if we are not allowed to use calculator, lets make some mental gymnastics!
take into account that dividing by a fraction is the same as multiplying by its inverse, that is changing numerator and denominator from one place another:
(15/124)(230/30)/(230/124)
= (15/124)(230/30)(124/230)
here we can see that 124 is in the denominator but in the numerator as well, so we can get rid of it altogether, the same reasoning for 230, so we simplify:
= (15/1)(1/30)(1/1)
= 15/30
= 1/2
that is the final result