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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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Eric Smith

Eric Smith

Order of Operations

Slide Duration:

Table of Contents

I. Properties of Real Numbers
Basic Types of Numbers

30m 41s

Intro
0:00
Objectives
0:07
Basic Types of Numbers
0:36
Natural Numbers
1:02
Whole Numbers
1:29
Integers
2:04
Rational Numbers
2:38
Irrational Numbers
5:06
Imaginary Numbers
6:48
Basic Types of Numbers Cont.
8:09
The Big Picture
8:10
Real vs. Imaginary Numbers
8:30
Rational vs. Irrational Numbers
8:48
Basic Types of Numbers Cont.
10:55
Number Line
11:06
Absolute Value
11:44
Inequalities
12:39
Example 1
13:16
Example 2
17:30
Example 3
21:56
Example 4
24:27
Example 5
27:48
Operations on Numbers

19m 26s

Intro
0:00
Objectives
0:06
Operations on Numbers
0:25
Addition
0:53
Subtraction
1:33
Multiplication & Division
2:19
Exponents
3:24
Bases
4:04
Square Roots
4:59
Principle Square Roots
5:09
Perfect Squares
6:32
Simplifying and Combining Roots
6:52
Example 1
8:16
Example 2
12:30
Example 3
14:02
Example 4
16:27
Order of Operations

12m 6s

Intro
0:00
Objectives
0:06
The Order of Operations
0:25
Work Inside Parentheses
0:42
Simplify Exponents
0:52
Multiplication & Division from Left to Right
0:57
Addition & Subtraction from Left to Right
1:11
Remember PEMDAS
1:21
The Order of Operations Cont.
2:27
Example
2:43
Example 1
3:55
Example 2
5:36
Example 3
7:35
Example 4
8:56
Properties of Real Numbers

18m 52s

Intro
0:00
Objectives
0:07
The Properties of Real Numbers
0:23
Commutative Property of Addition and Multiplication
0:44
Associative Property of Addition and Multiplication
1:50
Distributive Property of Multiplication Over Addition
3:20
Division Property of Zero
4:46
Division Property of One
5:23
Multiplication Property of Zero
5:56
Multiplication Property of One
6:17
Addition Property of Zero
6:29
Why Are These Properties Important?
6:53
Example 1
9:16
Example 2
13:04
Example 3
14:30
Example 4
16:57
II. Linear Equations
The Vocabulary of Linear Equations

12m 22s

Intro
0:00
Objectives
0:09
The Vocabulary of Linear Equations
0:44
Variables
0:52
Terms
1:09
Coefficients
1:40
Like Terms
2:18
Examples of Like Terms
2:37
Expressions
4:01
Equations
4:26
Linear Equations
5:04
Solutions
5:55
Example 1
6:16
Example 2
7:16
Example 3
8:45
Example 4
10:20
Solving Linear Equations in One Variable

28m 52s

Intro
0:00
Objectives
0:08
Solving Linear Equations in One Variable
0:34
Conditional Cases
0:51
Identity Cases
1:09
Contradiction Cases
1:30
Solving Linear Equations in One Variable Cont.
2:00
Addition Property of Equality
2:10
Multiplication Property of Equality
2:43
Steps to Solve Linear Equations
3:14
Example 1
4:22
Example 2
8:21
Example 3
12:32
Example 4
14:19
Example 5
17:25
Example 6
22:17
Solving Formulas

12m 2s

Intro
0:00
Objectives
0:06
Solving Formulas
0:18
Formulas
0:26
Use the Same Properties as Solving Linear Equations
1:36
Addition Property of Equality
1:55
Multiplication Property of Equality
1:58
Steps to Solve Formulas
2:43
Example 1
3:56
Example 2
6:09
Example 3
8:39
Applications of Linear Equations

28m 41s

Intro
0:00
Objectives
0:10
Applications of Linear Equations
0:43
The Six-Step Method to Solving Word Problems
0:55
Common Terms
3:12
Example 1
5:03
Example 2
9:40
Example 3
13:48
Example 4
17:58
Example 5
23:28
Applications of Linear Equations, Motion & Mixtures

24m 26s

Intro
0:00
Objectives
0:21
Motion and Mixtures
0:46
Motion Problems: Distance, Rate, and Time
1:06
Mixture Problems: Amount, Percent, and Total
1:27
The Table Method
1:58
The Beaker Method
3:38
Example 1
5:05
Example 2
9:44
Example 3
14:20
Example 4
19:13
III. Graphing
Rectangular Coordinate System

