  Mary Pyo

Multiplying Fractions and Mixed Numbers

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 answerLast reply by: SIMON XENITELLISMon Jun 24, 2019 7:04 AMPost by SIMON XENITELLIS on June 24, 2019The last example 14/15*10/3 is wrong.The teacher accidentally forgot that 15 reduces to 5, 0 answersPost by Rose A on February 24, 2017Hello Mary, In example 3, you said we can divide 203/72... We end up with a decimal... Can you explain what to do than? you said how many left overs becomes your numerator, well when you divide you get 2.81... Thanks! 0 answersPost by Karina Herrera on December 29, 2016Another great lesson! Thanks to you, I am now understanding cross-canceling. It is really going to come in handy. 0 answersPost by faisal madar on November 12, 2013cant show it better look at us 0 answersPost by Pasi MatalamÃ¤ki on July 30, 2013It would of been nice if you had explained cross cancelation of fractions 0 answersPost by judy lee on August 19, 2011Try dividing 600 wth 28, then you will get 150/7. 3 answersLast reply by: faisal madarTue Nov 12, 2013 5:47 PMPost by javier mancha on August 15, 2011you say we can multiply , 24 our numerator x,s 25 and get our answer, which equels, 600, , . then you go on to say,, or we can , cross cancel any numbers, . which is a total diffrent answer from 600. on the second example

### Multiplying Fractions and Mixed Numbers

• Change mixed numbers to improper fractions
• Multiply the numerators together
• Multiply the denominators together
• If the product is an improper fraction, convert it to a mixed number

### Multiplying Fractions and Mixed Numbers

Multiply the fraction:
[1/2] ×[5/6]
[5/12]
Multiply the fraction:
[3/4] ×[1/9]
[3/36] or [1/12]
Multiply the fraction:
[6/11] ×[7/11]
[42/121]
Multiply the fraction:
2[1/7] ×3[3/4]
• [15/7] ×[15/4]
[225/28] or 8[1/28]
Multiply the fraction:
3[5/6] ×4[1/2]
• [23/6] ×[9/2]
[207/12] or 17[1/4]
Multiply the fraction:
4[3/4] ×6[1/6]
• [19/4] ×[37/6]
[703/24] or 29[7/24]
Multiply the fraction:
2[7/8] ×3[1/3]
• [23/8] ×[10/3]
[230/24] or 9[7/12]
Multiply the fraction:
3[5/8] ×[2/3]
• [29/8] ×[2/3]
[58/24] or 2[5/12]
Multiply the fraction:
6[1/2] ×[4/5]
• [13/2] ×[4/5]
[52/10] or 5[1/5]
Multiply the fraction:
[5/6] ×4[1/3]
• [5/6] ×[13/3]
[65/18] or 3[11/18]

*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.

### Multiplying Fractions and 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
• Multiplying Fractions 0:07
• Step 1: Change Mixed Numbers to Improper Fractions
• Step2: Multiply the Numerators Together
• Step3: Multiply the Denominators Together
• 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

### Transcription: Multiplying Fractions and Mixed Numbers

Welcome back to Educator.com.0000

This lesson is on multiplying fractions; that includes mixed numbers.0002

If you are multiplying fractions and you do have mixed numbers,0009

then make sure to change them to improper fractions first.0013

I am going to do a few examples here.0018

But if you don't remember how to do that, just go back0020

to the previous lesson on switching between mixed numbers and improper fractions.0023

Once all of your fractions are either proper fractions or improper fractions,0029

then you are going to take the numerators which are the top numbers, multiply them together.0034

If we have A/B, A/B which are variables, they are going to represent numbers.0042

If this is a fraction, a number over number, times another fraction, C/D,0050

then you are going to take this top number, multiply it to this top number.0057

You get AC.0062

Then you are going to take your denominator, B, and multiply it to the other denominator, D.0064

It becomes AC/BD.0069

Don't get confused between multiplying and adding and subtracting fractions.0073

Remember when we add or subtract fractions, you have to make sure that these denominators are the same.0078

But in this case when you are multiplying fractions, you are just going to multiply the denominators together.0090

Here are some examples, 2/3 times 3/4.0099

2/3, that is not a mixed number; 3/4 is not a mixed number.0107

I can go ahead and multiply them.0112

2/3... I am just going to write it out again... 3/4.0116

You can do 2 times 3 which is 6 over... 3 times 4 which is 12.0123

6/12, they have a common factor; they have a common factor of 2.0132

Or the greatest common factor, the biggest factor that they have in common, is 6.0141

I can just divide the top number by 6 and then divide the bottom number by 6.0146

This is going to become 1/2; 1/2 is going to be the answer.0153

Another way when you have the problem like this,0160

I can go ahead and simplify straight from here and get my answer as 1/2.0163

I can do what is called cross cancelling.0172

If I have a 3 down here and a 3 up there, then I can cross this out because they are the same.0175

