# Subtraction of natural numbers and its properties

Unlike the sum, when subtracting two natural numbers, the first one has to be greater than the second (otherwise you do not get a natural number).

For example, you can do: $12-5$ (since $12$ is greater than $5$), but not $10-40$ (because $10$ is less than $40$).

Therefore, the subtraction does not satisfy the commutative property: we cannot change the order of the terms ina a subtraction. So, whenever we do a subtraction, we must start from the left side and proceed with the subtractions as they come.

If we have:$$10-3-2$$First we must do $10-3 = 7$ and later $7-2 = 5$.

On the other hand, the subtraction does not satisfy the associative property, that is, it is not possible to gather subtractions as please.

For example if you have:$$15-5-7-1$$this has to be done from left to right:

1. First: $15-5=10$
2. Later: $10-7=3$
3. Finally: $3-1=2$, and therefore: $15-5-7-1=2$

It is not possible, for instance, to do the subtraction $7-1$ first, then another, and so on. It has to be in order.