Mary Pyo

Solving Multiplication Equation

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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### Solving Multiplication Equation

• To solve equations, use inverse operations to get the variable by itself
• Inverse operation of multiplication is division
• Inverse operation of division is multiplication

### Solving Multiplication Equation

Use mental math to solve the equation
4x = 20
x = 5
Use mental math to solve the equation
42 = y · 7
y = 6
Use the inverse operation to solve the equation
- 5x = 35
• [( − 5)/( − 5)] ·x = [35/( − 5)]
• x = [35/( − 5)]
x = - 7
Use the inverse operation to solve the equation
- 36 = 6y
• [( − 36)/6] = [6/6] ·y
• [( − 36)/6] = y
y = - 6
Use the inverse operation to solve the equation
- 9t = - 36
• [( − 9)/( − 9)] ·t = [( − 36)/( − 9)]
• t = [( − 36)/( − 9)]
t = 4
Solve the equation
- 7m = 49
• [( − 7)/( − 7)] ·m = [49/( − 7)]
• m = [49/( − 7)]
m = - 7
Solve the equation
- 33 = - 11a
• [( − 33)/( − 11)] = [( − 11)/( − 11)] ·a
• [( − 33)/( − 11)] = a
a = 3
Solve the equation
- 7x = 56
• [( − 7)/( − 7)] ·x = [56/( − 7)]
• x = [56/( − 7)]
x = - 8
Is - 5 a solution to the equation?
- 25 = - 5s
• [( − 25)/( − 5)] = [( − 5)/( − 5)] ·s
• [( − 25)/( − 5)] = s
• s = 5
No
Is - 7 a soultion to this equation?
4x = - 28
• [4/4] ·x = [( − 28)/4]
• x = [( − 28)/4]
• x = − 7
Yes

*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 Multiplication Equation

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
• Multiplication Equations 0:08
• Inverse Operation of Multiplication
• 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

### Transcription: Solving Multiplication Equation

Welcome back to Educator.com.0000

For the next lesson, we are going to continue solving equations.0002

We are going to solve multiplication equations.0005

Equations that involve multiplication, we are going to continue to solve using inverse operations.0010

Again whenever you solve equations, you always have to try to get the variable by itself.0023

The inverse operation of multiplication is division.0030

If I have a number being multiplied to a variable, 2 times A...0037

Remember if you have a number times a variable, you can write it together like that.0044

Equals 10; that is my equation; this would be a multiplication equation.0050

This 2 times A, 2 times the variable; we can do this in our head.0056

We know that 2 times 5 equals 10; we know A is 5.0062

But if I were to solve this using inverse operations, again I want to get the variable by itself.0066

I have to get rid of whatever is next to the variable on that side.0078

On the left side, I have to get rid of everything except for the variable and get the variable by itself.0082

That means I have to get rid of this 2.0091

Since this is 2 times A, the inverse operation would be to divide.0094

To get rid of the 2, we have to divide the 2; divide this 2.0101

We know that 2 over 2 is going to go away.0107

It is going to become 1.0109

Whatever you do to this side, remember you have to do to the other side.0112

If I divide 2 from here, then I have to go to the right side and then divide 2 there.0116

This then becomes 1A; 1A is the same thing as A.0126

Whenever you have a variable with no number in front of it like this one does, there is an invisible 1 here.0139

It is just saying that you have 1 A.0148

How many As do you see?--you see 1 of them.0150

If I say I have an apple, you know I have only 1 apple.0154

I didn't say I have 1 apple.0159

But just because I said I have an apple and I made it singular, you know that I have 1.0161

In the same way, if I have an A, you know that I have 1 of them.0167

That just means that there is an invisible 1 in front of it.0172

When this number cancels out like that, you don't have to write 1A.0176

You can just write A which is the same thing as getting the variable by itself.0180

Again whether you write the 1 in front of the A or just leave it as A, it is the exact same thing.0186

By itself now, that is the whole point; you want to get it by itself.0196

We got rid of the 2; equals... on the right side, I have to actually solve that out.0199

That becomes 10 divided by 2.0207

Remember this line right here like a fraction; that represents divide.0211

This would be 10 divided by 2.0216

We know that 10 divided by 2 is 5; that would be my answer.0220

That is how you would solve multiplication equations using inverse operation.0227

