Question

Give an example of why division is not associative.

Answer 1

Heh, you already answered your own question: division is not associative because 0.25 does not equal 4.

If you have multiple divisions, then the problem usually has one fraction bar that's clearly bigger than the others, e.g.
1
---
2
-------
4

which would be 0.5/4 = 0.125.

If you have fraction bars of the same size, e.g.

1
---
2
---
4

... then the problem is ambiguously written. You can't really tell what the answer should be, and you're fully justified in whining at any instructor that gives you such poorly formatted problems.

If everything's written out on a line, e.g.

1 / 2 / 4

... then you should do the operations in the order they're given to you. However, it's bad form to write problems that way; good mathematicians don't do it.

Hopefully that helps!

Answer 2

\[\left( 10\div5 \right)\div2\neq10\div \left( 5\div2 \right)\]