22m 55s

Intro
0:00
Objectives
0:11
The Rectangular Coordinate System
0:39
The Cartesian Coordinate System
0:40
X-Axis
0:54
Y-Axis
1:04
Origin
1:11
Quadrants
1:26
Ordered Pairs
2:10
Example 1
2:55
The Rectangular Coordinate System Cont.
6:09
X-Intercept
6:45
Y-Intercept
6:55
Relation of X-Values and Y-Values
7:30
Example 2
11:03
Example 3
12:13
Example 4
14:10
Example 5
18:38
Slope & Graphing

27m 58s

Intro
0:00
Objectives
0:11
Slope and Graphing
0:48
Standard Form
1:14
Example 1
2:24
Slope and Graphing Cont.
4:58
Slope, m
5:07
Slope is Rise over Run
6:11
Don't Mix Up the Coordinates
8:20
Example 2
9:39
Slope and Graphing Cont.
14:26
Slope-Intercept Form
14:34
Example 3
16:55
Example 4
18:00
Slope and Graphing Cont.
19:00
Rewriting an Equation in Slope-Intercept Form
19:39
Rewriting an Equation in Standard Form
20:09
Slopes of Vertical & Horizontal Lines
20:56
Example 5
22:49
Example 6
24:09
Example 7
25:59
Example 8
26:57
Linear Equations in Two Variables

20m 36s

Intro
0:00
Objectives
0:13
Linear Equations in Two Variables
0:36
Point-Slope Form
1:07
Substitute in the Point and the Slope
2:21
Parallel Lines: Two Lines with the Same Slope
4:05
Perpendicular Lines: Slopes are Negative Reciprocals of Each Other
4:39
Perpendicular Lines: Product of Slopes is -1
5:24
Example 1
6:02
Example 2
7:50
Example 3
10:49
Example 4
13:26
Example 5
15:30
Example 6
17:43
IV. Functions
Introduction to Functions

21m 24s

Intro
0:00
Objectives
0:07
Introduction to Functions
0:58
Relations
1:03
Functions
1:37
Independent Variables
2:00
Dependent Variables
2:11
Function Notation
2:21
Function
3:43
Input and Output
3:53
Introduction to Functions Cont.
4:45
Domain
4:46
Range
4:55
Functions Represented by a Diagram
6:41
Natural Domain
9:11
Evaluating Functions
12:02
Example 1
13:13
Example 2
15:03
Example 3
16:18
Example 4
19:54
Graphing Functions

16m 12s

Intro
0:00
Objectives
0:09
Graphing Functions
0:54
Using Slope-Intercept Form
1:56
Vertical Line Test
2:58
Determining the Domain
4:20
Determining the Range
5:43
Example 1
6:06
Example 2
7:18
Example 3
8:31
Example 4
11:04
V. Systems of Linear Equations
Systems of Linear Equations

25m 54s

Intro
0:00
Objectives
0:13
Systems of Linear Equations
0:46
System of Equations
0:51
System of Linear Equations
1:15
Solutions
1:35
Points as Solutions
1:53
Finding Solutions Graphically
5:13
Example 1
6:37
Example 2
12:07
Systems of Linear Equations Cont.
17:01
One Solution, No Solution, or Infinite Solutions
17:10
Example 3
18:31
Example 4
22:37
Solving a System Using Substitution

20m 1s

Intro
0:00
Objectives
0:09
Solving a System Using Substitution
0:32
Substitution Method
1:24
Substitution Example
2:35
One Solution, No Solution, or Infinite Solutions
7:50
Example 1
9:45
Example 2
12:48
Example 3
15:01
Example 4
17:30
Solving a System Using Elimination

19m 40s

Intro
0:00
Objectives
0:09
Solving a System Using Elimination
0:27
Elimination Method
0:42
Elimination Example
2:01
One Solution, No Solution, or Infinite Solutions
7:05
Example 1
8:53
Example 2
11:46
Example 3
15:37
Example 4
17:45
Applications of Systems of Equations

24m 34s

Intro
0:00
Objectives
0:12
Applications of Systems of Equations
0:30
Word Problems
1:31
Example 1
2:17
Example 2
7:55
Example 3
13:07
Example 4
17:15
VI. Inequalities
Solving Linear Inequalities in One Variable

