Algebra Tutorials! Tuesday 24th of November Home 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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 Number of inequalities to solve: 23456789
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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

S - Subtraction

Example 1

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

Example 2

Evaluate 8 + 12 Ã· 3

 8 + 12 Ã· 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 Â· 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