Explanation:
first of all, remember. when dividing by a fraction, this is the same as multiplying by the upside-down fraction.
and all these signs (including the fraction sign) stand for divisions and really do the same thing and can be exchanged with each other : "/", "÷", ":"
and when writing a number like 4 1/2, it is a shortcut and means actually (4 + 1/2).
so,
4 1/2 ÷ 1/2 = 4 1/2 × 2/1 = 4 1/2 × 2 = (8/2 + 1/2)×2 =
= 9/2 × 2 = 18/2 = 9