  Mary Pyo

Comparing and Ordering Fractions

Slide Duration:

Section 1: Algebra and Decimals
Expressions and Variables

5m 57s

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

5m 34s

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

8m 40s

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

13m 37s

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

12m 31s

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

11m 30s

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

10m 30s

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

17m 49s

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

7m

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

12m 47s

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

10m 3s

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

14m 16s

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

13m 10s

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

12m 49s

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

15m 1s

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

5m 17s

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

23m 8s

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

19m 44s

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

21m 32s

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

18m

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

11m 5s

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

16m 36s

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

13m 24s

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

16m 5s

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

15m 25s

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

7m 33s

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

6m 42s

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

11m 9s

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

9m 15s

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

18m 3s

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

24m 53s

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

19m 46s

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

17m 58s

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

40m 21s

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

17m 22s

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

22m 1s

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

16m 31s

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

13m 43s

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

11m 51s

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

35m 5s

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

28m 18s

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

32m 31s

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

27m 9s

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

17m 15s

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

24m 17s

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

13m 35s

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

15m 10s

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

17m 41s

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

12m 44s

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

11m 29s

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

15m 4s

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

14m 43s

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

21m 49s

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

8m 59s

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

16m 15s

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

15m 55s

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

23m 28s

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

27m 41s

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

24m 32s

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

19m 43s

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

17m 54s

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

17m 42s

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

19m 59s

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

15m 35s

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

35m 19s

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

12m 13s

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

20m 5s

Intro
0:00
Event Not Occurring
0:07
Formula and Example
0:08
Extra Example 1: Use the Spinner to Find Each Probability
7:24
Extra Example 2: Probability of Event Not Occurring
11:21
Extra Example 3: Probability of Event Not Occurring
15:51
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• ## Related Books 0 answersPost by Jose Guerrero on July 5, 2017She pointed at the wrong fractions when she said bigger than half and less than half. 0 answersPost by Genevieve Carisse on June 3, 2017Awesome explanation!! 0 answersPost by Karina Herrera on December 28, 2016Thank you for the terrific instruction, Mary! :) 0 answersPost by Sameh Mahmoud on May 11, 2014Great, Thanks 0 answersPost by Ana Chu on February 6, 2014you can also do for 5/8 and 2/5 this method: 5/8= 25/40 because 8x5=40 and 5x5=25. and then, 2x8=16 and 5x8=40. they will have the same denominator of 40. 25/40 is greater than 16/40! :) 1 answer Last reply by: Professor PyoThu Jan 2, 2014 4:11 PMPost by amera arshed on November 23, 2013Or did you do who has more? 0 answersPost by amera arshed on November 23, 2013But you ate more "pieces of candy" shouldn't the opening face you? 0 answersPost by PABLO AGREDANO on November 24, 2012can't u also use cross multiplication to compare fractions. multiplying the denominator of one fraction to the numerator of the other fraction and then comparing the two 0 answersPost by Leili Reza on November 14, 2012thanks 1 answer Last reply by: Mary PyoSat Aug 20, 2011 12:28 AMPost by judy lee on August 17, 2011but the signs depend on what number it have on sides to decide if it is greater than or less than.Am I right? 0 answersPost by IVAN STRICKLAND on January 30, 2011VERY GOOD. Thanks.

### Comparing and Ordering Fractions

• > means “greater than”
• < means “less than”

