  Mary Pyo

Adding and Subtracting Fractions with Different Denominators

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 Karina Herrera on December 29, 2016I really appreciate using the factor tree method for finding the LCM/LCD. I feel it's a much quicker alternative than the lengthy listing of multiples. Thank you so much for sharing it, Mary! :) 1 answerLast reply by: Mingyang CenWed Aug 15, 2018 8:14 PMPost by Bruno Fulep on April 5, 2014Hi, there is a answer at the exercises that is wrong. 26/30 isn't 4/5. 0 answersPost by Ana Chu on February 27, 2014How did I got 14/18 and 4/16 and got the same answer??? 2 answersLast reply by: sahro AbdiOmarTue Nov 10, 2015 7:42 PMPost by Wasay Ahmad on January 23, 2013i have a question how do you know when to do LCM or LCD do you do both at the same time or one at a specific time? please help 0 answersPost by tenzing amji on January 9, 2013got a a+ on test!!! thanks but don't get example 2 0 answersPost by Frank Bautista on December 17, 2012good instructions....but...there are so many avenues where you can make mistakes because you are using too many long methods. you should also add examples in short methods. 1 answerLast reply by: sahro AbdiOmarTue Nov 10, 2015 7:42 PMPost by Leili Reza on November 16, 2012love you, best teacher 1 answerLast reply by: sahro AbdiOmarTue Nov 10, 2015 7:42 PMPost by Ahmed Mahdi on September 17, 2012this really great lectures. I could not emagine how much time it would have taken( time and money) if I went school for this. I would like to know if i can get the accual book for practicing.thanks. 2 answersLast reply by: Julie KrillsThu Aug 2, 2012 4:27 PMPost by Joseph Craft on July 24, 2012I some how missed the lesson on finding the LCM or LCD and the factor tree, plus prime numbers. Where can I find that lesson? Mary says they were in earlier lesson but I don't see them. 0 answersPost by Walter Osborne on May 9, 2012This lesson on fractions does help. It just seems that there are no standard rules with fractions and I guess that is what confuses me. It's starting to make sense though. Thank you. 0 answersPost by Abdihakim Ibrahim on February 29, 2012this helped me, thanks! 0 answersPost by Hereaux Regis on April 9, 2011She is a great instructor. The video is good.

### Adding and Subtracting Fractions with Different Denominators

• Least common denominator (LCD): The same thing as least common multiple (LCM), but for the denominators of fractions
• To add and subtract fractions, they need to have the same denominator

### Adding and Subtracting Fractions with Different Denominators

[5/8] − [1/4]
• [5/8] − [2/8]
[3/8]
[6/16] − [1/4]
• [6/16] − [4/16]
[2/16] or [1/8]
[3/12] + [1/3]
• [3/12] + [4/12]
[7/12]
[4/15] + [3/5]
• [4/15] + [9/15]
[13/15]
[1/3] + [4/9]
• [3/9] + [4/9]
[7/9]
[12/20] − [4/10]
• [12/20] − [(4 ×2)/(10 ×2)]
• [12/20] − [8/20]
[4/20] or [1/5]
[14/15] − [2/30]
• [(14 ×2)/(15 ×2)] − [2/30]
• [28/30] − [2/30]
[26/30] or [4/5]
[3/4] − [1/2]
• [3/4] − [(1 ×2)/(2 ×2)]
• [3/4] − [2/4]
[1/4]
[41/95] + [2/5]
• [41/95] + [(2 ×19)/(5 ×19)]
• [41/95] + [38/95]
[79/95]
[1/6] + [21/42]
• [(1 ×7)/(6 ×7)] + [21/42]
• [7/42] + [21/42]
[28/42] or [2/3]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Adding and Subtracting Fractions with Different Denominators

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
• Least Common Multiple 0:12
• LCM of 6 and 4
• From LCM to LCD 2:25
• Example: Adding 1/6 with 3/4
• 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

### Transcription: Adding and Subtracting Fractions with Different Denominators

Welcome back to Educator.com.0000

This lesson, we are going to add and subtract fractions with different denominators.0002

Before we begin with that, let's review over the lesson on least common multiple, the LCM.0013

This I believe was a few lessons ago.0022

If you want, you can go back to that lesson.0025

We are just going to do a brief example here.0028

To find the LCM of 6 and 4, I am going to take the two numbers.0031

I am going to do the factor tree method on each of them.0041

For 6, a factor pair of 6 is going to be 2 and 3.0046

They are both prime; I am going to circle them both.0053

For 4, it is going to be 2 and 2; I am going to circle them.0056

Here, to find the LCM, I am going to look at what they have in common.0072

I know that I have a 2 here; I also have a 2 here.0082

I am going to write that 2 by itself.0087

This pair cancels out one of them; I am going to write a 2.0093

The other numbers, 3 and 2, the other remaining numbers are going to go tag along with it.0098

Again to find the LCM, I just find what they have in common.0112

Since there is a 2 here and a 2 here, one of those 2s get cancelled.0119

It is going to be 2 times 3 times 2.0124

2 times 3 is 6; 6 times 2 is 12; my LCM is 12.0130

The LCM of 6 and 4 is going to be 12.0139

LCM is the same thing as LCD.0147

LCM stands for least common multiple; LCD is least common denominator.0154

When I am using those two numbers as my denominators, then it is going to be called LCD.0162

But I am still going to find the LCM between those two denominators.0170

The reason for this, whenever I add fractions or subtract fractions,0174

I have to make sure that these denominators are the same.0179

In order to make them the same, I need to find the LCM or the LCD between the two numbers.0184

Here 6 and 4, just like what we did, the example, we know that the LCM is 12.0193

