  Mary Pyo

Slide Duration:

Section 1: Algebra and Decimals
Expressions and Variables

5m 57s

Intro
0:00
Vocabulary
0:06
Variable
0:09
Expression
0:48
Numerical Expression
1:08
Algebraic Expression
1:35
Word Expression
2:04
Extra Example 1: Evaluate the Expression
2:27
Extra Example 2: Evaluate the Expression
3:16
Extra Example 3: Evaluate the Expression
4:04
Extra Example 4: Evaluate the Expression
4:59
Exponents

5m 34s

Intro
0:00
What Exponents Mean
0:07
Example: Ten Squared
0:08
Extra Example 1: Exponents
0:50
Extra Example 2: Write in Exponent Form
1:58
Extra Example 3: Using Exponent and Base
2:37
Extra Example 4: Write the Equal Factors
4:26
Order of Operations

8m 40s

Intro
0:00
Please Excuse My Dear Aunt Sally
0:07
Step 1: Parenthesis
1:16
Step 2: Exponent
1:25
Step 3: Multiply and Divide
1:30
2:00
Example: Please Excuse My Dear Aunt Sally
2:26
Extra Example 1: Evaluating Expression
3:37
Extra Example 2: Evaluating Expression
4:59
Extra Example 3: Evaluating Expression
5:34
Extra Example 4: Evaluating Expression
6:25
Comparing and Ordering Decimals

13m 37s

Intro
0:00
Place Value
0:13
Examples: 1,234,567.89
0:19
Which is the Larger Value?
1:33
Which is Larger: 10.5 or 100.5
1:46
Which is Larger: 1.01 or 1.10
2:24
Which is Larger: 44.40 or 44.4
4:20
Which is Larger: 18.6 or 16.8
5:18
Extra Example 1: Order from Least to Greatest
5:55
Extra Example 2: Order from Least to Greatest
7:56
Extra Example 3: Order from Least to Greatest
9:16
Extra Example 4: Order from Least to Greatest
10:42
Rounding Decimals

12m 31s

Intro
0:00
Decimal Place Value
0:06
Example: 12,3454.6789
0:07
How to Round Decimals
1:17
Example: Rounding 1,234.567
1:18
Extra Example 1: Rounding Decimals
3:47
Extra Example 2: Rounding Decimals
6:10
Extra Example 3: Rounding Decimals
7:45
Extra Example 4: Rounding Decimals
9:56

11m 30s

Intro
0:00
0:06
Align the Decimal Point First
0:12
0:47
Place the Decimal Point in the Same Place
0:55
Check by Estimating
1:09
Examples
1:28
Add: 3.45 + 7 + 0.835
1:30
Find the Difference: 351.4 - 65.25
3:34
5:32
Extra Example 2: How Much Money?
6:09
Extra Example 3: Subtracting Decimals
7:20
9:32
Multiplying Decimals

10m 30s

Intro
0:00
Multiply the Decimals
0:05
Methods for Multiplying Decimals
0:06
Example: 1.1 x 6
0:38
Extra Example 1: Multiplying Decimals
1:51
Extra Example 2: Work Money
2:49
Extra Example 3: Multiplying Decimals
5:45
Extra Example 4: Multiplying Decimals
7:46
Dividing Decimals

17m 49s

Intro
0:00
When Dividing Decimals
0:06
Methods for Dividing Decimals
0:07
Divisor and Dividend
0:37
Example: 0.2 Divided by 10
1:35
Extra Example 1 : Dividing Decimals
5:24
Extra Example 2: How Much Does Each CD Cost?
8:22
Extra Example 3: Dividing Decimals
10:59
Extra Example 4: Dividing Decimals
12:08
Section 2: Number Relationships and Fractions
Prime Factorization

7m

Intro
0:00
Terms to Review
0:07
Prime vs. Composite
0:12
Factor
0:54
Product
1:15
Factor Tree
1:39
Example: Prime Factorization
2:01
Example: Prime Factorization
2:43
Extra Example 1: Prime Factorization
4:08
Extra Example 2: Prime Factorization
5:05
Extra Example 3: Prime Factorization
5:33
Extra Example 4: Prime Factorization
6:13
Greatest Common Factor

12m 47s

Intro
0:00
Terms to Review
0:05
Factor
0:07
Example: Factor of 20
0:18
Two Methods
0:59
Greatest Common Factor
1:00
Method 1: GCF of 15 and 30
1:37
Method 2: GCF of 15 and 30
2:58
Extra Example 1: Find the GCF of 6 and 18
5:16
Extra Example 2: Find the GCF of 36 and 27
7:43
Extra Example 3: Find the GCF of 6 and 18
9:18
Extra Example 4: Find the GCF of 54 and 36
10:30
Fraction Concepts and Simplest Form

10m 3s

Intro
0:00
Fraction Concept
0:10
Example: Birthday Cake
0:28
Example: Chocolate Bar
2:10
Simples Form
3:38
Example: Simplifying 4 out of 8
3:46
Extra Example 1: Graphically Show 4 out of 10
4:41
Extra Example 2: Finding Fraction Shown by Illustration
5:10
Extra Example 3: Simplest Form of 5 over 25
7:02
Extra Example 4: Simplest Form of 14 over 49
8:30
Least Common Multiple

14m 16s

Intro
0:00
Term to Review
0:06
Multiple
0:07
Example: Multiples of 4
0:15
Two Methods
0:41
Least Common Multiples
0:44
Method 1: LCM of 6 and 10
1:09
Method 2: LCM of 6 and 10
2:56
Extra Example 1: LCM of 12 and 15
5:09
Extra Example 2: LCM of 16 and 20
7:36
Extra Example 3 : LCM of 15 and 25
10:00
Extra Example 4 : LCM of 12 and 18
11:27
Comparing and Ordering Fractions