They can cancel each other out.0186

2/4, there is a common factor between 2/4 which is 2.0187

I can just divide this by 2; that becomes a 1.0193

4 divided by 2 becomes a 2; I can simplify it that way.0199

Make sure if you are going to simplify two numbers,0204

one of the numbers has to be on the top, one of the numerators.0206

Another one has to be on the denominator.0211

It doesn't matter if one is on the top up here and the other one is a denominator here0213

or one is numerator up here and then the other one is a denominator here.0217

As long as one number is the numerator and the other number is the denominator, you can cross cancel them.0222

If you multiply 1 times... this is just a 1.0231

Then 3 cancels out to make a 1; 1 times 1 is 1.0234

1 times 2 is 2; either way you get the same answer.0240

In the other example here, I have 1 and 2/5 times 2 and 3/5.0246

These numbers, these fractions, are mixed numbers; I have a whole number in the front.0253

I have to change this fraction from a mixed number to an improper fraction, 1 and 2/5.0259

If I want to change this to an improper fraction, I take my bottom number, my denominator.0275

Multiply it to my whole number; it is going to be 5 times 1.0281

Then add the numerator; 5 times 1 is 5; plus 2 is 7.0285

This becomes 7/5; I have another mixed number here, 2 and 3/5.0291

I multiply my denominator to my whole number and then add my numerator.0304

5 times 2 is 10; I add the 3; that is 13; 13/5.0308

Instead of multiplying this number, the mixed number, I am going to multiply 7/5 times 13/5.0321

This is a 5 right here; this is a 5 right here.0337

I can't cancel those out because those are both numerators.0340

Remember if I want to cancel or simplify numbers, one of them has to be the denominator.0343

Another one has to be a numerator; in this case, they are both denominators.0349

5 to 13, nothing can simplify; I can't cancel anything out.0358

I am just going to go ahead and multiply my numerators.0364

7 times 13 is... you can use your calculator if you want.0367

7 times 13 is 91 over... 5 times 5 is 25.0376

If you look at this, they are not going to have any common factors, 91/25.0383

That is an improper fraction, but you can just leave it like that.0390

This will be my answer, 91/25.0393

Another example, we have 6/5 times 3/4.0400

6/5... let me rewrite this problem.0406

6/5 is an improper fraction because we know that 6 is bigger than the denominator.0413

This is an improper fraction.0422

This is a proper fraction because the numerator is smaller than the denominator.0423

It doesn't matter; we can still multiply it the same way.0429

From here, I can either just multiply it out.0434

If you don't feel like checking to see if numbers can cancel or can reduce,0439

Or you can see if you can simplify any of these numbers.0451

5 and 3, they have no common factors; the greatest factor is 1.0458

We have to leave those numbers.0463

But 4 and 6; 4 and 6 have the common factor of 2.0466

I can divide each number by 2 and just simplify that way.0472

4 divided by 2 is 2; 6 divided by 2 is 3.0477

When you cross cancel numbers, you have to make sure you are going to divide by that same number.0484

4 and 6, I have to divide by 2 to both numbers.0490

4 divided by 2; it becomes 2; 6 divided by 2; that becomes 3.0494

3 times 3 is 9; 5 times 2 is 10.0504

9/10, there are no common factors besides 1; that is my answer.0512

The next problem is 4 and 1/4 times 5/3.0521

This is a mixed number; I need to change that.0527

4 times 4, 16; add the 1; that is 17; 17/4 times 5/3.0530

Again here I need to check to see if any numbers can cancel out.0548

I can't because 17 and 3 have no common factors.0555

5 and 4 have no common factors besides 1 of course.0559

I can just multiply 17 times 5.0563

If you want to do that on the side, let's just do a little multiplication right here.0567

7 times 5 is 35; 5 times 1 is 5; plus 3 is 8.0573

Again when you have a double digit times a single digit, you are just going to do 7 times 5.0584

You are going to put that number, the 3... because it is 35.0590

The 3 goes up there; the 5 goes down here.0594

Then 5 times this number, 5; you are going to add this number right here.0597

5 times 1 plus 3; it becomes 8.0603

17 times 5 is 85 over... 4 times 3 is 12; this is my answer.0606

Some more examples; I want you guys to try to do these problems on your own.0620

You can just pause the video; look at these problems, write them out, and try them.0628

After you are done, you can play it again and just check your answers that way.0636

This problem, 7/8 times 3 and 2/9.0641

7/8 is a proper fraction; and we have a mixed number, 3 and 2/9.0646

Times... I need to change this.0655

It is 9 times 3 which is 27; plus 2 is 29; 29/9.0657

Remember the denominator has to stay the same.0666

When you are changing it from a mixed number to an improper fraction, you are going to keep the denominator.0669

7 and 9, do they have any common factors?--no.0680

8 and 29?--no, they have no common factors.0684

You are going to do 7 times 29; let's do that right here.0689

29 times 7; 9 times 7 is 63; the 6 goes up here.0692

The 3 goes down here below lined up with the 9 and the 7.0702

7 times 2 is 14; plus 6 is 20.0707

There is no number to carry over.0712

You are just going to write both numbers down here, 20; it becomes 203.0714

This is an improper fraction; you can leave it like that.0732

Or you can change it to a mixed number if you would like.0734

If you would like to do that, you would just take the 72.0738

See how many times it will fit into 203; you can do that by dividing.0743

You could just do 203 divided by 72 and see how many times it will go into there.0748

