first a reciprocal is a fraction but flipped over. So so if we have x/y, it's recipricam is y/x.
this helps to know when you understand that dividing by a fraction is the same thing as multiplying by that fractions reciprocal.
So ifnwenhave b/c and divide it by x/y we can also say b/c multiplied by y/x. it isnthensame thing.
now to use this for your problem.
5/31 divided by 15/23
or
5/31 times 23/15
all we have to do is multiple the 2 numerator and denominator and get:
115/465
now to reduce. divide both by 5 first
23/91
both numbers are prime so that would be answer