Onmatu- Pre-Algebra Article

Integer numbers


At first when we start to learn about numbers we learn about natural numbers. Those are numbers we see in the nature. If you live in the city you can see from you window one (1) building, two (2) buildings, or more. If you live near to the mountian and you take a look from your window again :), you can see one tree (1), two trees (2), three trees (3), or more. So, we exactly can see what natural numbers are everywhere around us. 
Now we start to learn about integer numbers. Did you know that natural numbers are integer numbers as well?
But the set of integer numbers is quite bigger than the set of natural numbers. That is the set of natural numbers (which we denote by N) is a subset of the set of integer numbers (which we denote by Z).
On a number axis we can see that number 1 is on the right hand side from zero (0). For distance we take our unit of measure (we will denote it here by u). On the other hand, number minus - 1 is on the left hand side from 0, and the distance from 0 is again u.
The same thing happens with number 2 which is on the right hand side from 0, and the distance from zero is 2u. Of course, number - 2 is on the left hand side from 0 with the distance 2u. The same thing happens with 3, - 3, 4, - 4... and similar.
When it comes to adding integer numbers, it is very easy. But there is much of space for making mistakes. 
Let us see how we add integer numbers.
We start with those "symmetrical" numbers. 
                        - 1 + 1 = 0,
  
                         - 2 + 2 = 0.

Guess what happens when we add - 10 and 10? It is easy, we get 0.

And what if numbers are not "symmetrical".

For example, when we add
                         - 5 + 3 = - 2.
You should think about number axis, and then you go from the number - 5 and count 3 measure units (u, right?) to the right. You go to the right because it is adding. You will come exatly to the number - 2. 
One more example,
                          - 2 + 8 = 6.

That is all for this lesson, we will continue to study more about integer numbers in our future lessons. Till then, please practice by yourself and think about the questions you have :).
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