Where ever you feel the delightful necessity to answer mathematical problems with the inclusion of fractions. Or in you math binder i guess.
Fractions are useful. If there are no fractions,
You can't calculate 9 divided by 5, because the answer is a decimal or a fraction, people won't even think of decimals without fractions. In calculating the potential energy of a spring, you use fractions, because in my memory, the formula involves something like \(\sqrt{\dfrac{l}{g}}\).
EDIT: Oops, that is the Cycle of Simple Pendulum Formula xD.