  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 1 answer Last reply by: Mary PyoWed Dec 18, 2019 1:06 PMPost by Hong Yang on December 1, 2019in the video u said on extra example 1 that u always do lcm 0 answersPost by Karina Herrera on December 29, 2016Thank you for another great lesson taught, Mary! :) I like how you pace the lessons to help us follow through. It's such a bummer when a teacher is going too fast, making it harder to fully understand. 1 answerLast reply by: Hong YangSun Dec 1, 2019 11:39 AMPost by antonio cooper on March 17, 2015On example 4 did you mean to say and write LCM instead of LCD? 1 answer Last reply by: Professor PyoSat Jan 18, 2014 2:24 PMPost by Robin Alsoffi on January 4, 2014Since both the numbers are prime, can we just assume that the LCM would be achieved by multiplying or are there cases where that is not least? Thanks and you have given me some good tips and reminders for improving my math skills. 2 answersLast reply by: DetectivePikachu_ yeetFri Nov 20, 2020 4:56 PMPost by Aimet Ruiz on January 29, 2013why do you hesitate

### Adding and Subtracting Mixed Numbers

• When adding/subtracting mixed numbers, add/subtract the whole numbers together and the fractions together
• If the new mixed number contains an improper fraction, convert the improper fraction into a mixed fraction

### Adding and Subtracting Mixed Numbers

2[2/6] + 3[1/2]
• 2[2/6] + 3[3/6]
5[5/6]
3[1/7] + 3[1/4]
• 3[4/28] + 3[7/28]
6[11/28]
6[1/2] − 2[2/6]
• 6[3/6] − 2[2/6]
4[1/6]
12[7/8] − 5[1/2]
• 12[7/8] − 5[4/8]
7[3/8]
6[3/5] − 2[1/10]
• 6[6/10] − 2[1/10]
4[5/10] or 4[1/2]
6[3/5] + 7[1/10]
• 6[6/10] + 7[1/10]
13[7/10]
9[2/9] + 6[1/2]
• 9[4/18] + 6[9/18]
15[13/18]
4[3/7] + 12[1/3]
• 4[9/21] + 12[7/21]
16[16/21]
15[3/4] − 3[1/6]
• 15[18/24] − 3[4/24]
12[14/24] or 12[7/12]
6[8/9] − 2[4/6]
• 6[16/18] − 2[12/18]
4[4/18] or 4[2/9]

*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.

### Adding and Subtracting Mixed Numbers

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
• Example 0:05
• 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

### Transcription: Adding and Subtracting Mixed Numbers

This lesson, we are going to be adding and subtracting mixed numbers.0000

Remember a mixed number is a fraction with a whole number in the front.0006

If I have a whole number with a proper fraction, then I have a mixed number.0012

When I am adding mixed numbers together, the main thing here is the fraction.0018

We are look at fractions here.0024

Whole numbers, 3 and 1, we can just add them together.0026

For the wholes, we have 4 wholes.0032

Then we have the fractions that we have to worry about.0036

In this case, I am going to just add the whole numbers and I am going to add the fractions.0040

3 plus 1, the whole numbers, that is going to become my new whole number.0047

Then 3/5 plus 1/5.0054

Again from the last few lesson in adding fractions, we have to make sure that they have a common denominator.0059

In this case, this fraction and this fraction both have a denominator of 5.0068

It is going to be 3 plus 1; I am adding the numerators; 3 plus 1 is 4.0075

My denominator stays the same as always as a 5.0081

This mixed number plus this mixed number equals this mixed number.0088

you have to make sure that this fraction here is a proper fraction.0098

Meaning the top number must be smaller than the bottom number.0104

If that is the case, then that is your answer, 4 and 4/5.0110

Let's do a few problems; we are adding 2 and 1/2 plus 2 and 2/3.0118

Again I am going to add the whole numbers together, this whole number and this whole number.0129

That is going to become 4.0136

Then I am going to add my fractions together, 1/2 plus 2/3.0139

But there is a problem; our denominators are different.0145

Whenever you have fractions with different denominators,0150

then you can't add them or subtract them until you make the denominators the same.0155

In order to make the denominators the same,0162

you have to look for the least common denominator or the least common multiple.0165