17m 13s

Intro
0:00
Objectives
0:08
Solving Linear Inequalities in One Variable
0:37
Inequality Expressions
0:46
Linear Inequality Solution Notations
3:40
Inequalities
3:51
Interval Notation
4:04
Number Lines
4:43
Set Builder Notation
5:24
Use Same Techniques as Solving Equations
6:59
'Flip' the Sign when Multiplying or Dividing by a Negative Number
7:12
'Flip' Example
7:50
Example 1
8:54
Example 2
11:40
Example 3
14:01
Compound Inequalities

16m 13s

Intro
0:00
Objectives
0:07
Compound Inequalities
0:37
'And' vs. 'Or'
0:44
'And'
3:24
'Or'
3:35
'And' Symbol, or Intersection
3:51
'Or' Symbol, or Union
4:13
Inequalities
4:41
Example 1
6:22
Example 2
9:30
Example 3
11:27
Example 4
13:49
Solving Equations with Absolute Values

14m 12s

Intro
0:00
Objectives
0:08
Solve Equations with Absolute Values
0:18
Solve Equations with Absolute Values Cont.
1:11
Steps to Solving Equations with Absolute Values
2:21
Example 1
3:23
Example 2
6:34
Example 3
10:12
Inequalities with Absolute Values

17m 7s

Intro
0:00
Objectives
0:07
Inequalities with Absolute Values
0:23
Recall…
2:08
Example 1
3:39
Example 2
6:06
Example 3
8:14
Example 4
10:29
Example 5
13:29
Graphing Inequalities in Two Variables

15m 33s

Intro
0:00
Objectives
0:07
Graphing Inequalities in Two Variables
0:32
Split Graph into Two Regions
1:53
Graphing Inequalities
5:44
Test Points
6:20
Example 1
7:11
Example 2
10:17
Example 3
13:06
Systems of Inequalities

21m 13s

Intro
0:00
Objectives
0:08
Systems of Inequalities
0:24
Test Points
1:10
Steps to Solve Systems of Inequalities
1:25
Example 1
2:23
Example 2
7:28
Example 3
12:51
VII. Polynomials
Integer Exponents

44m 51s

Intro
0:00
Objectives
0:09
Integer Exponents
0:42
Exponents 'Package' Multiplication
1:25
Example 1
2:00
Example 2
3:13
Integer Exponents Cont.
4:50
Product Rule for Exponents
4:51
Example 3
7:16
Example 4
10:15
Integer Exponents Cont.
13:13
Power Rule for Exponents
13:14
Power Rule with Multiplication and Division
15:33
Example 5
16:18
Integer Exponents Cont.
20:04
Example 6
20:41
Integer Exponents Cont.
25:52
Zero Exponent Rule
25:53
Quotient Rule
28:24
Negative Exponents
30:14
Negative Exponent Rule
32:27
Example 7
34:05
Example 8
36:15
Example 9
39:33
Example 10
43:16
Adding & Subtracting Polynomials

18m 33s

Intro
0:00
Objectives
0:07
Adding and Subtracting Polynomials
0:25
Terms
0:33
Coefficients
0:51
Leading Coefficients
1:13
Like Terms
1:29
Polynomials
2:21
Monomials, Binomials, Trinomials, and Polynomials
5:41
Degrees
7:00
Evaluating Polynomials
8:12
Adding and Subtracting Polynomials Cont.
9:25
Example 1
11:48
Example 2
13:00
Example 3
14:41
Example 4
16:15
Multiplying Polynomials

25m 7s

Intro
0:00
Objectives
0:06
Multiplying Polynomials
0:41
Distributive Property
1:00
Example 1
2:49
Multiplying Polynomials Cont.
8:22
Organize Terms with a Table
8:23
Example 2
13:40
Multiplying Polynomials Cont.
16:33
Multiplying Binomials with FOIL
16:48
Example 3
18:49
Example 4
20:04
Example 5
21:42
Dividing Polynomials

44m 56s

Intro
0:00
Objectives
0:07
Dividing Polynomials
0:29
Dividing Polynomials by Monomials
2:10
Dividing Polynomials by Polynomials
2:59
Dividing Numbers
4:09
Dividing Polynomials Example
8:39
Example 1
12:35
Example 2
14:40
Example 3
16:45
Example 4
21:13
Example 5
24:33
Example 6
29:02
Dividing Polynomials with Synthetic Division Method
33:36
Example 7
38:43
Example 8
42:24
VIII. Factoring Polynomials
Greatest Common Factor & Factor by Grouping

