Absolute Values

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This chapter is all about absolute values. Absolute value is a number regardless of its sign. In other words, absolute value is only how far or how near a number is to zero.

Examples:

1. |3|= 3


2. |9| = 9


3. |-5| = 5


4. |-34| = 34


5. |0| = 0


6. - |45| = - 45


7. |-786| = 786


8. |67| = 67


9. |-1| = 1

How to do math and solve absolute value

It is easier to solve and do math when the given number is an absolute value. Think about it, you don’t have to think of the negative or positive sign of the number. Below are some of the examples in solving absolute numbers.

Addition

There are no complicated steps in mind. Just add both numbers!

Examples:

1. |4| + |5| = |9|
   = 9
2. |67| + |3| = |70| = 70
3. |45| + |8| = |53| = 53
4. |7| + |23| = |30| = 30
5. |90| + |10| = |100| = 100

Subtraction

In subtracting between absolute values, the negative and positive signs are disregarded. We only find the difference between the absolute numbers.

Example:

1. |3-8| = |5| = 5
2. |56 – 2| = |54| = 54
3. |203 – 300| = |97| = 97
4. |45| - |5| = |40| = 40
5. |78| - |23| = |55| = 55

Multiplication

In this process, the signs are also disregarded. We just multiply the numbers.

Example:

1. |8 x -9| = |72| = 72
   
2. |3 x 3| = |9| = 9
3. |25 x 3| = |75| = 75
4. |6 x 3| = |18| = 18
5. |-5 x 2| = |10| = 10
   
   
   

Evaluate the following expressions.

1. 3 |4n| + 8
   When  n= -3
   

   Solution:

   = 3 |4 (-3)| + 8
   = 3 |-12| + 8
   = 3 (12) + 8
   = 36 + 8
   = 44
   
.

2. 6 |x| * 3 |y| + 2 |x+y*z|
   When  x = -2, y = 5, z = 3
   

   Solution:

   = 6 |-2| * 3 |5| + 2 |-2+5*3|
   = 6 (s) * 3 (5) + 2 (13)
   = 12 * 15 + 26
   = 206
   
   
   

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