### Comparing and Ordering Fractions

Compare the fractions [1/4] and [3/8]
• [(1 ×2)/(4 ×2)] = [2/8]
• [2/8] < [3/8]
[(1)/(4)] < [(3)/(8)]
Compare the fractions [1/2] and [2/12]
• [(1 ×6)/(2 ×6)] = [6/12]
• [6/12] > [2/12]
[(1)/(2)] > [(2)/(12)]
Compare the fractions [4/8] and [6/12]
• [(4 ÷4)/(8 ÷4)] = [1/2]
• [(6 ÷6)/(12 ÷6)] = [1/2]
• [1/2] = [1/2]
[(4)/(8)] =[(6)/(12)]
Compare the fractions [5/20] and [8/16]
• [(5 ÷5)/(20 ÷5)] = [1/4]
• [(8 ÷4)/(16 ÷4)] = [2/4]
• [1/4] < [2/4]
[(5)/(20)] < [(8)/(16)]
Compare the fractions [9/27] and [27/81]
• [(9 ÷3)/(27 ÷3)] = [3/9]
• [(27 ÷9)/(81 ÷9)] = [3/9]
• [3/9] = [3/9]
[(9)/(27)] =[(27)/(81)]
Compare the fraction [8/11] and [11/121]
• [(11 ÷11)/(121 ÷11)] = [1/11]
• [8/11] > [1/11]
[(8)/(11)] > [(11)/(121)]
Compare the fraction [12/18] and [35/42]
• [(12 ÷3)/(18 ÷3)] = [4/6]
• [(35 ÷7)/(42 ÷7)] = [5/6]
• [4/6] < [5/6]
[(12)/(18)] < [(35)/(42)]
Compare the fraction [2/3] and [15/21]
• [(2 ×7)/(3 ×7)] = [14/21]
• [14/21] < [15/21]
[(2)/(3)] < [(15)/(21)]
List in order from least to greatest [3/4],[1/2],[5/8],[6/16]
• [(3 ×4)/(4 ×4)] = [12/16], [(1 ×8)/(2 ×8)] = [8/16], [(5 ×2)/(8 ×2)] = [10/16]
• [6/16] < [8/16] < [10/16] < [12/16]
[(6)/(16)] < [(1)/(2)] < [(5)/(8)] < [(3)/(4)]
List in order from least to greatest [3/4],[4/8],[2/32],[6/16]
• [(3 ×8)/(4 ×8)] = [24/32], [(4 ×4)/(8 ×4)] = [16/32], [(6 ×2)/(16 ×2)] = [12/32]
• [2/32] < [12/32] < [16/32] < [24/32]
[(2)/(32)] < [(6)/(16)] < [(4)/(8)] < [(3)/(4)]

*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.

### Comparing and Ordering Fractions

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
• Terms Review 0:14
• Greater Than
• Less Than
• Compare the Fractions 1:00
• Example: Comparing 2/4 and 3/4
• Example: Comparing 5/8 and 2/5
• 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

### Transcription: Comparing and Ordering Fractions

Welcome back; this lesson is going to be on comparing fractions.0000

Since we are going to be comparing fractions, we are going to be able to order them least to greatest.0007

This symbol right here means greater than.0017

If I were to use it, if I said 5 with that symbol and another number 2,0023

then I can read this is as 5 is greater than 2.0034

This means less than; I can say 2 is less than 4.0040

You have to make sure that this opening is going to face the bigger number; the same with this.0051

We are going to use those symbols to compare fractions.0062

We have a fraction 2/4 and another fraction 3/4.0069

Let's say that this is me; this is you.0075

Let's say we both have the same number of candy pieces.0086

You have 4 pieces; I have 4 pieces.0091

If I ate 2 out of the 4 pieces and you ate 3 out of the 4 pieces, who ate more?0094

You did; my fraction, what I ate, is less than what you ate which is 3 out of 4.0103

We know that 2 out of 4 is less than 3 out of 4.0115

In the same way, 5 out of 8 with 2/5.0124

These denominators are different; we have different number of parts.0131

If I look at this, 5/8, I know that half of 8 is 4.0141

If I look at this, this would be greater than half because 4 out of 8 is half.0152

5 out of 8 is bigger than half.0163

2/5, if you have 5 candy pieces and you ate 2 out of those 5, then you ate less than half.0168

5/8 is greater than half; 2/5 is less than half.0180

Which one do you think is a bigger fraction?0188

This is bigger than half; this is less than half.0191

I know that this one right here, 5/8, is going to be greater than 2/5.0197

Let's compare this one; 1/2 and 3/4.0211

Again these parts, the number of parts, this is 1 out of 2 parts; this is 3 out of 4.0219

The total number of parts are different between the two fractions.0226

What I can do is I can either look at this as 1/2 and this as 3/4, 3 parts out of the 4.0230

That is bigger than 1/2; I can compare it that way.0241

Or I can make these denominators the same.0245

Try to make them the same equal number of parts.0249

That way we can just compare the number on top.0253

1/2, I can change this 2 to a 4 because a 4 is a multiple of 2.0260

If I change the 2 to a 4, to get it from 2 to 4, I multiplied by 2.0271

I can do the same thing for the top numbers.0283

If I take the top number and I multiply it by 2, then I get 2.0285

If you want to demonstrate this fraction becoming this fraction...0292

Say I have a circle, I can either cut it in half that way.0299

This would become 1 out of 2 parts.0306

Or I can cut this into 4 pieces and say that I am going to eat 1, 2 out of 4 parts.0312