28m 27s

Intro
0:00
Objectives
0:09
Greatest Common Factor
0:31
Factoring
0:40
Greatest Common Factor (GCF)
1:48
GCF for Polynomials
3:28
Factoring Polynomials
6:45
Prime
8:21
Example 1
9:14
Factor by Grouping
14:30
Steps to Factor by Grouping
17:03
Example 2
17:43
Example 3
19:20
Example 4
20:41
Example 5
22:29
Example 6
26:11
Factoring Trinomials

21m 44s

Intro
0:00
Objectives
0:06
Factoring Trinomials
0:25
Recall FOIL
0:26
Factor a Trinomial by Reversing FOIL
1:52
Tips when Using Reverse FOIL
5:31
Example 1
7:04
Example 2
9:09
Example 3
11:15
Example 4
13:41
Factoring Trinomials Cont.
15:50
Example 5
18:42
Factoring Trinomials Using the AC Method

30m 9s

Intro
0:00
Objectives
0:08
Factoring Trinomials Using the AC Method
0:27
Factoring when Leading Term has Coefficient Other Than 1
1:07
Reversing FOIL
1:18
Example 1
1:46
Example 2
4:28
Factoring Trinomials Using the AC Method Cont.
7:45
The AC Method
8:03
Steps to Using the AC Method
8:19
Tips on Using the AC Method
9:29
Example 3
10:45
Example 4
16:50
Example 5
21:08
Example 6
24:58
Special Factoring Techniques

30m 14s

Intro
0:00
Objectives
0:07
Special Factoring Techniques
0:26
Difference of Squares
1:46
Perfect Square Trinomials
2:38
No Sum of Squares
3:32
Special Factoring Techniques Cont.
4:03
Difference of Squares Example
4:04
Perfect Square Trinomials Example
5:29
Example 1
7:31
Example 2
9:59
Example 3
11:47
Example 4
15:09
Special Factoring Techniques Cont.
19:07
Sum of Cubes and Difference of Cubes
19:08
Example 5
23:13
Example 6
26:12
IX. Quadratic Equations
Solving Quadratic Equations by Factoring

23m 38s

Intro
0:00
Objectives
0:08
Solving Quadratic Equations by Factoring
0:19
Quadratic Equations
0:20
Zero Factor Property
1:39
Zero Factor Property Example
2:34
Example 1
4:00
Solving Quadratic Equations by Factoring Cont.
5:54
Example 2
7:28
Example 3
11:09
Example 4
14:22
Solving Quadratic Equations by Factoring Cont.
18:17
Higher Degree Polynomial Equations
18:18
Example 5
20:22
Solving Quadratic Equations

29m 27s

Intro
0:00
Objectives
0:12
Solving Quadratic Equations
0:29
Linear Factors
0:38
Not All Quadratics Factor Easily
1:22
Principle of Square Roots
3:36
Completing the Square
4:50
Steps for Using Completing the Square
5:15
Completing the Square Works on All Quadratic Equations
6:41
The Quadratic Formula
7:28
Discriminants
8:25
Solving Quadratic Equations - Summary
10:11
Example 1
11:54
Example 2
13:03
Example 3
16:30
Example 4
21:29
Example 5
25:07
Equations in Quadratic Form

16m 47s

Intro
0:00
Objectives
0:08
Equations in Quadratic Form
0:24
Using a Substitution
0:53
U-Substitution
1:26
Example 1
2:07
Example 2
5:36
Example 3
8:31
Example 4
11:14
Quadratic Formulas & Applications

29m 4s

Intro
0:00
Objectives
0:09
Quadratic Formulas and Applications
0:35
Squared Variable
0:40
Principle of Square Roots
0:51
Example 1
1:09
Example 2
2:04
Quadratic Formulas and Applications Cont.
3:34
Example 3
4:42
Example 4
13:33
Example 5
20:50
Graphs of Quadratics

26m 53s

Intro
0:00
Objectives
0:06
Graphs of Quadratics
0:39
Axis of Symmetry
1:46
Vertex
2:12
Transformations
2:57
Graphing in Quadratic Standard Form
3:23
Example 1
5:06
Example 2
6:02
Example 3
9:07
Graphs of Quadratics Cont.
11:26
Completing the Square
12:02
Vertex Shortcut
12:16
Example 4
13:49
Example 5
17:25
Example 6
20:07
Example 7
23:43
Polynomial Inequalities

21m 42s

Intro
0:00
Objectives
0:07
Polynomial Inequalities
0:30
Solving Polynomial Inequalities
1:20
Example 1
2:45
Polynomial Inequalities Cont.
5:12
Larger Polynomials
5:13
Positive or Negative Intervals
7:16
Example 2
9:01
Example 3
13:53
X. Rational Equations
Multiply & Divide Rational Expressions