13m 10s

Intro
0:00
Terms Review
0:14
Greater Than
0:16
Less Than
0:40
Compare the Fractions
1:00
Example: Comparing 2/4 and 3/4
1:08
Example: Comparing 5/8 and 2/5
2:04
Extra Example 1: Compare the Fractions
3:28
Extra Example 2: Compare the Fractions
6:06
Extra Example 3: Compare the Fractions
8:01
Extra Example 4: Least to Greatest
9:37
Mixed Numbers and Improper Fractions

12m 49s

Intro
0:00
Fractions
0:10
Mixed Number
0:21
Proper Fraction
0:47
Improper Fraction
1:30
Switching Between
2:47
Mixed Number to Improper Fraction
2:53
Improper Fraction to Mixed Number
4:41
Examples: Switching Fractions
6:37
Extra Example 1: Mixed Number to Improper Fraction
8:57
Extra Example 2: Improper Fraction to Mixed Number
9:37
Extra Example 3: Improper Fraction to Mixed Number
10:21
Extra Example 4: Mixed Number to Improper Fraction
11:31
Connecting Decimals and Fractions

15m 1s

Intro
0:00
Examples: Decimals and Fractions
0:06
More Examples: Decimals and Fractions
2:48
Extra Example 1: Converting Decimal to Fraction
6:55
Extra Example 2: Converting Fraction to Decimal
8:45
Extra Example 3: Converting Decimal to Fraction
10:28
Extra Example 4: Converting Fraction to Decimal
11:42
Section 3: Fractions and Their Operations
Adding and Subtracting Fractions with Same Denominators

5m 17s

Intro
0:00
Same Denominator
0:11
Numerator and Denominator
0:18
Example: 2/6 + 5/6
0:41
Extra Example 1: Add or Subtract the Fractions
2:02
Extra Example 2: Add or Subtract the Fractions
2:45
Extra Example 3: Add or Subtract the Fractions
3:17
Extra Example 4: Add or Subtract the Fractions
4:05
Adding and Subtracting Fractions with Different Denominators

23m 8s

Intro
0:00
Least Common Multiple
0:12
LCM of 6 and 4
0:31
From LCM to LCD
2:25
3:12
Extra Example 1: Add or Subtract
6:23
Extra Example 2: Add or Subtract
9:49
Extra Example 3: Add or Subtract
14:54
Extra Example 4: Add or Subtract
18:14

19m 44s

Intro
0:00
Example
0:05
0:17
Extra Example 1: Adding Mixed Numbers
1:57
Extra Example 2: Subtracting Mixed Numbers
8:13
Extra Example 3: Adding Mixed Numbers
12:01
Extra Example 4: Subtracting Mixed Numbers
14:54
Multiplying Fractions and Mixed Numbers

21m 32s

Intro
0:00
Multiplying Fractions
0:07
Step 1: Change Mixed Numbers to Improper Fractions
0:08
Step2: Multiply the Numerators Together
0:56
Step3: Multiply the Denominators Together
1:03
Extra Example 1: Multiplying Fractions
1:37
Extra Example 2: Multiplying Fractions
6:39
Extra Example 3: Multiplying Fractions
10:20
Extra Example 4: Multiplying Fractions
13:47
Dividing Fractions and Mixed Numbers

18m

Intro
0:00
Dividing Fractions
0:09
Step 1: Change Mixed Numbers to Improper Fractions
0:15
Step 2: Flip the Second Fraction
0:27
Step 3: Multiply the Fractions
0:52
Extra Example 1: Dividing Fractions
1:23
Extra Example 2: Dividing Fractions
5:06
Extra Example 3: Dividing Fractions
9:34
Extra Example 4: Dividing Fractions
12:06
Distributive Property

11m 5s

Intro
0:00
Distributive Property
0:06
Methods of Distributive Property
0:07
Example: a(b)
0:35
Example: a(b+c)
0:49
Example: a(b+c+d)
1:22
Extra Example 1: Using Distributive Property
1:56
Extra Example 2: Using Distributive Property
4:36
Extra Example 3: Using Distributive Property
6:39
Extra Example 4: Using Distributive Property
8:19
Units of Measure

16m 36s

Intro
0:00
Length
0:05
Feet, Inches, Yard, and Mile
0:20
Millimeters, Centimeters, and Meters
0:43
Mass
2:57
Pounds, Ounces, and Tons
3:03
Grams and Kilograms
3:38
Liquid
4:11
Gallons, Quarts, Pints, and Cups
4:14
Extra Example 1: Converting Units
7:02
Extra Example 2: Converting Units
9:31
Extra Example 3: Converting Units
12:21
Extra Example 4: Converting Units
14:05
Section 4: Positive and Negative Numbers
Integers and the Number Line

13m 24s

Intro
0:00
What are Integers
0:06
Integers are all Whole Numbers and Their Opposites
0:09
Absolute Value
2:35
Extra Example 1: Compare the Integers
4:36
Extra Example 2: Writing Integers
9:24
Extra Example 3: Opposite Integer
10:38
Extra Example 4: Absolute Value
11:27

16m 5s

Intro
0:00
Using a Number Line
0:04
Example: 4 + (-2)
0:14
Example: 5 + (-8)
1:50
3:00
3:10
3:37
4:44
Extra Example 1: Add the Integers
8:21
Extra Example 2: Find the Sum
10:33
Extra Example 3: Find the Value
11:37
Extra Example 4: Add the Integers
13:10
Subtracting Integers

15m 25s

Intro
0:00
How to Subtract Integers
0:06
Two-dash Rule
0:16
Example: 3 - 5
0:44
Example: 3 - (-5)
1:12
Example: -3 - 5
1:39
Extra Example 1: Rewrite Subtraction to Addition
4:43
Extra Example 2: Find the Difference
7:59
Extra Example 3: Find the Difference
9:08
Extra Example 4: Evaluate
10:38
Multiplying Integers

