Absolute Value
The absolute value of a variable x is represented by x which is pronounced as 'Mod x' or 'Modulus of x'. 'Modulus' is a Latin word, which means 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value represents only the numeric value and does not include the sign of the numeric value. The modulus of any vector quantity is always taken positive and is its absolute value. Also, quantities like distance, price, volume, time, are always represented as absolute values.
As an example the absolute value: +5 = 5 = 5. There is no sign assigned to absolute value. Let's learn more about the 'Absolute value' on this short page!
1.  What are Absolute Values? 
2.  What is the Absolute Value Symbol? 
3.  Absolute Value Function 
4.  FAQs 
5.  Properties of Right Triangle 
What are Absolute Values?
The absolute value of a number is its distance from 0. We know that distance is always a nonnegative quantity. Since the absolute value is a distance, the absolute value is always nonnegative. Sometimes a sign is attributed to a numeric value to signify the direction, in addition to the value. The increase or a decrease of a quantity, values above or below the mean value, profit, or loss in a transaction, is sometimes explained by assigning a positive or negative value to the numeric value. But for absolute value, the sign of the numeric value is ignored and only the numeric value is considered.
In the above figure we can observe the absolute values on the number line using the illustration. The absolute value is represented by x, and in the above illustration,  4  =  4  = 4.
What is the Absolute Value Symbol?
To represent the absolute value of a number (or a variable), we write a vertical bar on either side of the number. For example, the absolute value of 4 is written as 4. Also, the absolute value of 4 is written as 4. As we discussed earlier, the absolute value results in a nonnegative value all the time. Hence, 4=4 =4. That is, it turns negative numbers also into positive numbers. The following figure represents the absolute value symbol.
Important Notes
The following summary points help in representing the absolute values.
 The absolute value of x is represented by either x or abs(x).
 The absolute value of any number always results in a nonnegative value.
 We pronounce x as 'mod x' or 'modulus of x.'
Absolute Value Function
The absolute value function is defined as f(x) = x, { x = +x for x > 0, and x = x for x < 0} Using the definition of absolute value, we know that it always results in a nonnegative number. Thus, the graph of f(x) = x looks as follows.
From the definition of absolute value function, the value of x depending on the sign of x. x= + x. We also know that √ {x^{2}} = + x. Therefore we have √{x^{2}} =  x .
Think Tank
Now having understood the concepts and formula of absolute value, let us now think and try to answer the following two questions.
 We know that absolute value results in a nonnegative number. Then why do we have x in the above definition of Absolute Value Function?
(Hint: What is the sign of x when x<0 ? Is x= x OR x when x<0 ?)
Solved Examples on Absolute Value

Example 1: Mohan wants to find the values of the following. Shall we help her using the definition of absolute value? (I) 13/5, (II)   3, (III) 2(3) +4 .
Solution:
We know that absolute value results in nonnegative values all the time. Thus, we have the following solutions.
(I)  13/15 = 13/15
(II).  3 = (3) = 3
(III). 2(3) +4 = 6+4 = 2=2
Therefore(I)  13/15 = 13/15, (II)   3  = 3, (III) 2(3) + 4 = 2

Example 2: Ria is instructed by her teacher to solve the following absolute value equation using the definition of the absolute function. x2=4. Can we try to help her?
Solution:
The given equation is x2=4. Using the definition of the absolute value function, when we remove the absolute value sign on one side of the equation. We then get + sign on the other side. x2= + 4. This results in two equations, which we solve separately.
x  2 = +4
x = +4 + 2
x = +6
x  2 = 4
x = 4 + 2
x = 2
Therefore, the solutions of the given equation are x = 6, x = 2.

Example 3: Rohan wants to find the value of x when x>0. How can we help Rohan to find the absolute value?
Solution:
Let's help him using the definition of the absolute value function. It is given that x>0, then we have, x<0. Now, byy the definition of the absolute value function we have: x= (x) = x. Therefore, x = x.
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FAQs on Absolute Value
What is the absolute value of 11?
The absolute value of 11 is 11 because absolute value turns negative numbers into positive numbers, i.e., 11=11
What is Meant by Absolute Value?
The absolute value only gives the numeric value and does not show any sign. The absolute value of 5 is 5, and the absolute value of 3 is 3.
How Do you Find the Absolute Value of a Negative Number?
The absolute value of a negative number is also a positive value.  2 = 2. Irrespective of the sign of the numeric value, the absolute value is always positive.
What Is the Use of Absolute Value?
The absolute value is used to inform the numeric value of a quantity, irrespective of the sign of the quantity. Numerous quantities such as length, price, volume, do not signify any meaning for the sign and are written without any sign. Here the concept of absolute value is helpful to represent such quantities.
What is the Absolute Value of a Negative Integer?
The absolute value of a negative integer is also a positive value.   5 = 5. For example, the distance value is sometimes written as 5 meters, but the ve sign only means the direction, and the distance is only 5 meters.
Can the Absolute Value be Negative?
The absolute value is always positive. Even for a positive or negative value within the modulus, the absolute value is always positive. +X = X.
Can Two Different Numbers have the Same Absolute Value?
The two numbers can also have the same absolute value. For example, the two numbers 7, or +7 have the same absolute value of 7.  7 = +7 = 7.