Chapter 1.3, Problem 60HP

To determine

To prove : Commutative property applies to division or not.

Explanation of Solution

Formula used: 

Commutative property is given by:

  $a÷b=b÷a$

Proof: 

Commutative Property:

According to commutative property an expression must give the same answer if we swap the operands. It can be applied to addition and multiplication.

Commutative property doesn’t apply to division.

This can be proved with the help of a simple example where, $a=6$ and $b=3$

Thus, $a÷b$ = $6÷3$

  $=2$

And if the values are swapped, that is

  $a=3$

  $b=6$

Thus, $a÷b=3÷6$

  $=0.4$

which is not equal to the above value

Therefore, $a÷b\ne b÷a$

Hence, it is proved that division is not commutative.