$$1$$ hour is $$60$$ minutes, and there are four $$15$$ minute intervals. So, if there are four intervals of $$15$$ minutes that add up to $$60$$, just take three of them and put them over four:
$$\cfrac{15.15.15}{15.15.15.15}=\cfrac{45}{60}$$
Or we could multiply one hour or $$60$$ minutes by $$\cfrac{3}{4}$$
$$=60\times \cfrac{3}{4}=\cfrac{60}{1}.\cfrac{3}{4}=\cfrac{60.3}{4.1}=\cfrac{180}{4}=45$$