In mathematics, absolute value is a worth that defines the given number"s distance ~ above the number heat from 0. The absolute worth of a number is always positive even if the number is negative. That is additionally known as the numerical worth or the size of the offered number.

You are watching: Why is absolute value always positive

In this article, we room going to learn around the meaning of pure value, the symbol of pure value, and the properties of pure value.

1.Meaning of pure Value
2.Absolute worth Symbol
3.Absolute worth Functions
4.Solved Examples 
5.Practice Questions 
6.FAQs on absolute Values

Meaning of absolute Value


The absolute value of a number or essence is the distance of the number from zero, in a number heat irrespective of the direction. It is the street from 0 and is expressed together a positive integer. The symbol offered to stand for an pure value are vertical bars, i.e., |x| wherein x is one integer. The street on the number heat from the origin is always a non-negative quantity. For example: the absolute value of 4 is composed as |4| and the absolute of -4 is additionally written as |4|.

The following number represents the absolute value of the integer 4 native the beginning 0 on a number line. Irrespective of the direction, the absolute worth of the integer is always positive. 

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Absolute worth Symbol


To represent the absolute value of a number x (or a variable), we write a upright bar ~ above either side of the number, i.e., |x|, where x is an integer and also is pronounce as mod x or Modulus the x. Words modulus is a Latin native that method measure. Due to the fact that the absolute value is the street of a number indigenous the beginning it can display both an unfavorable and confident numbers. If the integer is confident then the absolute value will it is in a positive number. If the number is negative, also then the absolute worth of this number will certainly be a hopeful number. Because that example, the absolute worth of 7 is composed as |7| and the absolute value of -7 is composed as |-7|. This method that the absolute value of any type of number deserve to never be negative because the distance is never represented in a an adverse form. Hence, |7| = 7 and also |-7| = 7 

The following figure represents just how the absolute worth is the exact same for the hopeful and an adverse numbers. 

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Absolute value Functions 


If x is a genuine number, the absolute worth will meet the adhering to functions:

| x | = x, if x ≥ 0

| x | = – x, if x

Solved Examples


Example 1: Megan desires to find the worths of the following. Deserve to you assist her making use of the meaning of pure value?

a) |-13/15|

b) - |- 3|

c) |2(-3) +4 |

Solution: 

We know that the absolute value of a number is always positive.

Thus,

a) |-13/15| = 13/15

b) - | - 3| = -3

c) |2(-3) +4 | = |-6 +4| = |-2| = 2


Show solution >

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FAQs on absolute Value


What is an absolute Value?

The absolute worth of a number or essence is the distance that the given number from zero, in a number line, irrespective of the direction. It is always expressed together a optimistic integer.The symbol offered to stand for an pure value are vertical bars, i.e., |x| whereby x is an integer. Because that example: the absolute value of 6 is created as |6|, and also the absolute value of -6 is additionally written as |6|.

Why is the pure Value always Positive?

Absolute value means the street of the number indigenous the beginning 0. The number stood for on a number line have the right to be negative but the absolute value is constantly positive since the street is never ever negative. Because that example: the absolute worth of -9 is 9 which means that the street from the number -9 to the beginning 0 is 9 units on a number line. 

What is the One Basic Rule that an absolute Value?

The straightforward rule of an absolute value states that the absolute worth of any kind of number is constantly positive. If the number is a hopeful integer, the absolute worth of the number is positive, i.e., |15| = 15. If the number is a negative integer, even then, the absolute worth is positive, i.e., |-20| = 20.

What is the Absolute worth of 10?

The absolute worth of 10 is 10 itself. The is written as |10| = 10.

See more: How To Add Fractions On Ti-84 Plus, How To Work With Fractions On The Ti

What is the Absolute value of |-11|?

The absolute value of |-11| is 11 due to the fact that absolute worth is never negative. If the given number is negative, its absolute value is expressed together the number without the an adverse sign.