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Operations with absolute value: Problem type 1
The absolute value of a number ‘a’ is denoted as |a|
|a| = a, if a is positive
|a| = −a, if a is negative
|0| = 0
Absolute value of a number is the distance of the number on the number line from 0. The absolute value of a number is never negative.
For example, the absolute value of both 5 and −5 is 5. The absolute value of 0 is 0.
Finding absolute value of a number is like removing any negative sign in front of a number, and considering all numbers as positive.
In this lesson, we solve problems involving operations with absolute values.
Evaluate the following
|13 − 19| − |11|
Solution
Step 1:
Simplifying
|13 − 19| − |11| = |−6| − 11 = 6 – 11
Step 2:
It is a subtraction of integers problem
The signs are different. So, we take the difference of absolute values
|−11| − |6| = 11 – 6 = 5
Step 3:
The sign of the numbers with larger absolute value (−11) is −.
We keep this sign with the difference obtained in above step
So, |13 − 19| − |11| = − 5
Evaluate the following
|7 − 23| − |−6|
Solution
Step 1:
Simplifying
|7 − 23| − |−6| = |−16| − 6 = 16 – 6
Step 2:
It is a subtraction of integers problem
The signs are different. So, we take the difference of absolute values
|16| − |−6| = 16 – 6 = 10
Step 3:
The sign of the numbers with larger absolute value (16) is +.
We keep this sign with the difference obtained in above step
So, |7 − 23| − |−6| = + 10
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