7m 33s

Intro
0:00
When Multiplying Integers
0:05
If One Number is Negative
0:06
If Both Numbers are Negative
0:18
Examples: Multiplying Integers
0:53
Extra Example 1: Multiplying Integers
1:27
Extra Example 2: Multiplying Integers
2:43
Extra Example 3: Multiplying Integers
3:13
Extra Example 4: Multiplying Integers
3:51
Dividing Integers

6m 42s

Intro
0:00
When Dividing Integers
0:05
Rules for Dividing Integers
0:41
Extra Example 1: Dividing Integers
1:01
Extra Example 2: Dividing Integers
1:51
Extra Example 3: Dividing Integers
2:21
Extra Example 4: Dividing Integers
3:18
Integers and Order of Operations

11m 9s

Intro
0:00
Combining Operations
0:21
Solve Using the Order of Operations
0:22
Extra Example 1: Evaluate
1:18
Extra Example 2: Evaluate
4:20
Extra Example 3: Evaluate
6:33
Extra Example 4: Evaluate
8:13
Section 5: Solving Equations
Writing Expressions

9m 15s

Intro
0:00
Operation as Words
0:05
Operation as Words
0:06
Extra Example 1: Write Each as an Expression
2:09
Extra Example 2: Write Each as an Expression
4:27
Extra Example 3: Write Each Expression Using Words
6:45
Writing Equations

18m 3s

Intro
0:00
Equation
0:05
Definition of Equation
0:06
Examples of Equation
0:58
Operations as Words
1:39
Operations as Words
1:40
Extra Example 1: Write Each as an Equation
3:07
Extra Example 2: Write Each as an Equation
6:19
Extra Example 3: Write Each as an Equation
10:08
Extra Example 4: Determine if the Equation is True or False
13:38

24m 53s

Intro
0:00
Solving Equations
0:08
inverse Operation of Addition and Subtraction
0:09
Extra Example 1: Solve Each Equation Using Mental Math
4:15
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:44
Extra Example 3: Solve Each Equation
14:51
Extra Example 4: Translate Each to an Equation and Solve
19:57
Solving Multiplication Equation

19m 46s

Intro
0:00
Multiplication Equations
0:08
Inverse Operation of Multiplication
0:09
Extra Example 1: Use Mental Math to Solve Each Equation
3:54
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:55
Extra Example 3: Is -2 a Solution of Each Equation?
12:48
Extra Example 4: Solve Each Equation
15:42
Solving Division Equation

17m 58s

Intro
0:00
Division Equations
0:05
Inverse Operation of Division
0:06
Extra Example 1: Use Mental Math to Solve Each Equation
0:39
Extra Example 2: Use Inverse Operations to Solve Each Equation
2:14
Extra Example 3: Is -6 a Solution of Each Equation?
9:53
Extra Example 4: Solve Each Equation
11:50
Section 6: Ratios and Proportions
Ratio

40m 21s

Intro
0:00
Ratio
0:05
Definition of Ratio
0:06
Examples of Ratio
0:18
Rate
2:19
Definition of Rate
2:20
Unit Rate
3:38
Example: \$10 / 20 pieces
5:05
Converting Rates
6:46
Example: Converting Rates
6:47
Extra Example 1: Write in Simplest Form
16:22
Extra Example 2: Find the Ratio
20:53
Extra Example 3: Find the Unit Rate
22:56
Extra Example 4: Convert the Unit
26:34
Solving Proportions

17m 22s

Intro
0:00
Proportions
0:05
An Equality of Two Ratios
0:06
Cross Products
1:00
Extra Example 1: Find Two Equivalent Ratios for Each
3:21
Extra Example 2: Use Mental Math to Solve the Proportion
5:52
Extra Example 3: Tell Whether the Two Ratios Form a Proportion
8:21
Extra Example 4: Solve the Proportion
13:26
Writing Proportions

22m 1s

Intro
0:00
Writing Proportions
0:08
Introduction to Writing Proportions and Example
0:10
Extra Example 1: Write a Proportion and Solve
5:54
Extra Example 2: Write a Proportion and Solve
11:19
Extra Example 3: Write a Proportion for Word Problem
17:29
Similar Polygons

16m 31s

Intro
0:00
Similar Polygons
0:05
Definition of Similar Polygons
0:06
Corresponding Sides are Proportional
2:14
Extra Example 1: Write a Proportion and Find the Value of Similar Triangles
4:26
Extra Example 2: Write a Proportional to Find the Value of x
7:04
Extra Example 3: Write a Proportion for the Similar Polygons and Solve
9:04
Extra Example 4: Word Problem and Similar Polygons
11:03
Scale Drawings

13m 43s

Intro
0:00
Scale Drawing
0:05
Definition of a Scale Drawing
0:06
Example: Scale Drawings
1:00
Extra Example 1: Scale Drawing
4:50
Extra Example 2: Scale Drawing
7:02
Extra Example 3: Scale Drawing
9:34
Probability

11m 51s

Intro
0:00
Probability
0:05
Introduction to Probability
0:06
Example: Probability
1:22
Extra Example 1: What is the Probability of Landing on Orange?
3:26
Extra Example 2: What is the Probability of Rolling a 5?
5:02
Extra Example 3: What is the Probability that the Marble will be Red?
7:40
Extra Example 4: What is the Probability that the Student will be a Girl?
9:43
Section 7: Percents
Percents, Fractions, and Decimals

