Question

Give an example of why division is not commutative.

Answer 1

No, division is not commutative, because a/b does not necessarily equal b/a.

A simple proof by counter-example:

Assuming a = 10 and b = 5, we test the property of commutativity with:

10/5 = 2
5/10 = 0.5.

This is an example of division failing to be commutative. In general, for a/b to equal b/a, a must equal b. For all other pairs (a,b) the property fails.

Answer 2

There is no commutative property of division. Commutative means to exchange places of numbers. If you exchange the place of numbers in a division problem, you would affect the answer.