# Absolute Value of an Integer

Absolute value of an integer is its numerical value without taking the sign into consideration.

The absolute values of -9 = 9; the absolute value of 5 = 5 and so on.

The symbol used to denote the absolute value is, two vertical lines (| |), one on either side of an integer.

Therefore, if 'a' represents an integer, its absolute value is represented by |a| and is always non-negative.

Note:

(i) |a| = a; when 'a' is positive or zero.

(ii) |a| = -a; when 'a' is negative.

Find the absolute value of the following:

(i) -76

(ii) +50

(iii) -100

Solution:

(i) -76 = |76|

(ii) +50 = |50|

(iii) -100 = |100|

Examples on absolute value of an integer:

(i) Absolute value of - 7 is written as |- 7| = 7 [here mod of - 7 = 7]

(ii) Absolute value of + 2 is written as |+ 2| = 2 [here mod of + 2 = 2]

(iii) Absolute value of - 15 is written as |- 15| = 15 [here mod of - 15 = 15]

(iv) Absolute value of + 17 is written as |+ 17| = 17 [here mod of + 17 = 17]

On a number line the number indicates the distance from 0 and the sign before the number tells us whether the distance is to the right or left of 0. For example +5 is 5 units away to the right of 0 where as -5 is 5 units away to the left of 0 on the number line. The numerical value of the unit regardless of the sign is called absolute value of an integer. The absolute value of an integer is always positive. Thus, the absolute value of 5 and -5 is 5. It is written as |5|

So, |5| = 5 and |-5| = 5

Find the mod of:

(i) |14 - 6| = |8| = 8

(ii) - |- 10| = - 10

(iii) 15 - |- 6| = 15 - 6 = 9

(iv) 7 + |- 7| = 7 + 7 = 14

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