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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
Equations
   
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Variables and Expressions

After completing this lesson, you will be able to:

  • Evaluate expressions using the order of operations

In mathematics, we use the order of operations to perform mathematical operations. Always follow this order when performing operations:

  1. Simplify within grouping symbols first. Grouping symbols include braces, \{ \} , brackets,[ ] ,and parentheses ( )
  2. Evaluate all exponents
  3. Perform all multiplication and division, left to right
  4. Perform all addition and subtraction, left to right

A good way to remember this is by the saying

Please Excuse My Dear Aunt Salley

The first letter of each word stands for:

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

 

Example 1

Evaluate

=    
  3 · 12 ÷ 4 + 9 Since we have an exponent we do that first
  36 ÷ 4 + 9 Since we have multiplication we do that next ( 3 · 12 = 36 )
  9 + 9 Since we have division we do that next ( 36 ÷ 4 = 9 )
  18 Last, we do the addition to achieve the final answer of 18

 

Example 2

Evaluate 8 + 12 ÷ 3

8 + 12 ÷ 3 =    
  8 + 4 (Divide 12 by 3)
  12 (Add 8 and 4)

 

Example 3

Evaluate

=    
  Complete the addition within the parentheses first (2 + 3)
  5(25) - 25 Evaluate the exponent
  125 - 25 Complete the multiplication ( 5 · 25 )
  100 Complete the subtraction

 

Example 4

   
  Since we are given values for a and b, we substitute first
  Complete the addition inside the parentheses
  Complete the multiplication 2 times 3 and 3 times 1
  Add 6 and 3
    Multiply (This easily done by multiplying 2 times 9and then dividing by 3)

 

Example 5

Evaluate for x = 6

   
  Substitute 6 for each x in the expression
  2 times 6 in the numerator and 6 minus 2 in the denominator
  12 plus 4
  4 16 divided by 4
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