So in other words when you multiply two numbers in a set of integers, or group as they are called formally, you just take their product normally and take the modulus of it, order n, assuming the group is Zn.
by definition, yes that is how modular multiplication is defined but in practice it would be very slow to perform it like this since x*y if both are n-bits would become as big as 2n-bits and then division (to find the remainder) is a slow process. instead optimized algorithms such as Montgomery is used.