OP had an ambiguous notation. One that tends to be taught in schools as the way to present a 'proper fraction' (or perhaps compound fraction, i forget, it's not important) by factoring out the integer component.

Later on in schooling, one is discouraged from using the notation because of the entirely reasonable way of interpreting it that you've used when thinking algebraicly.

It's like that Facebook shit that uses the division operator. It's ambiguous, so there is no way to be authoritative in the interpretation.