Please help me understand how to multiply by the reciprocal.

The reciprocal of a number is the expression of 1 over that same number. So if the number is 5, the reciprocal would be 1/5. If the number is 1/2, then the reciprocal would be 2/1 or just 2. So for any case, if x is the expression, the reciprocal would be 1/x.

The reciprocal of a number times the number itself will always be 1 (except for the reciprocal of 0... it is undefined).

Hope that helped.