Then you find how many leftovers you have.0755

But otherwise just leave it like this, improper fraction.0764

The next example, 5/4 times 9/11.0768

Since we are multiplying these fractions, they are both...0781

5/4 is improper; 9/11 is a proper fraction; we can go ahead and multiply that0787

Let's see; can we cancel anything?0794

5 and 11, they have no common factors besides 1.0795

4 and 9 have no common factors besides 1.0799

5 times 9 is 45; 4 times 11 is 44; that is an improper fraction.0806

But we can still leave it like that; that is our answer, 45/44.0820

The last couple of examples, we have 3 and 3/7 times 6 and 1/4.0828

These are both mixed numbers.0836

Remember when we multiply fractions, we have to make sure that the fractions are not mixed numbers.0838

We have to change these mixed numbers to make it an improper fraction.0846

3 and 3/7, to change this to a mixed number, again I take the denominator of 7.0852

I am going to multiply it to my whole number.0861

It is going to be 7 times 3 which is 21.0864

Then you are going to add the numerator, plus 3.0867

It is 7 times 3 is 21; plus 3 is 24.0871

You are going to keep the same denominator of 7.0879

3 and 3/7 becomes 24/7; they are the same fraction.0883

But you are changing it from a mixed number to improper fraction.0888

We have to do this one because that is also a mixed number.0894

6 and 1/4, I am going to multiply my denominator to my whole number.0898

4 times is 6 is 24; add the 1; this is 25/4.0904

Now that I converted this to an improper fraction and this one as well, I can now multiply those fractions.0913

From here, you can just multiply your numerators.0934

Before you do that, you can just see if you can cross cancel any numbers.0950

7 with 25, one has to be denominator; the other number has to be the numerator.0956

7 and 25, do they have any common factors?0964

I know that all the factors of 7 are just 1 and 7.0969

It is a prime number; in that case, no.0972

They do not have any common factors besides 1.0975

4 and 24, 4 and 24, they are both even numbers.0979

I know that since the factors of 4 are 2 and 4 and 4 goes into 26, I can reduce these numbers by 4.0988

I am going to take these two numbers and divide both by 4.1000

4 divided by 4 is 1; 24 divided by 4 is 6.1006

Again when you simplify it, you have to make sure that one is on the top and another one is on the bottom.1014

Then you are going to see what common factor they have and divide both numbers by that same factor.1022

That is the most I can simplify; I need to multiply 6 times 25.1034

You are just going to do that on the side; 25 times 6.1043

5 times 6 is 30; you put the 3 up here; 0 down there.1047

6 times 2 is 12; plus the 3 is 15.1052

Since you have no numbers to bring it up, you write the whole number down there.1057

150 over... 7 times 1 is 7; this is an improper fraction.1062

But you can just leave it like that; that would be the answer.1073

The next example, we have 2 and 4/5 times 10/3.1078

2 and 4/5 is a mixed number; we have to change that.1084

I am going to take my denominator, 5; multiply it to my whole number.1091

It is 5 times 2 which is 10; then add the top number.1095

That is 14; it will be 14/5 times 10/3.1101

Again you can just do numerator times the numerator and get the numerator of your solution.1113

5 times 3, that becomes your denominator.1121

Or first you can just see if any of these numbers will cancel; let's see.1125

14 and 10 have a common factor because they are both even numbers.1133

But I can't cancel those out; I can't reduce those because they are both on the top.1139

Remember if you want to reduce the numbers, you have to make sure1146

that one is on the top and one is on the bottom.1148

14 and 3 have no common factors.1153

5 and 10 have a common factor of 5.1156

I can take both numbers and divide it by that factor of 5.1161

5 divided by 5 is 1; 10 divided by 5 is 2.1166

You have to make sure that you are going to divide both numbers by that same factor.1171

Then you are going to do 14 times 2.1178

Now that everything is simplified here, we are going to go ahead and multiply.1180

It is 14 times 2 is 28; 1 times 3 is 3.1184

If you want to change it to a mixed number, you can go back a few lessons1201

to the lesson where I talk about how to change improper fractions to mixed numbers.1206

Just to change this real quick, if you want to change this to a mixed number,1214

I have to see how many times the 3 is going to fit into 28.1218

How many times 3 fits into 28; I can do that by dividing.1223

I do 28... this bar right here means divide.1228

I can do 28 divided by 3; 28; I do 3.1231

How many times does 3 go into 28?1240

Let's see, 9; 9 times 3 is 27; I have 1 left over.1245

Or if you need to change it to a mixed number, you are going to see how many whole numbers.1257

Since 3 fits into 28 nine times, 9 becomes your whole number.1264

Then how many you have left over, I had 1 left over.1270

That becomes your numerator; you are going to keep the same denominator.1274

That is it for this lesson; thank you for watching Educator.com.1290

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