Download VUB Mini Course Notes Absolute Value & Order... Name___________ Page one ABSOLUTE VALUE

VUB Mini Course
Notes Absolute Value & Order of Operations
Name___________
Page one
ABSOLUTE VALUE
Absolute value is the distance between zero and the given number on the number line.
Since absolute value is a distance it is never negative. However there may be a minus
sign out in front of the absolute value bars. If there is, it is understood to be a negative
one in front of the absolute value bars. Then the final answer would be negative.
Absolute value has two vertical bars as the symbol.
The absolute value of zero is zero, since we haven’t moved either left or right on the
number line. These bars act as one of the grouping symbols. Simplify inside the bars
first, before taking the absolute value of what is inside the bars.
8  11
26  4

82

 3  3

 210 
20
 20
32   9   9
 11  4
 2   64   2   64  2  62
Remember the distributive property is used continuously in Algebra.
So let’s look at a few examples.
DISTRIBUTIVE PROPERTY
ab  c   ab  ac
39x  7  27x  21
26x  5z  12x  10z
 5a11b  2   55ab  10a
Distribute the .2 to both the 3c and the 4.
.23c  4  .6c  .8
Distribute the fraction to both terms inside the parentheses.
3
4x  16  3 4x   3 16  3x  12
4
4
4
 7  7
VUB Mini Course
Notes Absolute Value & Order of Operations
Name___________
Page two
When a number is divided by zero the answer is undefined.
Zero divided by a number is zero.
Empty set or null set is a set that has no elements. The symbol for empty set is  .
This is another symbol for empty set  , but use  .
Variables are letters that can take on different values depending on the problem.
Multiplication can be shown with a dot  , or parentheses around one or both of the
numbers. Write the dot between the two numbers so it doesn’t look like the decimal.
Please don’t use the times sign, as it looks like the letter x.
Order of Operations
1.
Copy the problem.
2.
Substitution, if there are any variables in the problem substitute the given values
into the problem and simplify.
3.
Parentheses, Brackets, the Division Bar, the Absolute Value Bars, all act as
grouping symbols. Work inside the innermost one first and simplify.
4.
Simplify all roots and radicals in order from left to right.
5.
Multiply and divide in order from left to right.
6.
Add or Subtract in order from left to right.
PBMDAS
PLEASE BURY MY DEAD AUNT SALLY
PARENTHESES, POWERS& ROOTS, BRACKETS, MULTIPLICATION,
DIVISION, ADDITION, AND SUBTRACTION
PEMDAS
PLEASE EXCUSE MY DEAD AUNT SALLY
PARENTHESES, BRACKETS, EXPONENTS & ROOTS,
MULTIPLICATION,
DIVISION, ADDITION, AND SUBTRACTION
Evaluate the following when x  2
Substitution is the first step.
Substitute the given value into the problem.
Use parentheses when substituting.
2x 2  3 x  4
2 22  3 2  4
24   6  4
8  6  4  18
This problem we first simplify the exponent.
Next we do the division, and then multiplication.
The last step is the addition.
10  2  6   3 2
10  2  6  9
56  9
30  9  39
VUB Mini Course
Notes Order of Operations Page three Name_______________
When working with exponents be careful on problems where there are parentheses and
problems where there are no parentheses.
In the problem below, the base is negative three and the exponent three. The exponent
tells how many times to take the base times itself.
 33   3 3 3   27
In the problem below, the base is negative eight and the exponent is two. The exponent
tells how many times to take the base times itself.
 82   8 8  64
In the next problem the base is two, not negative two. So the answer is the additive inverse
or opposite of 16.
 24  124   116  16
In the next problem the base is four, not negative four. So the answer is the additive
inverse or opposite of 16.
 42  142   116  16
Try the following problems.
 53
 62
Let’s look at some sample problems.
 57  3    3 2
 54    9
 20  9
 29
 38
 5
  25
  32
 5  32  37
4 49  21  4 
23   26  2
6  9  42
47   25 
6  9  16
28  10
 3  16
38
 2
 19
100 
8  24 
10  2
88
12
0
0
12
3
8
5 3  2 25
 2 2  3 64
125  25 
4  4
125  10
0
135
0
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