Let's go ahead and do our examples.0234

The first set of examples, we are going to use mental math0237

meaning we are just going to solve it in our head.0240

We don't have to divide or use inverse operations.0241

Here again this means 3 times F; 3F means 3 times F.0247

3 times what is 9?--3 times what equals 9?0257

I know 3 times 3 equals 9; F has to be 3.0263

Again when you are solving equations, you don't want to just write 3.0268

You don't want to just write the number.0271

You have to write what that number represents; you are saying that F is 3.0273

Once you write it like that, variable by itself equaling the number, then that is your answer.0283

10 times what equals 100?--10 times 10 equals 100.0290

Then I have to say A is equal to 10.0296

18 equals C times 6; this C times 6, same thing.0305

Whether you see it like this or whether you see it like that, they both mean multiplication.0314

What times 6 is 18?--I know 3 times 6 is 18.0321

That means C has to be 3.0327

The next one, 21 equals 3 times a number; 3 times what equals 21?0335

3 times 7 equals 21; that means P has to be 7.0344

Now let's use the inverse operation to solve the equation.0357

We are going to use that method that we did earlier.0360

We are going to use that same method to go out and solve for our variable.0364

This is -10 times S equals 100.0370

I am solving for S; I am solving for my variable.0377

I can circle it just to see that that is what I want.0381

That is my goal; that is what I am solving for.0385

I am separating my sides.0388

Since this is -10, that number times S, inverse operation of times is divide.0393

To get rid of this -10, I have to divide it.0404

I am going to use the inverse operation to get rid of the number and get the variable by itself.0407

I need to divide.0415

Remember this line right here, writing it as a fraction; that means divide.0415

Whatever I do to one side, remember I have to do to the other side.0423

I have to divide this side by -10 also; what is left on this side?0428

On my left side of the equal sign, I got rid of that number.0435

I want to get the variable S by itself.0440

Now that I got rid of -10, I have S by itself now.0444

I am going to write S; that is what is left on my left side.0448

Equals... what became of my right side?--100 divided by -10.0452

Remember when you multiply or divide integers, meaning positive and negative numbers like this, you still get the same number.0459

Let's say I don't see that negative sign.0474

Then I am still going to do 100 divided by 10.0476

Whether or not this number is negative or positive, you are still going to divide 100 to 10.0480

But if you have one negative number, if only one is negative, then your answer becomes negative.0487

It is the same number when you divide.0496

You are just going to do 100 divided by 10.0498

Then my answer becomes a negative.0506

If I have two negatives signs, whether it is a negative times a negative0513

or a negative number divided by a negative number, whenever you see two of them,0520

those two negative signs will pair up and become a positive.0526

This is only when you multiply or divide; two negatives make a positive.0532

One negative, it remains a negative.0541

If you have two negatives, it becomes a positive number.0544

This is 100 divided by 10; that is still 10.0549

But because there is only one negative sign here within this problem,0553

there is only one, so then my answer becomes a negative.0558

S equals -10; that is my answer.0562

The next one; again you are solving for T; separate the sides.0571

I have to get rid of the 2.0579

To get T by itself, I have to get rid of the 2.0581

This is 2 times T; my inverse operation, I have to divide; divide the 2.0584

Remember this line means divide also; that goes away.0591

Then I have to divide this side by 2.0595

On my left side, I only have T left which is what I want.0602

Equals -16 divided by 2.0606

A +16 divided by 2 is 8; I know 2 times 8 is 16.0611

But since I have only one negative sign within this problem, my answer, it stays a negative.0619

Be careful not to confuse multiplying and dividing positive and negative numbers and adding and subtracting positive and negative numbers.0628

When you add two negative numbers, that doesn't become a positive.0635

Only when you multiply or divide two negative numbers; so that is my answer.0641

For the third one, I am solving for my variable R.0653

It is on the right side of my equal sign.0659

This is my left side; this is my right side; I am solving for R.0661

I have to get rid of the 5 because R, the variable, has to be by itself.0667

This is 5 times R.0673

I have to get rid of the 5 using the inverse operation, dividing.0675

That is my way of making that go away.0681

Since I did it to this side, I have to do to the other side.0685

Now I am going to simplify; I am going to solve everything out now.0691

25 divided by 5 is 5.0694

We don't have to worry about any positive or negative numbers because there is no negatives.0697