Between 2 and 3, the least common denominator will be 6.0170

The multiples of 2 would be 2, 4, 6, 8, so on.0178

For 3, 3, 6, 9, and so on; the least common multiple is 6.0188

I have to change these fractions.0203

I have to convert the fractions so that the denominators will become a 6.0206

1/2, I am going to multiply this 2 by 3 to get a 6.0214

2 times 3 is 6.0226

Whatever I do to this part, I have to do to the top.0228

1 times 3 is 3.0233

Again you have to multiply the top and the bottom by the same number.0235

If you don't, then it is going to be wrong because these fractions have to stay the same.0240

All you are doing is changing the numbers, but it is still the same fraction.0246

Then we have to do this next one, 2/3.0253

2/3, I have to change this so the denominator will become a 6.0258

3 times 2 became 6.0264

I have to multiply the top number by the same number.0269

It is going to be 4.0272

This mixed number could be the same thing as 2 and 3/6.0276

This one can change to 2 and 4/6.0286

They might look different; but they are the same thing.0294

This problem is the same problem as this one as long as you did everything correctly.0297

All you did was just change the fractions so that their denominators would be the same.0301

Again I am going to add the whole numbers.0309

It is 2 plus 2 which is 4.0312

Then since their denominators are the same for the fractions, I can add them.0317

It is going to be 3 plus 4 which is 7 over...0322

The denominator always stays the same; it is going to be 6.0328

Let's look at this answer right here; I have a problem.0333

Because I have 4 and 7/6, remember my mixed number, this is supposed to be a mixed number.0339

The mixed number has to be a whole number with a proper fraction.0346

But since my numerator is bigger than my denominator, this is actually an improper fraction.0351

I have to change this so that this will no longer be an improper fraction.0359

Let's just look at just this part right here, 7/6.0366

7/6, since it is an improper fraction, we can change this so that it becomes a mixed number.0371

Remember I ask myself how many times can 6 fit into the top number 7?0381

I know that 6 can only fit into 7 one time.0389

If 6 fits into 7 one time, how many do I have left over?0395

I only have 1 because I have 7; 7 minus 6 would be 1.0400

Again my denominator stays the same.0408

This right here, 7/6, became 1 and 1/6.0412

But then again I have a 4 right here; I have another whole number, 4.0418

I have a whole number 4; I have a whole number of 1.0422

Since this 4 and 7/6 is the same thing as 4 plus 7/6,0429

I can just take this whole number and add them together.0442

This will become 5 and 1/6.0451

Again if your answer, your mixed number, has an improper fraction, you have to take out the whole number,0458

7/6 became 1 and 1/6.0478

I have a whole number 4 that I have to consider.0481

I am going to add that 4 to that mixed number.0484

It is going to be 5 and 1/6; that is my answer.0487

Another example here, I have 6 and 5/7 minus 2 and 1/5.0495

The main problem here is my fraction.0505

I have to look at my fractions, 5/7 and 1/5; my denominators are different.0507

I have to make sure to make a common denominator.0516

Normally you can do the factor tree to find the least common denominator.0523

But for 7 and for 5, they are both prime numbers.0527

If they are both prime numbers, then you can just list out all the multiples0531

or the first few until you find the common multiple--7, 14, 21, 28, 35.0536

For 5, the multiples are 5, 10, 15, 20, 25, let me continue right here, 30, 35.0553

I found one, 35.0568

You have to make sure when you find the least common denominator that it is the smallest one.0570

They are going to have more than one common denominator or common multiple.0575

You just have to make sure it is the least common multiple.0580

It is the smallest common multiple; in this case, it is 35.0583

I am going to change just this fraction.0590

I am going to ignore my whole number for now.0592

I am just going to change the fractions.0596

5/7, I want to make the denominator become 35.0599

7, what did I multiply by 7 to get 35?--multiplied 5.0607

Then I have to multiply this top number by 5; this becomes 25.0614

Then I am going to look at this fraction right here, 1/5.0621

5 times 7 became 35; multiply this top number by 7; get 7.0630

I am going to rewrite my mixed numbers, my problem, so that I will have common denominators for each of these.0639

This becomes 6 and 25/35 minus 2 and 7/35.0648

Now that I have common denominators, I can go ahead and subtract these two fractions.0666

Let's do 6 minus 2; the whole number is 6 minus 2 which is 4.0673

Then I can take my numerator here, subtract it by this numerator.0680

25 minus 7 is 18; my denominator stays the same as 35.0685

My answer here is 4 and 18/35.0700

Again you have to look at this fraction right here, this mixed number.0707

Make sure that this is a proper fraction.0710

Your top number, your numerator, is going to be smaller than the denominator.0712

