	Algebra Tutorials!

Thursday 21st of November



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	Rotating a Parabola
	Multiplying Fractions
	Finding Factors
	Miscellaneous Equations
	Mixed Numbers and Improper Fractions
	Systems of Equations in Two Variables
	Literal Numbers
	Adding and Subtracting Polynomials
	Subtracting Integers
	Simplifying Complex Fractions
	Decimals and Fractions
	Multiplying Integers
	Logarithmic Functions
	Multiplying Monomials
	Mixed
	The Square of a Binomial
	Factoring Trinomials
	The Pythagorean Theorem
	Solving Radical Equations in One Variable
	Multiplying Binomials Using the FOIL Method
	Imaginary Numbers
	Solving Quadratic Equations Using the Quadratic Formula
	Solving Quadratic Equations
	Algebra
	Order of Operations
	Dividing Complex Numbers
	Polynomials
	The Appearance of a Polynomial Equation
	Standard Form of a Line
	Positive Integral Divisors
	Dividing Fractions
	Solving Linear Systems of Equations by Elimination
	Factoring
	Multiplying and Dividing Square Roots
	Functions and Graphs
	Dividing Polynomials
	Solving Rational Equations
	Numbers
	Use of Parentheses or Brackets (The Distributive Law)
	Multiplying and Dividing by Monomials
	Solving Quadratic Equations by Graphing
	Multiplying Decimals
	Use of Parentheses or Brackets (The Distributive Law)
	Simplifying Complex Fractions 1
	Adding Fractions
	Simplifying Complex Fractions
	Solutions to Linear Equations in Two Variables
	Quadratic Expressions Completing Squares
	Dividing Radical Expressions
	Rise and Run
	Graphing Exponential Functions
	Multiplying by a Monomial
	The Cartesian Coordinate System
	Writing the Terms of a Polynomial in Descending Order
	Fractions
	Polynomials
	Quadratic Expressions
	Solving Inequalities
	Solving Rational Inequalities with a Sign Graph
	Solving Linear Equations
	Solving an Equation with Two Radical Terms
	Simplifying Rational Expressions
	Exponents
	Intercepts of a Line
	Completing the Square
	Order of Operations
	Factoring Trinomials
	Solving Linear Equations
	Solving Multi-Step Inequalities
	Solving Quadratic Equations Graphically and Algebraically
	Collecting Like Terms
	Solving Equations with Radicals and Exponents
	Percent of Change
	Powers of ten (Scientific Notation)
	Comparing Integers on a Number Line
	Solving Systems of Equations Using Substitution
	Factoring Out the Greatest Common Factor
	Families of Functions
	Monomial Factors
	Multiplying and Dividing Complex Numbers
	Properties of Exponents
	Multiplying Square Roots
	Radicals
	Adding or Subtracting Rational Expressions with Different Denominators
	Expressions with Variables as Exponents
	The Quadratic Formula
	Writing a Quadratic with Given Solutions
	Simplifying Square Roots
	Adding and Subtracting Square Roots
	Adding and Subtracting Rational Expressions
	Combining Like Radical Terms
	Solving Systems of Equations Using Substitution
	Dividing Polynomials
	Graphing Functions
	Product of a Sum and a Difference
	Solving First Degree Inequalities
	Solving Equations with Radicals and Exponents
	Roots and Powers
	Multiplying Numbers

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Order of Operations

When an expression contains more than one operation, we must decide which operation to carry out first. To do so, we use the following procedure.

Procedure

To Use the Order of Operations to Simplify an Expression

Step 1 Perform operations inside grouping symbols (such as parentheses), starting with the innermost set of grouping symbols.

Step 2 Simplify exponents, square roots, and absolute values.

Step 3 Multiply or divide, working in order from left to right.

Step 4 Add or subtract, working in order from left to right.

The grouping symbols referred to in Step 1 include the following:

Symol	Name	Example
( )	parentheses	6 Ã· (2 + 1) = 6 Ã· 3 = 2
[ ]	brackets	12 - [8 - (4 - 1)] = 12 - [8 - 3] = 12 - 5 = 7
	fraction bar
\| \|	absolute value	3 Â· \|1 - 5 \| = 3 Â· \|-4\| = 3 Â· 4 = 12
	radical symbol

Example 1

Find 5 - 6² Ã· 2 - (9 - 5) Â· 3

Solution	5 - 6² Ã· 2 - (9 - 5) Â· 3
Step 1 Perform operations inside grouping symbols.	= 5 - 6² Ã· 2 - 4 Â· 3
Step 2 Simplify exponents, square roots, and absolute values.	= 5 - 36 Ã· 2 - 4 Â· 3
Step 3 Multiply or divide, working in order from left to right.	= 5 - 18 - 12
Step 4 Add or subtract, working in order from left to right.	= -25

So, the result is -25.

Example 2

Find:

Solution
Step 1 Perform operations inside grouping symbols.
Step 2 Simplify exponents, square roots,and absolute values.	= 3 + 16 Ã· 2
Step 3 Multiply or divide, working in order from left to right.	= 3 + 8
Step 4 Add or subtract, working in order from left to right.	= 11

Thus, the result is 11.

Example 3

Find 20 Ã· 2 [1 - (8 - 12)]

Solution	20 Ã· 2 [1 - (8 - 12)]
Step 1 Perform operations inside grouping symbols, starting with the innermost grouping symbol.
First, simplify (8 - 12). Now simplify [1 - (-4)].	= 20 Ã· 2[1- (-4)] = 20 Ã· 2[5] = 20 Ã· 2 Â· 5
Step 2 Simplify exponents, square roots, and absolute values. There are none to simplify.
Step 3 Multiply or divide, working in order from left to right.
First, simplify 20 Ã· 2. Now simplify 10 Â· 5.	= 10 Â· 5 = 50

Therefore, the result is 50.