35m 5s

Intro
0:00
Percents
0:06
Changing Percent to a Fraction
0:07
Changing Percent to a Decimal
1:54
Fractions
4:17
Changing Fraction to Decimal
4:18
Changing Fraction to Percent
7:50
Decimals
10:10
Changing Decimal to Fraction
10:11
Changing Decimal to Percent
12:07
Extra Example 1: Write Each Percent as a Fraction in Simplest Form
13:29
Extra Example 2: Write Each as a Decimal
17:09
Extra Example 3: Write Each Fraction as a Percent
22:45
Extra Example 4: Complete the Table
29:17
Finding a Percent of a Number

28m 18s

Intro
0:00
Percent of a Number
0:06
Translate Sentence into an Equation
0:07
Example: 30% of 100 is What Number?
1:05
Extra Example 1: Finding a Percent of a Number
7:12
Extra Example 2: Finding a Percent of a Number
15:56
Extra Example 3: Finding a Percent of a Number
19:14
Extra Example 4: Finding a Percent of a Number
24:26
Solving Percent Problems

32m 31s

Intro
0:00
Solving Percent Problems
0:06
Translate the Sentence into an Equation
0:07
Extra Example 1: Solving Percent Problems
0:56
Extra Example 2: Solving Percent Problems
14:49
Extra Example 3: Solving Percent Problems
23:44
Simple Interest

27m 9s

Intro
0:00
Simple Interest
0:05
Principal
0:06
Interest & Interest Rate
0:41
Simple Interest
1:43
Simple Interest Formula
2:23
Simple Interest Formula: I = prt
2:24
Extra Example 1: Finding Simple Interest
3:53
Extra Example 2: Finding Simple Interest
8:08
Extra Example 3: Finding Simple Interest
12:02
Extra Example 4: Finding Simple Interest
17:46
Discount and Sales Tax

17m 15s

Intro
0:00
Discount
0:19
Discount
0:20
Sale Price
1:22
Sales Tax
2:24
Sales Tax
2:25
Total Due
2:59
Extra Example 1: Finding the Discount
3:43
Extra Example 2: Finding the Sale Price
6:28
Extra Example 3: Finding the Sale Tax
11:14
Extra Example 4: Finding the Total Due
14:08
Section 8: Geometry in a Plane
Intersecting Lines and Angle Measures

24m 17s

Intro
0:00
Intersecting Lines
0:07
Properties of Lines
0:08
When Two Lines Cross Each Other
1:55
Angles
2:56
Properties of Angles: Sides, Vertex, and Measure
2:57
Classifying Angles
7:18
Acute Angle
7:19
Right Angle
7:54
Obtuse Angle
8:03
Angle Relationships
8:56
Vertical Angles
8:57
10:38
Complementary Angles
11:52
Supplementary Angles
12:54
Extra Example 1: Lines
16:00
Extra Example 2: Angles
18:22
Extra Example 3: Angle Relationships
20:05
Extra Example 4: Name the Measure of Angles
21:11
Angles of a Triangle

13m 35s

Intro
0:00
Angles of a Triangle
0:05
All Triangles Have Three Angles
0:06
Measure of Angles
2:16
Extra Example 1: Find the Missing Angle Measure
5:39
Extra Example 2: Angles of a Triangle
7:18
Extra Example 3: Angles of a Triangle
9:24
Classifying Triangles

15m 10s

Intro
0:00
Types of Triangles by Angles
0:05
Acute Triangle
0:06
Right Triangle
1:14
Obtuse Triangle
2:22
Classifying Triangles by Sides
4:18
Equilateral Triangle
4:20
Isosceles Triangle
5:21
Scalene Triangle
5:53
Extra Example 1: Classify the Triangle by Its Angles and Sides
6:34
Extra Example 2: Sketch the Figures
8:10
Extra Example 3: Classify the Triangle by Its Angles and Sides
9:55
Extra Example 4: Classify the Triangle by Its Angles and Sides
11:35

17m 41s

Intro
0:00
0:05
0:06
Parallelogram
0:45
Rectangle
2:28
Rhombus
3:13
Square
3:53
Trapezoid
4:38
Parallelograms
5:33
Parallelogram, Rectangle, Rhombus, Trapezoid, and Square
5:35
Extra Example 1: Give the Most Exact Name for the Figure
11:37
Extra Example 2: Fill in the Blanks
13:31
Extra Example 3: Complete Each Statement with Always, Sometimes, or Never
14:37
Area of a Parallelogram

12m 44s

Intro
0:00
Area
0:06
Definition of Area
0:07
Area of a Parallelogram
2:00
Area of a Parallelogram
2:01
Extra Example 1: Find the Area of the Rectangle
4:30
Extra Example 2: Find the Area of the Parallelogram
5:29
Extra Example 3: Find the Area of the Parallelogram
7:22
Extra Example 4: Find the Area of the Shaded Region
8:55
Area of a Triangle

11m 29s

Intro
0:00
Area of a Triangle
0:05
Area of a Triangle: Equation and Example
0:06
Extra Example 1: Find the Area of the Triangles
1:31
Extra Example 2: Find the Area of the Figure
4:09
Extra Example 3: Find the Area of the Shaded Region
7:45
Circumference of a Circle

15m 4s

Intro
0:00
Segments in Circles
0:05
0:06
Diameter
1:08
Chord
1:49
Circumference
2:53
Circumference of a Circle
2:54
Extra Example 1: Name the Given Parts of the Circle
6:26
Extra Example 2: Find the Circumference of the Circle
7:54
Extra Example 3: Find the Circumference of Each Circle with the Given Measure
11:04
Area of a Circle

14m 43s

Intro
0:00
Area of a Circle
0:05
Area of a Circle: Equation and Example
0:06
Extra Example 1: Find the Area of the Circle
2:17
Extra Example 2: Find the Area of the Circle
5:47
Extra Example 3: Find the Area of the Shaded Region
9:24
Section 11: Geometry in Space
Prisms and Cylinders