25 divided by 5 is just 5; bring down the equal sign; this is R.0700

R by itself because we got rid of the 5; that is my answer.0707

Again if you want, you can leave it like that as your answer.0712

Or you can say R equals 5.0715

You can rewrite it 5 equals R or R equals 5.0718

It is the same exact thing.0722

This last one, again I am solving for D, the variable.0727

Separate my two sides; this is 8 times D.0733

To get rid of it, inverse operation would be to divide.0736

Whatever you do to one side, you have to do to the other side.0742

What is left here?--D only, equals... 64 divided by 8 is 8.0747

But because I have one negative sign when I am dividing numbers, my answer becomes a negative.0755

It is -8; that is my answer.0761

Here, is -2 a solution of each equation?0771

That means I can plug this in.0786

I can substitute a -2 for the variable to see if my equation is going to be true or false.0788

4 times S; instead of writing S, I can write -2 to see if -2 is what S is going to equal.0797

4 times -2; then remember the best way to show two numbers being multiplied together0810

is to write each of them in parentheses like that; equals -8.0818

You are just seeing if 4 times -2 equals -8.0827

4 times -2 is -8; 4 times 2 is 8.0832

You only have one negative sign; that makes that negative.0837

They do equal each other; this does equal -8; so this one is yes.0841

Is this -2 a solution for this equation?--this one is yes.0847

Next one, 10 equals 5 times -2; I want to write it out.0855

Again I can write both of these in parentheses to show that those are two numbers being multiplied together.0866

What is 5 times -2?--isn't this -10?0873

because again 5 times 2 is 10 but then you have only negative number.0880

So this is not true; this one is no or false.0884

This one, -6 times -2 equals +12.0892

Again I am going to write that in parentheses to show that I am going to multiply them.0900

6 times 2 we know is 12; here I have two negatives signs.0909

For this, the two numbers that I am multiplying, they are both negative.0915

That means I have two negatives which makes a positive.0919

When you multiply or divide, two negatives make a positive.0923

This becomes +12 or just 12; I don't even have to write the positive.0927

12 equals 12; this one is yes; this one works.0933

Let's do a few more; we are going to solve this using inverse operation.0944

Here again we are solving for the variable.0952

Circle it; draw a line to separate the sides.0954

This is -4 times W; I am going to divide -4.0959

Whatever I do to one side, I have to do to the other side.0965

That was my way of making that number go away and make the variable by itself.0970

Equals... 28 divided by 4; we have a negative divided by a negative.0975

Does that make it a positive when you divide two negatives?0987

Yes; that becomes a +7 because 4 times 7 equals 28.0992

Be careful; this is a +7.1000

Or if you just write 7 without the plus sign, that is okay.1003

Number two, you are solving for N; I am going to separate my sides.1012

Here again I need to get rid of this number.1022

Do not divide this number; do not try to move this number; don't use this.1025

We are going to try to get rid of this number because that is what is next to the variable.1032

Again we are trying to get the variable by itself.1037

Divide -8; again I divided because that was -8 times N.1041

Dividing is the inverse operation.1046

Whatever you do to one side, you have to do to the other side.1049

Negative divided by a negative is a positive.1054

This becomes 10 because 8 times 10 is 80.1057

Equals; went away; left with N; same thing here.1063

I know some of you guys can still do this in your head.1080

If you can, that is fine.1083

But it is important to know inverse operations and know how to do these steps1084

because later on, the equations are going to get a lot harder.1090

If you know how to do it this way, then solving equations becomes really easy.1094

Just try to practice it a few times; just keep practicing.1102

Circle the variable because that is what you are solving for.1105

To get the variable by itself, I have to get rid of this number.1109

Divide; divide; this goes away; this becomes -2.1113

Again positive divided by negative; I only have one negative sign so my answer is a negative.1122

11 times 2 is 22; that is why it is a 2.1129

Equals K; there is my answer.1133

If you want, you can flip this and make it K equal to -2.1140

Or not flip but switch the sides; you can write it like that.1146

The last one, going to circle the A; this is 9 times A.1151

Divide the 9; inverse operation to get rid of it.1158

45 divided by 9 is 5; I only have one negative.1163

That is it for these multiplication equations; thank you for watching Educator.com.1180

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