Reduced residue system

A reduced residue system is a way of counting things using numbers in base 10 (which is the same as the numbers we use every day, from 0 to 9). It's called "reduced residue" because it reduces (or simplifies) the number of different possible numbers that can be used to count things. For example, instead of having one number for each different thing you want to count, you only need two or three numbers. That makes counting things much easier.