The recurrence $T(n)=aT(\frac{n}{b})+f(n)$ describes an algorithm that divides a problem of size $n$ into and solves them recursively.

b sub$-$problems, each of size $n.$

n sub$-$problems, each of size a$/$b$.$

b sub$-$problems, each of size n$/$a$.$

a sub$-$problems, each of size $\frac{n}{b}.$