26m 41s

Intro
0:00
Objectives
0:09
Multiply and Divide Rational Expressions
0:44
Rational Numbers
0:55
Dividing by Zero
1:45
Canceling Extra Factors
2:43
Negative Signs in Fractions
4:52
Multiplying Fractions
6:26
Dividing Fractions
7:17
Example 1
8:04
Example 2
14:01
Example 3
16:23
Example 4
18:56
Example 5
22:43
Adding & Subtracting Rational Expressions

20m 24s

Intro
0:00
Objectives
0:07
Adding and Subtracting Rational Expressions
0:41
Common Denominators
0:52
Common Denominator Examples
1:14
Steps to Adding and Subtracting Rational Expressions
2:39
Example 1
3:34
Example 2
5:27
Adding and Subtracting Rational Expressions Cont.
6:57
Least Common Denominators
6:58
Transitioning from Fractions to Rational Expressions
9:08
Identifying Least Common Denominators for Rational Expressions
9:56
Subtracting vs. Adding
10:41
Example 3
11:19
Example 4
12:36
Example 5
15:08
Example 6
16:46
Complex Fractions

18m 23s

Intro
0:00
Objectives
0:09
Complex Fractions
0:37
Dividing to Simplify Complex Fractions
1:10
Example 1
2:03
Example 2
3:58
Complex Fractions Cont.
9:15
Using the Least Common Denominator to Simplify Complex Fractions
9:16
Both Methods Lead to the Same Answer
10:07
Example 3
10:42
Example 4
14:28
Solving Rational Equations

16m 24s

Intro
0:00
Objectives
0:07
Solving Rational Equations
0:23
Isolate the Specified Variable
1:23
Example 1
1:58
Example 2
5:00
Example 3
8:23
Example 4
13:25
Rational Inequalities

18m 54s

Intro
0:00
Objectives
0:06
Rational Inequalities
0:18
Testing Intervals for Rational Inequalities
0:38
Steps to Solving Rational Inequalities
1:05
Tips to Solving Rational Inequalities
2:27
Example 1
3:33
Example 2
12:21
Applications of Rational Expressions

20m 20s

Intro
0:00
Objectives
0:07
Applications of Rational Expressions
0:27
Work Problems
1:05
Example 1
2:58
Example 2
6:45
Example 3
13:17
Example 4
16:37
Variation & Proportion

27m 4s

Intro
0:00
Objectives
0:10
Variation and Proportion
0:34
Variation
0:35
Inverse Variation
1:01
Direct Variation
1:10
Setting Up Proportions
1:31
Example 1
2:27
Example 2
5:36
Variation and Proportion Cont.
8:29
Inverse Variation
8:30
Example 3
9:20
Variation and Proportion Cont.
12:41
Constant of Proportionality
12:42
Example 4
13:59
Variation and Proportion Cont.
16:17
Varies Directly as the nth Power
16:30
Varies Inversely as the nth Power
16:53
Varies Jointly
17:09
Combining Variation Models
17:36
Example 5
19:09
Example 6
22:10
XI. Radical Equations
Rational Exponents

14m 32s

Intro
0:00
Objectives
0:07
Rational Exponents
0:32
Power on Top, Root on Bottom
1:05
Example 1
1:37
Rational Exponents Cont.
4:04
Using Rules from Exponents for Radicals as Exponents
4:05
Combining Terms Under a Single Root
4:50
Example 2
5:21
Example 3
7:39
Example 4
11:23
Example 5
13:14
Simplify Rational Exponents

15m 12s

Intro
0:00
Objectives
0:07
Simplify Rational Exponents
0:25
Product Rule for Radicals
0:26
Product Rule to Simplify Square Roots
1:11
Quotient Rule for Radicals
1:42
Applications of Product and Quotient Rules
2:17
Higher Roots
2:48
Example 1
3:39
Example 2
6:35
Example 3
8:41
Example 4
11:09
Adding & Subtracting Radicals

17m 22s

Intro
0:00
Objectives
0:07
Adding and Subtracting Radicals
0:33
Like Terms
1:29
Bases and Exponents May be Different
2:02
Bases and Powers Must be Same when Adding and Subtracting
2:42
Add Radicals' Coefficients
3:55
Example 1
4:47
Example 2
6:00
Adding and Subtracting Radicals Cont.
7:10
Simplify the Bases to Look the Same
7:25
Example 3
8:23
Example 4
11:45
Example 5
15:10
Multiply & Divide Radicals

