Example of why division is not associative.

The order of division determines the numerator and the denominator and this can effect the value. And example of this:

3/2 = 1.5

2/3 = 0.6667

Whereas, multiplication is not affected by the order:

2 x 3 = 6

3 x 2 = 6

2: (1:2) = 4≠1 = (2:1) : 2

Division is not associative, as if you look at one of the operands to a nest of divisions, the result will vary either in proportion to it or inversely to it depending on whether it's to the right of an odd or even number of divisions. And the basic associative law changes the number of operations the rightmost operand is to the right of by 1.