Either way I represent this, they are the same fraction.0325

I changed 1/2 to 2/4; I am going to compare it to 3/4.0335

Again 4 pieces, I ate 2; out of 4 pieces, let's say you ate 3.0342

Who ate more? 2/4 is less than 3/4.0350

I am going to write this symbol to show that this fraction is less than this fraction.0359

Another example, 3/9 with 4/12.0369

3/9, I can take this fraction; I can change it to look different0380

because this fraction and this fraction, they have different number of parts.0393

I am going to change them so that I can look at this in a more simpler way.0399

3/9; if I divide a common factor of 3 to both numbers, this is the same thing as 1/3.0405

Out of 3 parts, this is 1.0421

For 4/12, I also know that there is a common factor between the top number and the bottom number.0426

I am going to take the common factor which is 4, divide it to the top and to the bottom.0436

4 divided by 4 is 1; 12 divided by 4 is 3.0447

3/9 became 1/3; 4/12 also became 1/3.0456

These two fractions are actually the same; this is 1/3, 1 out of 3 parts.0465

This is also 1 out of 3 parts.0472

I am going to write equals; these two fractions are the same.0475

This next example, 8/11 and 21/100; these numbers are of big.0483

What I can do is I can look at these fractions and see how they compare with each other.0495

8/11, if I have 11 total number of parts and I use up 8,0504

or let's say you have 11 pieces of candy and you are going to eat 8 of them.0513

Did you eat more than half or less than half?0522

I know about 5 and 1/2 is half of 11.0525

8 is more than half; 8 is more than half of 11.0529

Let's look at this one, 21/100; 21 is smaller than half of 100.0536

Half of 100 is 50; 21 is less than that.0547

This one right here is bigger than half.0552

This one right here is smaller than half.0555

If I compare them, I know, even though these numbers are smaller than these numbers,0558

this fraction is actually more than this fraction.0563

This 8/11 is going to be greater than 21/100.0568

This example, we are going to compare these four fractions.0580

We are going to order them from least to greatest.0586

Since we are able to compare fractions, let's see which fraction is the smallest and which fraction is the greatest.0593

Let's look at these--3/4, 1/6, 1/2, and 4/4.0604

3/4, if I think of this fraction, 3/4 is 3 out of 4 parts.0615

Say you have a cake that is cut up into 4 pieces.0624

You ate 3 out of the 4 slices; that is more than half.0630

1/6, if you take that same cake and you cut it up into 6 pieces.0635

now the pieces are smaller and you ate 1 of those.0642

Then you are eating less than half of your cake.0645

You are eating a small piece; same thing for this fraction.0651

You are going to take the same cake.0655

You are going to cut it up into 2 pieces.0657

You are going to eat 1 of those.0661

Imagine, is that going to be a big slice or a small slice?0663

It is going to be half of your cake.0667

This last one right here, 4 out of the 4.0671

If you cut your cake into 4 pieces and you eat all 4, you are eating the whole cake.0674

Which fraction is the smallest?0684

3/4, 3 slices out of 4, 1 slice out of 6, 1 out of 2, or 4/4?0689

Which one represents the smallest piece of cake?0699

1/6 would actually be the smallest because if you cut it up into 6 pieces,0707

that means you are cutting them up into smaller pieces.0713

You are only going to be eating one of those.0715

The smallest fraction is going to be 1/ 6.0719

The next one... I am done with this one.0726

The other three, the next smallest would be 1/20731

because I know this one is going to be more than half the cake.0739

4 out of 4, that is the whole cake.0745

Half the cake would be the next smallest.0748

Then 3/4 is going to be the next smallest0752

because if you eat 3 out of 4 slices, you still have some cake left over.0758

Whereas if you eat 4 out of 4 slices, then you ate the whole cake.0763

The next fraction is going to be 3/4.0768

Then the greatest fraction is going to be 4/4.0774

This was the lesson on comparing fractions; thank you for watching Educator.com.0784

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