21m 49s

Intro
0:00
Prisms
0:06
Polyhedron
0:07
Regular Prism, Bases, and Lateral Faces
1:44
Cylinders
9:37
Bases and Altitude
9:38
Extra Example 1: Classify Each Prism by the Shape of Its Bases
11:16
Extra Example 2: Name Two Different Edges, Faces, and Vertices of the Prism
15:44
Extra Example 3: Name the Solid of Each Object
17:58
Extra Example 4: Write True or False for Each Statement
19:47
Volume of a Rectangular Prism

8m 59s

Intro
0:00
Volume of a Rectangular Prism
0:06
Volume of a Rectangular Prism: Formula
0:07
Volume of a Rectangular Prism: Example
1:46
Extra Example 1: Find the Volume of the Rectangular Prism
3:39
Extra Example 2: Find the Volume of the Cube
5:00
Extra Example 3: Find the Volume of the Solid
5:56
Volume of a Triangular Prism

16m 15s

Intro
0:00
Volume of a Triangular Prism
0:06
Volume of a Triangular Prism: Formula
0:07
Extra Example 1: Find the Volume of the Triangular Prism
2:42
Extra Example 2: Find the Volume of the Triangular Prism
7:21
Extra Example 3: Find the Volume of the Solid
10:38
Volume of a Cylinder

15m 55s

Intro
0:00
Volume of a Cylinder
0:05
Volume of a Cylinder: Formula
0:06
Extra Example 1: Find the Volume of the Cylinder
1:52
Extra Example 2: Find the Volume of the Cylinder
7:38
Extra Example 3: Find the Volume of the Cylinder
11:25
Surface Area of a Prism

23m 28s

Intro
0:00
Surface Area of a Prism
0:06
Surface Area of a Prism
0:07
Lateral Area of a Prism
2:12
Lateral Area of a Prism
2:13
Extra Example 1: Find the Surface Area of the Rectangular Prism
7:08
Extra Example 2: Find the Lateral Area and the Surface Area of the Cube
12:05
Extra Example 3: Find the Surface Area of the Triangular Prism
17:13
Surface Area of a Cylinder

27m 41s

Intro
0:00
Surface Area of a Cylinder
0:06
Introduction to Surface Area of a Cylinder
0:07
Surface Area of a Cylinder
1:33
Formula
1:34
Extra Example 1: Find the Surface Area of the Cylinder
5:51
Extra Example 2: Find the Surface Area of the Cylinder
13:51
Extra Example 3: Find the Surface Area of the Cylinder
20:57
Section 10: Data Analysis and Statistics
Measures of Central Tendency

24m 32s

Intro
0:00
Measures of Central Tendency
0:06
Mean
1:17
Median
2:42
Mode
5:41
Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data
6:24
Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data
11:14
Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data
15:13
Extra Example 4: Find the Three Measures of the Central Tendency
19:12
Histograms

19m 43s

Intro
0:00
Histograms
0:05
Definition and Example
0:06
Extra Example 1: Draw a Histogram for the Frequency Table
6:14
Extra Example 2: Create a Histogram of the Data
8:48
Extra Example 3: Create a Histogram of the Following Test Scores
14:17
Box-and-Whisker Plot

17m 54s

Intro
0:00
Box-and-Whisker Plot
0:05
Median, Lower & Upper Quartile, Lower & Upper Extreme
0:06
Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme
6:04
Extra Example 2: Draw a Box-and-Whisker Plot Given the Information
7:35
Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme
9:31
Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data
12:50
Stem-and-Leaf Plots

17m 42s

Intro
0:00
Stem-and-Leaf Plots
0:05
Stem-and-Leaf Plots
0:06
Extra Example 1: Use the Data to Create a Stem-and-Leaf Plot
2:28
Extra Example 2: List All the Numbers in the Stem-and-Leaf Plot in Order From Least to Greatest
7:02
Extra Example 3: Create a Stem-and-Leaf Plot of the Data & Find the Median and the Mode.
8:59
The Coordinate Plane

19m 59s

Intro
0:00
The Coordinate System
0:05
The Coordinate Plane
0:06
0:50
The Coordinate Plane
7:02
Write the Coordinates for Points A, B, and C
7:03
Extra Example 1: Graph Each Point on the Coordinate Plane
9:03
Extra Example 2: Write the Coordinate and Quadrant for Each Point
11:05
Extra Example 3: Name Two Points From Each of the Four Quadrants
13:13
Extra Example 4: Graph Each Point on the Same Coordinate Plane
17:47
Section 11: Probability and Discrete Mathematics
Organizing Possible Outcomes

15m 35s

Intro
0:00
Compound Events
0:08
Compound Events
0:09
Fundamental Counting Principle
3:35
Extra Example 1: Create a List of All the Possible Outcomes
4:47
Extra Example 2: Create a Tree Diagram For All the Possible Outcomes
6:34
Extra Example 3: Create a Tree Diagram For All the Possible Outcomes
10:00
Extra Example 4: Fundamental Counting Principle
12:41
Independent and Dependent Events

35m 19s

Intro
0:00
Independent Events
0:11
Definition
0:12
Example 1: Independent Event
1:45
Example 2: Two Independent Events
4:48
Dependent Events
9:09
Definition
9:10
Example: Dependent Events
10:10
Extra Example 1: Determine If the Two Events are Independent or Dependent Events
13:38
Extra Example 2: Find the Probability of Each Pair of Events
18:11
Extra Example 3: Use the Spinner to Find Each Probability
21:42
Extra Example 4: Find the Probability of Each Pair of Events
25:49
Disjoint Events

12m 13s

Intro
0:00
Disjoint Events
0:06
Definition and Example
0:07
Extra Example 1: Disjoint & Not Disjoint Events
3:08
Extra Example 2: Disjoint & Not Disjoint Events
4:23
Extra Example 3: Independent, Dependent, and Disjoint Events
6:30
Probability of an Event Not Occurring

