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High School Mathematics - 2
1.2 Absolute Value of Integer

The absolute value of x is defined as the distance from x to zero on the number line. It is always greater than or equal to zero. The absolute value of x is written as |x| .

For all real numbers x :
|x| =
x, if x >= 0
-x, if x < 0

For example:
|2| = 2, since 2 >0
|-2| = 2, since -2 <0
|0|= 0

To understand what absolute value means, read the following example.

Two friends, Sally and Molly, starting from point "0", traveled a distance of 50 yards in opposite directions. If we denote the place reached by Sally by positive integer +50, then the place reached by Molly could be denoted by the negative integer -50. If we do not take the direction into consideration and try to find how far each one of them has traveled, we say that both Sally and Molly are at a distance of 50 yards from starting point "0".

The absolute value of an integer is the numerical value of the integer regardless of its sign. Therefore, the absolute value of an integer is always non-negative. The absolute value of an integer on the number line is nothing but the distance of the integer from "0" irrespective of its direction.

Therefore, in the above example, the distance traveled by either friend is the absolute value of 50. We use two vertical lines, one on either side of the integer to show its absolute value. Therefore, the absolute value of -50 is expressed by writing |-50|.

Absolute value of -50 = |-50| = 50.
Absolute value of +50 = |+50| = 50.

In general, absolute value of an integer 'a' is defined by
|a| = a if a is positive or zero.
|a| = -a if a is negative.

Examples:
1. a is a positive integer, i.e., if a=5 then |5| = 5.
2. a is negative integer, i.e., if a=-5 |-5| = -(-5) = 5.


Directions: Write the absolute value of the given integers. Also write at least 10 examples of your own.
Q 1: The absolute value of 80 is expressed by writing
%80%
@80@
#80#
|80|

Q 2: Write the absolute value of -40.
Answer:

Q 3: Solve the expression: -|-7-10|
Answer:

Q 4: Write the absolute value of 700.
Answer:

Q 5: |-50|
Answer:

Q 6: What is the absolute value of -(a+b)?
-a+b
a+b
a-b
-a-b

Q 7: The absolute value of -60 is expressed by writing
'-60'
^-60^
|-60|
!-60!

Q 8: What is the absolute value of -659?
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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