The set of whole numbers, represented by, includes natural numbers and excludes exclusively rational or irrational numbers. Therefore, inside the integers, there are all positive and negative numbers as long as they are not decimals. To demonstrate the distribution of whole numbers, we use the number line:
The (+3) and (-3) have the same modulus, as both are three units away from the origin
On this line are highlighted the numbers – 3 and +3. We want to check the distance of these numbers from the point zero, that we can call origin. If we consider that the spaces between one number and another have the same size, we can call this distance "one unit”. Therefore, in the drawing, each arrow represents a unit.
Analyzing the image, we see that the – 3 is three units from the origin, and that the +3 is also three units from the origin, but in the opposite direction to the – 3.
This distance of a number to the origin is called module or absolute value of a number and is represented as follows: modulus of – a = |– a| = the
. The modulus of a number will always be positive, as it represents a positive variable distance. So, let's look at some example modules:|– 3| = 3
|+ 2| = 2
| 0 | = 0
|– 9| = 9
|+10| = 10
|– a|= a
|+ a| = the
we call for opposite numbers or symmetrical those numbers that have the same modulus or absolute value, that is, those numbers that are the same distance from the origin, but in opposite directions. Therefore, we can say that:
– 2 and + 2 are opposite or symmetric
– 3 and + 3 are opposite or symmetric
+ 4 and – 4 are opposite or symmetric
+a and -a are opposite or symmetrical
And what happens when we operate opposite or symmetric numbers?
|- 4| + |+ 3| = 4 + 3 = 7
|+ 1| – |- 5| = 1 – 5 = – 4
|- 5|+|+7|-|-10| = 5 + 7 – 10 = + 2
(+4) + (– 4) = 0
(– 2) + (+ 2) = 0
If we are performing operations with the modulus or the absolute value of the numbers, it is enough that we do the calculation independently of the value of the number within the modulus. Now, if we add numbers that differ only by sign, since they are symmetrical, our sum will always result in zero.
By Amanda Gonçalves
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-modulo-ou-valor-absoluto-um-numero.htm