20m 5s

Intro
0:00
Event Not Occurring
0:07
Formula and Example
0:08
Extra Example 1: Use the Spinner to Find Each Probability
7:24
Extra Example 2: Probability of Event Not Occurring
11:21
Extra Example 3: Probability of Event Not Occurring
15:51
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• ## Related Books 0 answersPost by Mr. Pikachu_ Pikapika on November 15 at 01:55:22 PMa=3 for  5-a=2 1 answerLast reply by: Jason SunSat Jun 6, 2020 9:09 AMPost by LeTaotao Xue on August 26, 2018cats?i love cats! 0 answersPost by LeTaotao Xue on August 26, 2018pretty helpful 2 answersLast reply by: Hubery YangMon Oct 5, 2020 3:12 PMPost by Roy Vaughn on November 4, 20169-a=7 How did you get 2 if the inverse operation of 9 is -9. So you should of got -2, but I guess for that question you don't have to use the inverse operation???? 2 answersLast reply by: Hubery YangMon Oct 5, 2020 3:13 PMPost by April Dutollo on July 30, 2015On example 4 (second question), if you add nine to both sides through inverse operation you would get a negative 2. Can some one explain what I'm doing wrong? 2 answersLast reply by: Milan RayTue Apr 15, 2014 10:52 AMPost by Ramez Hajelsawi on March 17, 2013it really depends on what a represents dose'nt it? 2 answersLast reply by: Hubery YangMon Oct 5, 2020 3:12 PMPost by Ramez Hajelsawi on February 21, 2013How does a+1=2?

### Solving Addition and Subtraction Equations

• To solve an equation means to solve for the unknown variable
• Use inverse operations to get the variable by itself
• Inverse operation of addition is subtraction
• Inverse operation of subtraction is addition
• Whatever you do to one side of an equal sign, you must do to the other side

### Solving Addition and Subtraction Equations

Solve each equation using mental math:
5 - a = 2
a = 3
Solve each equation using mental math:
30 = 3 + x
x = 27
Use inverse operations to solve each equation
y + 5 = 23
• y + 5 - 5 = 23 - 5
• y = 23 - 5
y = 18
Use inverse operations to solve each equation
- 5 + x = 14
• - 5 + 5 + x = 14 + 5
• x = 14 + 5
x = 19
Use inverse operations to solve each equation
5 + x = 12
• 5 - 5 + x = 12 - 5
• x = 12 - 5
x = 7
Solve each equation:
b - 9 = 17
• b - 9 + 9 = 17 + 9
• b = 17 + 9
b = 26
Solve each equation:
8 + z = 14
• 8 - 8 + z = 14 - 8
• z = 14 - 8
z = 6
Solve each equation:
x - 9 = - 12
• x - 9 + 9 = - 12 + 9
• x = - 12 + 9
x = - 3
Translate each to an equation and solve:
x more than 12 is 32
• x + 12 = 32
• x + 12 - 12 = 32 - 12
• x = 32 - 12
x = 20
Translate each to an equation and solve:
The sum of 3 an y is 15
• 3 + y = 15
• 3 - 3 + y = 15 - 3
• y = 15 - 3
y = 12

*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.

### Solving Addition and Subtraction Equations

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
• Solving Equations 0:08
• inverse Operation of Addition and Subtraction
• Extra Example 1: Solve Each Equation Using Mental Math 4:15
• Extra Example 2: Use Inverse Operations to Solve Each Equation 5:44
• Extra Example 3: Solve Each Equation 14:51
• Extra Example 4: Translate Each to an Equation and Solve 19:57

### Transcription: Solving Addition and Subtraction Equations

Welcome back to Educator.com.0000

For the next lesson, we are going to be solving equations that involve adding and subtracting.0002

To solve an equation means to solve for the unknown variable.0011

Whenever you have an equation and you have one variable only, you can solve for it.0018

Once you get the variable by itself, you are going to solve the equation.0026

In order to get the variable by itself, you are actually going to use inverse operations.0032

If you have A plus 1 equals 2, here A this is what you are solving for.0037

That means I want to get rid of this number.0050

I want to get rid of this number so that I have A by itself.0058

Some equations are easy to do; you can do it in your head.0063

I know something plus 1 equals 2; that something has to be 1.0066

A has to be 1 because 1 plus 1 equals 2.0073

But when you write it, you are going to write it like that.0076

I'm sorry... like this because you know that A is 1.0081

This is how you are going to have to write the answer.0089

When the equation gets a little bit tough, a little bit harder,0092

you want to use inverse operations to solve for this variable.0096

because once you have the variable by itself like this here, you have solved the equation.0102

If I want to solve for this variable, I have to get rid of this 1.0111

The inverse operation of addition is subtraction; it is like the opposite.0117

What is the opposite operation?--it is subtraction.0124

What is the opposite of subtraction?--it is addition.0128

Here this is A plus 1; this involves addition.0133

That means the inverse operation would be subtraction.0138

We would have to subtract this to get rid of it because 1 minus 1 equals 0.0143

That is how you get rid; that is how you make it go away.0151

But whatever you do to one side of an equal sign for an equation, you have to do to the other.0155