This next example, 3 and 3/4 plus 4 and 1/10.0722

Again I have to look at my fractions because I can't add them until I have a common denominator.0729

In this case, you can either, just like the other examples, to find the LCD, you can list out their multiples.0738

Since these are not prime numbers, you can do factor trees.0746

I am just going to do the factor tree; this is 2 and 2.0751

For 10, it is going to be 5 and 2.0759

There is a common number of 2; cross one out.0765

My LCD, my least common denominator... I am going to write out all the remaining circled numbers.0771

2 times 2 is 4; times 5 is 20; my LCD is 20.0783

I am going to change these two fractions so that my denominators will become 20.0792

3/4; 4, I multiplied it by 5 to get a 20.0797

I am going to do the same thing to the top, 15.0806

The other fraction, 1/10; 10 times 2 became 20; 1 times 2 is 2.0813

Again this fraction 3/4 is the same thing as 15/20 and 1/10 is 2/20.0825

I am going to rewrite this problem, 3 and 15/20 plus 4 and 2/20.0833

I add my whole numbers together; it is going to be 7.0851

Then I have to add my fractions.0856

They have a common denominator so I can add them together.0859

I am going to take my numerators, 15 and 2; add them up.0862

I get 17 over... guess what my denominator is going to be?0866

20, your denominator has to stay the same.0873

Is my top number in my fraction smaller than my bottom number?0879

If it is, then it is a proper fraction.0883

This is going to be my answer, 7 and 17/20.0887

This next example, 12 and 9/11 minus 12 and 3/22.0895

Before I begin here, I have to make sure that the denominators for these fractions are the same.0904

I am looking at this fraction here and this fraction here.0910

Here I have an 11 as my denominator; this one, I have a 22.0916

I have to change these denominators so that they are the same in order for me to be able to subtract these fractions.0922

I need to find the least common denominator.0930

I am going to write out the multiples of 11--11, 22, 33, and so on.0935

For 22, it is going to be 22, 44, and so on.0944

My least common multiple is 22.0952

Since they are denominators, it becomes the least common denominator.0961

Make sure, if you are going to list out the multiples to find the LCD,0965

then you have to find the one that is smallest.0969

It has to be the smallest common multiple because these two numbers,0973

they are going to have more than one common multiple.0976

It has to be the smallest one.0979

Now that I have my LCD, I have to make sure that these fractions0983

will be converted so that I will have my denominator as 22.0994

This fraction right here, 9/11... I know that I have whole numbers here.0999

But I am just going to worry about my proper fractions first.1004

9/11, I want to make that denominator 22.1009

I take this number, 22, divide it by 11.1017

Or I can just figure out 11 times 2 gave me 22.1020

Whatever I do to that number, I have to do to the top number.1026

I have to multiply the top number by 2 as well.1030

9 times 2 is 18.1034

This next fraction, 3/22, the denominator is already 22.1039

We don't have to change it; we can just keep it the way it is.1045

I know that 9/11 is the same thing, is the same fraction as 18/22.1050

I can just rewrite this whole problem so that they will have common denominators.1059

12 and 18... let me erase that.1069

12 and 18... it has to change to this fraction right here.1076

12 and 18/22 minus 12 and 3/22; again double check your denominators.1082

Make sure that they are the same; then we can go ahead and subtract those.1094

For this, my whole numbers, 12 minus 12, is going to be 0.1101

Then I don't have to worry about my whole numbers for now.1109

I have to subtract my numerators; 18 minus 3 is 15.1113

My denominator again, it is the same as 22.1124

My denominator for my answer has to also stay the same; it is 15/22.1129

I don't have a whole number because 12 minus 12 gave me 0.1136

I don't have a whole number here.1140

Here I have to make sure when I have my fraction that this top number is smaller than the bottom number.1144

This is a proper fraction.1150

I can't simplify it because 15 and 22 do not have any common factors.1154

There is no number that can go into both the top number and the bottom number.1160

Once I ask myself all those questions and I can't simplify, then this would be my answer.1165

12 and 9/11 minus 12 and 3/22 became 15/22.1173

That is it for this lesson; thank you for watching Educator.com.1181

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