Absolute Value :
Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies.
The absolute value of a number is never negative. The absolute value of -5 is 5.
Opposite Integers :
The number which are having same numerical value but opposite signs are know as opposite integers. For example opposite integer of -5 is +5. That is they have same value but different signs.
When we add a number with its opposite integer, we will get zero.
Example 1 :
Find the absolute value of |-4|
Solution :
When we look at the number line, -4 is 4 units from 0.
Since -4 is 4 units from 0, we say that the absolute value of "-4" is 4.
Hence, the value of |-4| = 4.
Example 2 :
Find the absolute value of |8|
Solution :
When we look at the number line, 8 is 8 units from 0.
Since 8 is 8 units from 0, we say that the absolute value of "8" is 8.
Hence, the value of |8| = 8.
Example 3 :
Find the absolute value of |-7|
Solution :
When we look at the number line, -7 is 7 units from 0.
Since -7 is 7 units from 0, we say that the absolute value of "-7" is 7.
Hence, the value of |-7| = 7.
Example 4 :
Find the absolute value of |-1|
Solution :
When we look at the number line, -1 is 1 units from 0.
Since -1 is 1 unit from 0, we say that the absolute value of "-1" is 1.
Hence, the value of |-1| = 1.
Example 5 :
Find the opposite integer of -46
Solution :
Opposite integer means, the numerical value must be same, but different in signs.
Hence, the opposite integer of -46 is 46.
Example 6 :
Find the opposite integer of 6
Solution :
Opposite integer means, the numerical value will be same, but different in signs.
Hence, the opposite integer of 6 is -6.
Example 7 :
Jane completes several example problems that ask her to the find the opposite of the opposite of a number, and for each example, the result is a positive number. Jane concludes that when she takes the opposite of the opposite of any number, the result will always be positive. Is Jane correct? Why or why not?
Solution :
She is not correct. The opposite of the opposite of a number is the number itself. So, if Jane starts with a negative
number, she will end with a negative number.
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