19m 24s

Intro
0:00
Objectives
0:08
Multiply and Divide Radicals
0:25
Rules for Working With Radicals
0:26
Using FOIL for Radicals
1:11
Don’t Distribute Powers
2:54
Dividing Radical Expressions
4:25
Rationalizing Denominators
6:40
Example 1
7:22
Example 2
8:32
Multiply and Divide Radicals Cont.
9:23
Rationalizing Denominators with Higher Roots
9:25
Example 3
10:51
Example 4
11:53
Multiply and Divide Radicals Cont.
13:13
Rationalizing Denominators with Conjugates
13:14
Example 5
15:52
Example 6
17:25
Solving Radical Equations

15m 5s

Intro
0:00
Objectives
0:07
Solving Radical Equations
0:17
Radical Equations
0:18
Isolate the Roots and Raise to Power
0:34
Example 1
1:13
Example 2
3:09
Solving Radical Equations Cont.
7:04
Solving Radical Equations with More than One Radical
7:05
Example 3
7:54
Example 4
13:07
Complex Numbers

29m 16s

Intro
0:00
Objectives
0:06
Complex Numbers
1:05
Imaginary Numbers
1:08
Complex Numbers
2:27
Real Parts
2:48
Imaginary Parts
2:51
Commutative, Associative, and Distributive Properties
3:35
Adding and Subtracting Complex Numbers
4:04
Multiplying Complex Numbers
6:16
Dividing Complex Numbers
8:59
Complex Conjugate
9:07
Simplifying Powers of i
14:34
Shortcut for Simplifying Powers of i
18:33
Example 1
21:14
Example 2
22:15
Example 3
23:38
Example 4
26:33
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Lecture Comments (5)

1 answer

Last reply by: Professor Eric Smith
Tue Aug 18, 2015 1:19 PM

Post by Terrance Goins on August 17, 2015

Evaluate if x = − 5, y = 3, and z = 2x2 − 3(y2 + 4z)
In this problem i am confused is it any error that the # 2 has disappeared from the problem shouldnt it be.
2(-5)second power -3 (3second power + 42) = ?

0 answers

Post by Mohamed Elnaklawi on April 11, 2014

Thank you! This lesson was very helpful, and you have a good way of teaching!   :-)

0 answers

Post by Professor Eric Smith on October 30, 2013

You are right, the large number is 16, but since we are taking away a smaller number 10, we will still be left with a positive number, or in this case a positive 6.

If the number were switched around, with say the larger number second like 10 - 16, then it would be -6.  Keep an eye on subtraction, the order makes a huge difference!  :^D

0 answers

Post by Asia Hassan on October 23, 2013

in example 2 the answer you told is 6  and I think it should be -6 because we are subtracting and the big number is 16 therefore and should have negative sign. I might be wrong, so plz tell me. Thanks.

Related Articles:

Order of Operations

  • The order of operations is a “road map” of what operations need to be done first in a problem.
  • The order of operations tells us to do the following
    • Work inside grouping symbols
    • Simplify exponents
    • Work on remaining multiplication and division from left to right
    • Work on remaining addition and subtraction from left to right.
  • You can memorize the order of operations by using PEMDAS. (Please Excuse My Dear Aunt Sally.)
  • When working with large fractions you can think of the numerator and denominators as their own group. In other words simplify the top and bottom of the fraction before taking care of the division that the fraction represents.

