4}$ × $\frac{3}{2}$ = $\frac{1}{2}$ × $\frac{4}{3}$

     => $\frac{3}{6}$ ≠ $\frac{2}{3}$

     => Left Hand Side ≠ Right Hand Side

Therefore, it is proved that division is not associative for rational numbers.