Dividing fractions

Question

When dividing fractions, you can find the quotient by multiplying them with the second fraction reciprocated. e.g. 5/6 divided by 7/8 = 5/6 times 8/7. Why does this work?

Answer 1

Because:

If a : x = b, then what is y such that a . y = b ?

I mean express y in terms of x and you will see why it works.