Order of Operations

6 + (72 − 33)/2
  • 6 + (49 − 27)/2
  • 6 + 22/2
  • 6 + 11
17
92 − [(4 ×7) + (32/2)]
  • 92 − [28 + 16]
  • 81 − 44
37
(√{64} − 23) ×21 + 62
  • (8 − 8) ×21 + 62
  • 0 ×21 + 36
  • 0 + 36
36
[(5 + 3 ×42 − 9)/(3 ×7 − 10)]
  • [(5 + 3 ×16 − 9)/(3 ×7 − 10)]
  • [(5 + 48 − 9)/(21 − 10)]
  • [44/11]
4
21/7 + 14 ×2
  • 3 + 14 ×2
  • 3 + 28
31
[(102 − 43)/3] ×5 − 17
  • [(100 − 64)/3] ×5 − 17
  • (36/3) ×5 − 17
  • 12 ×5 − 17
  • 60 − 17
43
Evaluate if x = − 5, y = 3, and z = 2x2 − 3(y2 + 4z)
  • ( − 5)2 − 3[(3)2 + 4(2)]
  • ( − 5)2 − 3[9 + 4(2)]
  • ( − 5)2 − 3(9 + 8)
  • ( − 5)2 − 3(17)
  • ( − 5)2 − 51
  • 25 − 51
- 26
Evaluate if x = 12, y = 6, and z = 8[(5x/6 − 5)/(y2 + 2 ×z)]
  • [((5 ×12)/6 − 5)/(62 + 2 − 8)]
  • [((60)/6 − 5)/(62 + 2 − 8)]
  • [(10 − 5)/(62 + 2 − 8)]
  • [5/(62 + 2 − 8)]
  • [5/(36 + 2 − 8)]
  • [5/(38 − 8)]
  • [5/30]
[(1)/(6)]
Evaluate if x = 2 and y = 13
[36/(14 − x3)] ×[y − 4x]
  • [36/(14 − 23)] ×[13 − 4(2)]
  • [36/(14 − 8)] ×[13 − 4(2)]
  • [36/(14 − 8)] ×[13 − 8]
  • (36/6) ×[13 − 8]
  • 6 ×[13 − 8]
  • 6 ×5
30
Evaluate if x = 2 and y = 5[(y3 − 15 ×4)/((8x + 22))]
[(5315 ×4)/((8x + 22))]
Evaluate if x = 3 and y = 5[(y3 − 15 ×4)/((9x + 22))]
  • [(53 − 15 ×4)/((9 ×3 + 22))]
  • [(125 − 15 ×4)/((9 ×3 + 22))]
  • [(125 − 60)/((9 ×3 + 22))]
  • [65/((9 ×3 + 22))]
  • [65/((27 + 22))]
[(65)/(49)]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Order of Operations

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Objectives 0:06
  • The Order of Operations 0:25
    • Work Inside Parentheses
    • Simplify Exponents
    • Multiplication & Division from Left to Right
    • Addition & Subtraction from Left to Right
    • Remember PEMDAS
  • The Order of Operations Cont. 2:27
    • Example
  • Example 1 3:55
  • Example 2 5:36
  • Example 3 7:35
  • Example 4 8:56

Transcription: Order of Operations

Welcome back to www.educator.com.0000

In this lesson we are going to take a look at the order of operations.0002

As we will see the order of operations is a great way that we can start combining numbers and figure out what we should do first.0009

This one involve things like what should we do at parentheses and exponents0015

and when should we do our multiplication, division, addition and subtraction.0020

When trying to simplify much larger expression with many different types of operations present, we have to figure out what to do first.0027

Our order of operations gives us a nice run back on what we should be doing.0037

The very first thing that we should do is work inside our grouping symbols.0042

It means if you see parentheses or brackets work inside of those first.0047

Then move on to simplifying your exponents, things raised to a power.0052

Once you have both these in care, move on to your multiplication and division.0058

If you see lots of multiplication and division next to each other, remember to work these ones from left to right.0063

Now you have to do any remaining addition and subtraction.0072

And again when it comes to which of those is more important simply work those from left to right as well.0074

One handy way that you can remember of this entire list of that is the order of operations is to remember PEMDAS.0081

PEMDAS stands for parentheses, exponents, multiplication, division, addition and subtraction.0090

Let us try it out.0096

A great way that you can remember these is Please Excuse My Dear Aunt Sally.0105

I often heard a lot of my students use that one to make sure that they came out straight.0110

Start with your parentheses and then move on to exponents.0116

Be very careful if you are using this to memorize what to do first because sometimes when using it, it looks like multiplication is more important.0120

But work these ones from left to right.0129

The same thing applies to your addition and subtraction, work those from left to right.0135

Sometimes you will deal with a larger expression that has a fraction in it.0150

Even though you might not see some grouping symbols, think of the top and bottom as their own group.0157

That means work to simplify the numerator and get everything together up there.0163

And work to simplify your denominator, get everything together down there before we continue on with the simplification process.0166

As a quick example, let us look at this slide.0173

We have (-2 × 5) + (3 × -2) / (-5-3).0176

I'm going to work on the top part as its own group, and the bottom part as its own group.0183

Let us see what does this, -2 × 5 would give me -10, 3 × -2 =-6.0191

On the bottom in that group I have that -5 -3 =-8.0202

Okay -10 - 6=-16 and on the bottom I still have a -8.0212

We worked to look inside each of those groups and simplify them using our order of operations in there.0220

I simply have a -16 / -8 and that is a 2.0226

Watch for those large fractions to play a part.0232

Let us try some examples now that we know more about the order of operations and see how we can bring these into a much simpler expression.0237