If I am going to subtract 1 from this, this is the left side.0162

If I subtract one here, then I have to subtract one over here too.0168

Whatever you do to one side, you must do to the other side.0172

This goes away.0178

We want it to go away because we want to get the variable by itself.0180

We want to isolate the variable; that is why we had to subtract the 1.0183

This becomes A equal to... 2 minus 1 is 1.0189

Again in order for you to solve an equation, if you can't do it in your head,0197

if you can't use mental math, you want to get the variable by itself0204

by getting rid of whatever is next to it on that side of the equal sign.0211

In this equation here, it is a +1.0216

To get rid of a +1, I need to subtract it; do the inverse operation.0220

Subtract it; because it is +1, I need to subtract 1.0226

Whatever I do to one side, I have to do to the other side.0230

This will cancel out because it will be a 0.0234

You are just going to bring this down.0237

This is the only thing left on the left side.0239

What is left on the right side of the equal sign?0242

2 minus 1, you have to solve that out; that becomes 1.0244

Once the variable is by itself, you have solved the equation.0248

Let's do a few examples; let's try it.0255

For these problems, let's just use mental math.0258

That means we are just going to do it in our head.0260

4 minus a number is 3; what do you subtract from 4 to get 3?0263

Isn't that 1?--4 minus 1 equals 3.0271

Instead of just writing 1, I want to write that my variable A is 1.0275

You would have to write it like this.0282

You are writing that the variable, the unknown value, is 1.0285

X minus 3 is 4; what number subtract 3 will give you 4?--7.0292

Instead of just writing 7, I am going to write X is 7; X equals 7.0303

Here 5 plus something equals 11; 5 plus 6.0311

Again V, the variable, equals 6.0316

26 equals 8 plus C; 8 plus what equals 26?0322

If you subtract it from here, that will be 18.0331

C equals 18 because 8 plus 18 is 26.0338

For these, we want to use the inverse operation so that we can solve.0346

That means if it is plus, I want to subtract; that is the inverse operation.0352

Inverse operation of plus is minus; inverse operation of minus is plus; the opposite.0363

I am just going to draw a line just to split my two sides, my left side and my right side.0374

I want to solve for this variable A.0382

I want to keep going until I have A all by itself on the left side.0387

Since I want this to be by itself, I have to get rid of this number here.0392

That means in order to get rid of it, since it is +3, how do I get rid of a +3?0399

I have to subtract 3; the inverse operation of plus is minus.0407

I am going to subtract it so that I can make it go away.0412

Whatever I do to one side, remember I have to do to the other side.0416

On my left side, since this is no longer there, all I have left is this A.0426

I can just write A down there.0432

Because this becomes 0, I don't have to write A plus 0.0435

A plus 0 is just A.0438

I am going to write A; then bring down the equal sign.0440

10 minus 3, I need to solve this out on the right side.0445

10 take away 3 is 7.0448

This one is an easy equation; you can just do it in your head.0452

You know that 7 plus 3 is 10.0454

But we want to be able to know how to solve equations in this way using inverse operations.0457

My answer is A equals 7.0463

The next one, -2 plus C equals 11.0468

Again I am going to draw a line through just to separate my two sides--left side, right side of the equal sign.0475

Again what am I solving for?--always know what you are solving for.0484

Here is my variable; I want it to be by itself on the left side.0488

It is not by itself; it has this number right here next to it.0493

I want to get rid of it; how do I get rid of a -2?0497

This is negative; again it is the same thing as minus.0502

Minus, negative, they are the exact same thing.0506

If this is a -2, if I owe \$2, how do I get rid of that?0511

How do I make that into 0?--I have to give a +2.0517

-2 plus 2; that makes 0.0523

Whatever I do to this side, I have to do to the other side.0527

What is left on my left side?0538

This went away; this is just a +C.0539

I don't have to write a plus in front of it because plus C is the same thing as +C.0544

Even if I don't write the positive sign, I know that the C is positive still.0550

This is C equals... 11 plus 2 is 13; C equals 13.0558

For this next one, a common mistake here would be to subtract this 4 to the other side.0568

But again you are solving for the variable.0580

This time, the variable is on the right side; that is OK.0584

Just make sure that you identify the variable.0588

You want to get the variable by itself on whichever side it is on.0591

That means I want to get rid of this number here because that is on the same side of the variable.0595

The whole point is to get the variable by itself.0604

To get this by itself, let's get rid of that number; this is a +5.0609

If there is no negative sign in front of it, then it is always a positive.0614

This is 5 minus 5 to get 0.0619

Whatever I do to one side, I have to do to the other side.0624

This is a positive.0632

Again if there is no sign in front of it, it is a positive.0633

+4 minus 5; +4 minus 5.0636

With these integers, it still might be a little bit difficult to do 4 minus 5.0643

If it is, think of this as having 4 apples.0654

But again you need 5 apples.0661

If you have 4, you need 5, you are short.0665

If you need 5 apples but you only have 4, then you need 1 more.0671

Whenever you need something, whenever you don't have it, it is a negative number.0675

You can also think of this as having 4 dogs.0681

Let's say dogs are positive numbers; D is for dog; we have 4 dogs.0690

Whenever you have a negative number, that is going to be a cat.0697

We are going to have 5 cats because we have a -5.0701

A dog and a cat cancels out; those cancel out; those cancel out; and cancels out.0707

What do you have left?--you have 1; is this a positive or negative?0715

Cats are negative; that would be a -1; here this becomes -1.0721

Be careful, do not put 1; this has to be a -1.0729

If you want, you can also use a number line.0734

This is again only if you are having trouble with integers.0738

Here is a 0; I am going to start off at my first number.0742

That is 4; I am going to start here; then minus 5.0747

If I subtract, then I have to go this way; how many?--5.0753

I am going to go 1, 2, 3, 4; then I have to go one more, 5.0759

What is 1 more?--this is a -1.0766

This is not 1; 1 is right here; -1 is right there.0770

You can do it that way too.0777

Continuing, this I bring down; that went away.0784

That was the whole point--to make that go away so that this variable M will be by itself like that.0788

Now that I have the variable by itself, I have my answer.0798

This is the same thing as... if you want, you can rewrite it like this.0801

If you don't like that variable on that side,0810

since you are probably used to having variables on this left side, you can rewrite it.0812

