ABSOLUTE VALUE AND OPPOSITE INTEGERS

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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