# 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.