-1 equals M; or you can say M equals -1.0819

For this next one, be careful here because the variable is here.0826

The variable is already by itself.0834

There is no need to move anything over.0837

There is no need to add, subtract, do any inverse operations.0839

We can just go ahead and solve this.0843

2 plus -2, if I have 2 of something, I take away 2.0847

It is like having 2 apples and then eating 2 apples.0854

You have 0 apples left.0856

Equals; then D; this is my answer.0860

0 is still a number; see how we have 0 right there?0870

It is still a number; D equals 0; that would be your answer.0875

Or again if you want to write the variable first, you can write D equals 0 like that.0881

They are both correct.0888

Let's do a few more; solve each equation; we are going to use inverse operations.0890

Again we are solving for B.0898

If you want, you can circle it to help you know what you are solving for and help you to see what to get rid of.0901

I am going to separate my sides with the line.0910

You don't have to draw the line; but it helps to see it.0912

This is the left side; this is the right side; you are moving this.0915

You are getting rid of it by doing the inverse operation to this side and to that side.0921

Whatever you do to one side, you must do to the other side.0928

The inverse operation of minus is plus.0933

I have to add 7 so that this will go away; add 7 here.0938

This is nothing; what is left on my left side?--on that side?0948

B equals -1 plus 7.0952

Again if the numbers are small, then you can just use the dog-cat example.0959

You can also say you need 1 apple; you have 7.0964

After you use that 1 that you need, how many do you have left?0974

You have 6 left.0978

To show you the dog and cat example again, a negative number is a cat.0981

That is 1 cat; then 7 dogs; 1, 2, 3, 4, 5, 6, 7.0988

7 Ds represents a +7; this cancels; how many dogs do you have left?0998

1, 2, 3, 4, 5, 6; this is 6; is that positive or negative?1006

Dogs are positive; it is +6; that is my answer.1011

Then here again you are solving for E; you can separate the sides.1020

I have to get rid of whatever is next to it which is the 4.1026

You don't have to get rid of pluses because plus is the same thing as positive.1030

Just like minus is the same thing as negative, a plus is the same thing as a positive.1035

Here this is a +4; there is no negative sign in front of it.1042

It automatically gets a positive; if that helps, you can write that in.1047

To get rid of a +4, you have to subtract 4; you have to take 4 away.1052

Whatever you do to one side, you have to do to the other side.1057

This becomes nothing; E is left only on that side which is what we want.1063

Equals; this is dog, dog, cat, cat, cat, cat; cancel, cancel.1069

This becomes 2; cats are negative; E is -2.1081

The next one, circle the variable.1092

Here this is what I have to get rid of because it is next to the variable on that side of the equal sign.1101

To get rid of a -6, I have to add 6; that is the inverse operation.1108

Whatever I do to one side, I have to do to the other side.1113

This goes away; P by itself now equals -5 plus 6; 1.1118

If you borrowed 5, you have 6, so after paying that 5 back, you have 1 left over.1134

For this one, you can circle and draw the line.1147

You are getting rid of the 3, not the 8, because the 3 is on the same side of the variable.1153

The whole point is to get the variable by itself.1159

Again this is a +3; I need to subtract 3 to make this 0.1163

Whatever I do to one side, I have to do to the other side which is over here.1169

Be careful, you don't do it to the same side.1173

It has to be to the other side.1176

That is why you draw this line just to make it easier to see this side and that side.1179

Went away; what is left?--my variable equals 5.1187

For these, we are going to translate to an equation first.1200

Then we are going to solve them.1203

The sum of A... this is the variable A... and 8 is -1.1206

Sum we know is plus of A and 8.1216

That means we are going to add A and 8 together.1222

A plus 8, is means equals, -1.1226

To solve this, again we are going to solve for A.1235

Separate the two sides to get rid of this because that is still on the same side.1243

Subtract it; that is the inverse operation.1251

Whatever I do to this side, I have to do to the other side.1257

Went away; A is left by itself; equals -1 minus 8.1263

Here is a negative; here is a negative.1271

You have 1 cat; you have 8 more cats.1273

How many cats do you have total?--9 cats.1276

Cats we know are negative so it has to be a negative number.1281

There is my answer; A is -9.1286

The next one, 9 minus A is 7; 9 minus A equals 7.1293

I am solving for this.1309

For this one, we don't have to use the inverse operation.1315

If you can solve it in your head, if it is easy, then you can just go ahead and do that.1319

We know 9 minus what equals 7?--that is 2.1324

Just be careful that you are not going to just write 2 as your answer.1329

If you just write 2, you have to identify it as your variable.1333

That is what you found A to be.1338

You want to write A equals 2 because 9 minus 2 equals 7.1344

Next one, K more than 14 is 20.1354

We know more than is plus; this is plus.1359

But then I see this word here.1365

Remember whenever you see that word, you have to switch them.1367

You have to write it in the opposite order.1371

Instead of K plus 14, you are going to say 14 plus K is 20.1375

Again you are solving for K; you can just do this in your head.1386

You know that 14 plus 6 more is going to give you 20.1392

You can say K equals 6.1396

Or if you want, you can just practice doing the inverse operation.1401

You are going to subtract 14 because this is a +14.1405

Whatever you do to one side, you have to do to the other side.1409

Goes away; K is left by itself which is what you want.1415

Equals, this is 6.1419

The last one, 5 less than Q is 11; 5 less than Q is 11.1429

Less than we know is minus; but then again here is that word.1438

It is going to be Q minus 5 equals 11.1445

A number Q, if you take 5 away, is going to be 11.1453

We know Q is going to be 16.1459

Again just to show you the inverse operation, I am solving for Q so get rid of everything on that side.1463

You are going to add 5 to get rid of it.1471

Whatever you do to one side, you have to do to the other side.1474

You are going to have Q equal to 16.1480

That is it for this lesson; thank you for watching Educator.com.1490

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