Do you need **calculate the absolute value of a number**? Don't worry, we have for you a tool that will allow you to calculate the result of this function so often used in mathematics.

You only need to enter the number of the number you want **know its absolute value and press the calculate button.** to get the result you are looking for.

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## What is the absolute value of a number?

The absolute value or modulus of a real number is another number whose value corresponds to its **numerical value regardless of its sign**regardless of whether the number is positive or negative.

To denote the absolute value function or modulus, **is entered to the number between the slashes** in the following form: |-3| = 3.

Based on the above, we can define that the absolute value for an integer, rational or real number will be:

- |a| = a if the number 'a' is greater than or equal to zero (a ≥ 0).
- |-a| = a if the number 'a' is negative

By **example.**Let's calculate the absolute value of the number 5 and that of -5:

- |5| = 5
- |-5| = 5

As you can see, in both cases we have as the result of the absolute value the numerical value of the quantity, regardless of its sign. In short, we can say that the absolute value function, abs (x) =|x|, is defined as follows:

- x, if x ≥ 0
- -x, if x ≤ 0

If we plot this on a graph, we get something like this:

In the absolute value graph you can see much more clearly the properties that we will see in the next section. For example, **can never be negative** and will always take values greater than or equal to zero.

## Absolute value properties

Here are some of the main ones **properties associated with the module** of a number:

### Opposite numbers have the same absolute value

As you have seen in the previous example, the modulus of |a| = |-a|.

Let's see it with other examples:

- |4| = |-4|
- |6| = |-6|
- |8| = |-8|

### The absolute value of a product

If you have an absolute value of a product, then the result can be interpreted as **the product of the absolute values of each of the factors**. This is represented as follows:

- |a - b| = |a| - |b|

Let's see the same with a practical example:

- |-3 - 2| = |-3| - |2| = 6

### The modulus of a sum

If you have the modulus of a sum, the result will be less than or equal to the sum of the modulus of each of the addends, that is:

- |a + b| ≤ |a| + |b|

Let's see it with an example to clear up any doubts:

- |3 + (-4)| ≤ |3| + |(-4)|

|-1| ≤ |3| + |4|

1 ≤ 7

If you have any doubts about the abs(x) function, leave us a comment and we will help you clear all your doubts.

Hi can you help me with the absolute value of |1-x|. Thank you very much :D

My question is the following, I have to prove that in the set Z the following properties are satisfied:

|a+b| is less than or equal to |a+b|.

|a-b| is less than or equal to |a-b|

|a| × |b| equals |a×b|

|a| / |b| equals |a/b|

I do not understand.

please could you help me solve these exercises: a)x=/18-3/ b)/x/=9 c)x=/-7/ d) /x/=3,,,,, thanks