ABSOLUTE VALUE AND OPPOSITE INTEGERS

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.

Example 8 :

In a sailboat race series, a boat’s score indicates the number of points it is behind the winning boat. Your boat has score —18 and your friend's boat has score —23.

a. Find the absolute value score of each boat. Your boat, Your friend's boat

b. Whose boat is farther behind the winning boat?

Solution :

a) Absolute value score of your boat = |-18|

= 18

Absolute value score of your friend's score = |-23|

= 23

b) You boat is behind the winning boat and it is farther of

= 23 - 18

= 5 units

Example 9 :

Tell whether the statement is always, sometimes, or never true. Explain.

a) The absolute value of a negative number is its opposite. 

b) The absolute value of a number is less than the number.

c) The absolute value of a negative number is equal to the number.

Solution :

a) For example, Opposite of |-5| is 5. So, it is always true.

b) By finding absolute value of any number its numerical value cannot be changed. So, the given statement is never true.

c) The absolute value of a negative number is equal to its opposite. So, it is never true.

Example 10 :

Complete the statement using <, >, or =.

a) | -6| ___  4

b) 10 ____ | -10|

c) -4.5| ____ |-52|

d) 4 ____ 4

Solution :

a) | -6| ___  4 ==> 6 > 4

b) 10 ____ | -10| ==> 10 = 10

c) -|4.5| ____ -|5.2| ==> -4.5 < -5.2

d) 4 ____ 4 ==> 4 = 4

Example 11 :

An oceanographer takes readings at the following positions relative to sea level:

—2.48 kilometers, —2.83 kilometers, —2.70 kilometers, and —2.15 kilometers.

Order the positions from farthest from sea level to closest to sea level.

Solution :

|-2.48| = 2.48

|-2.83| = 2.83

|-2.70| = 2.7

|-2.15| = 2.15

Arranging the values from greatest to least,

2.83, 2.7, 2.48, 2.15

Example 12 :

The position of a deep sea probe is 23 fathoms relative to sea level. After finishing taking data, it moves to 22 fathoms relative to sea level. Which was deeper, the first mission or the second?

Solution :

Distance between the first position from sea level

= 23

Distance between the second position from the second level

= 22

So, the first position is deeper.

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