This one is ((5 - 2)2 + 1))/ -5, we also write down PEMDAS.0245

This will act as our roadmap as we are going through the problem.0257

I want to look for grouping symbols or parentheses to see where I need to start.0261

That 5 - 2 looks like a good area, we will do that first, 5 - 2 is 3.0266

The only other grouping that I'm concerned with is the top and bottom of the fraction.0278

There is only one thing on the bottom so I'm just going to now focus on the numerator.0283

I can see that I have some exponents, I have a 32 in there.0290

And now let us do that, 32 is 9, it is getting better.0294

I want to move on to my multiplication and division.0302

Looking at the top and bottom of the fraction individually I do not see any multiplication or division, I can move on.0306

Addition and subtraction, why I do have some addition on the top, I put those together to get 10/-5.0314

We are looking at 10 ÷ -5 and now I can say that my result is a -2, this one is done.0322

You can see how we move through that order of operations as our road map.0330

In this next one we want to evaluate a (-12 × -4/3) - (5 × 6) ÷ 3, let us go over the map.0338

I do not see too much in terms of grouping but I do have this group of numbers over here.0354

Let us go ahead and take care of those.0361

Inside I have (5 × 6) ÷ 3, what should I do in there? I got multiplication and division.0363

Those ones remember we are working from left to right.0370

On the left side there I have multiplication then we actually do the division.0374

5 × 6 is a 30, now do the 30 ÷ 3 and get 10.0383

We have taken care of that grouping.0394

I'm just going to copy down some these other things and then we will continue on.0396

Our grouping is done, now on to exponents.0406

I do not see any exponents here so now on to multiplication and division.0410

We will do multiplication I got a -12 × -4/3.0416

A negative × a negative would give me a positive, multiplying on the top that would be 48/3.0421

Because of my fraction there, I do have some division I could take 48 and divided by 3 = 60.0434

On to addition and subtraction 16 – 10 = 6.0444

I have completely simplified this one and I can call it done.0451

This next one I have (12 ÷ 4) × (√5 - 1).0458

Starting with my grouping symbols and parentheses, I could consider everything underneath the square root as its own little group.0469

Let us work on simplifying that, I'm writing here 5-1 is a 4,12÷ 4 × √4, taking care of the square root entirely.0475

I'm looking at 12 ÷ 4 × 2, moving on do I see any exponents? No exponents.0499

On to multiplication and division, this is that tough one.0509

It is tempting to say that multiplication is more important but it is not.0512

Simply work these guys from left to right.0516

In this case, we are going to do the division first, 12 ÷ 4 is 3.0519

Then we are actually taking that and multiply it by 2 and get 6, this one is completely simplified.0527

Let us look at our example that involves lots and lots of different things.0538

I have (8 × 4) - (32 × 5) + (2 × the absolute value of -1) / (-3 × 2/3) +10542

With so many different things in here we have to be careful in what to do first.0562

I'm dealing with a fraction here I want the top as its own group and the bottom as its own0567

and work inside each of those and try to simplify them.0572

Let us look at the top a little bit.0575

Inside of that I do not see any additional grouping symbols so I will try and do any exponents on the top.0578

I do have a 32, let us change that into a 9.0587

I have the absolute value of -1, might as well we go ahead and take care of that as well.0594

We are doing a little bit of simplifying on the top, let us see if there is any exponents in the bottom.0602

83 × 23 and change out into -3 × 8 and of course we still have the + 1.0607

Continuing on, looking at the top I do not have any additional parentheses, I do not have any additional exponents, multiplication and division.0621

A lot of multiplication on the top, 4 × 8 would give me 32, 9 × 5 =45, 2 × 1=2.0629

On to the bottom, -3 × 8=-24 and then +1, multiplication and division done.0644

On to addition and subtraction and we are going to do this from left to right.0655

I will do 32 - 45, what do we got from there?0660

Let us imagine our technique for combining numbers that have different signs.0665

I'm just subtracting here, I get a result of 13.0673

The one that is larger in absolute value is the -45 so my result is a -13.0677

Looking at the bottom-23 almost done.0685

-11 at the top divided by -23, this one is completely simplified as 11/23.0693

When dealing with multiple operations it is important that we do have a roadmap in order to get through all of these.0705

Feel free to use PEMDAS also that you keep everything in order.0711

As you use PEMDAS, if you get down to your multiplication and division then use them from left to right.0715

If you get down to your addition and subtraction, again use those from left to right.0720

Thank you for watching www.educator.com0725

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