The LCM, 1/6, what I am going to do is I am going to make 1/6 the same fraction with the denominator becoming 12.0204

Same thing here, 3/4, the denominator is going to change to 12.0221

I want to figure out what these top numbers are going to be, my numerators.0229

How do I go from a 6 to a 12?--what do I multiply it by?0235

I multiplied this by 2; or I can do 12 divided by 6; I get 2.0240

Since I multiplied the 6 by 2 to get 12, I need to also multiply the top number by 2.0250

1 times 2 is 2; the fraction 1/6 became 2/12.0258

These are the same fractions; 1/6 is the same thing as 2/12.0267

Same thing here, 3/4; to go from 4 to 12, I have to multiply it by a 3.0274

Then I have to multiply the top number by 3; 3 times 3 is 9.0285

3/4, because I multiplied the top and the bottom by the same number, these fractions become the same.0294

They are the same fraction; 3/4 is the same thing as 9/12.0304

Now since I know that 2/12 is the same thing as 1/6 and 9/12 is the same thing as 3/4,0310

I can add these two fractions, this fraction and this fraction.0318

If I add these two, then my answer will be the same as if I add these two.0330

I have to do that because these denominators are different.0337

I have to make them the same by converting these fractions,0341

by changing these fractions so that the denominators will be the same.0344

Now that they are, I am going to take my numerators and add them together.0351

2 plus 9 is 11; here the denominator is 12; 12.0357

Then my denominator here has to stay the same as a 12.0365

2/12 plus 9/12 is 11/12; or I can say that 1/6 plus 3/4 is 11/12.0369

Let's do another example; here I am going to subtract.0382

But before I do that, I have to check my denominators.0388

This denominator is an 8; this one is a 4; they are different.0391

I have to find the LCD or the LCM between 8 and 4 so that I can make the denominators the same.0397

I am going to take 8 and 4; you could do the factor tree.0407

4 and 2; circle that one; that is a prime.0419

2 and 2; this is 2 and 2; look at this one.0424

There is a common one here; I am going to cancel out one of them.0433

I have another common between these two so I am going to cancel out one of them.0438

Then I just multiply all the remaining circled numbers.0442

It is 2 times 2 times 2 which is 8.0447

If I look at these, I can just look at them and figure out what the LCM is by looking at the multiples.0455

Multiples of 8 would be 8, 16, 24, and so on.0464

For 4, it would be 4, 8, 12, 16, and so on.0469

You are going to find the smallest common multiple between them which is 8.0473

Here I am going to change this fraction and this fraction so that their denominators will be the same.0480

For this fraction, 7/8, my LCM is already 8.0489

My LCM or my LCD, it is already 8.0494

For that one, I can just keep it the way it is.0498

For this one however, 1/4, I have to convert it; I have to change it.0504

I need a top number; 4; to get 8, I multiply it by 2.0515

Again I have to multiply the same number to the top which is 2.0523

Whenever you are converting fractions, as long as you multiply the top0530

and the bottom by the same number, then your fraction will stay the same.0533

Even if you change the numbers, it is still the same fraction; 1/4 became 2/8.0538

Now I am going to rewrite my problem, 7/8 minus 2/8.0548

Make sure the denominators are the same.0556

If they are not the same, then you did something wrong.0558

Go back and check your work.0561

Since they are the same, I can go ahead and subtract them.0565

7 minus 2 which is 5; then my denominator, 8.0568

8 here; it stays an 8 there; 7/8 minus 1/4 is going to equal 5/8.0576

Let's add this next problem, 9/10 plus 3/15.0591

Again I have to check my denominators; they are not the same.0599

I have to find the least common denominator with them.0602

I am going to take 10; do the factor tree which is 5 and 2.0606

Circle them if they are prime; only circle them if they are prime.0612

Then 15, this becomes 5 and 3.0616

If you are confused about how to find the LCD or LCM,0625

then you can go back and look at the lesson on that one before continuing.0630

My LCM or I am just going to call it the LCD since they are my denominators.0636

I look for any common numbers between them; they have a 5; 5 is common.0642

Whenever they have something in common, just cancel one of them out.0650

That is all they have in common.0654

Then for my LCD, I am just going to write out the remaining circled numbers.0656

Remember they can only be circled; 5 times 2 times 3.0662

5 times 2 is 10; 10 times 3 is 30; my LCD is going to be 30.0667

I have to change this fraction so that my denominator will become 30.0676

Same thing here, change this fraction so my denominator will be 30.0681

9/10, going to convert it; I can take 30 divided by 10; that is 3.0688

I know that I did 10 times 3 to get 30.0702

Again you have to do it to both the top and the bottom, the same number.0707

That is the only way you are going to have the same fraction because you don't want to change your fraction.0711

Even if you are changing the numbers, it is still the same fraction.0715

9 times 3 is 27.0720

I am going to do the same thing for the other fraction.0727

15 times 2 was 30; 3 times 2... again multiply it by the same number.0733

It is going to be 6.0742

Since 9/10 is the same thing as 27/30 and 3/15 is the same as 6/30, I need to add my new fractions.0747

Again double check your denominators; make sure they are the same.0764

It is going to be 27 plus 6.0769

27 plus 6 is 33 over... your denominator will stay the same.0772

It is 33/30; let's look at this fraction.0785

But I have an improper fraction because the top number, the numerator, is bigger than the denominator.0793

You can either leave it like this; this is still the correct answer; or I can simplify it.0800

I know that a 3 goes into 33 and a 3 goes into 30.0811

I can take that number, the common number, the common factor between 33 and 30,0819

divide it to both the top and the bottom.0828

Remember as long as you are doing the same thing to the top and to the bottom of the fraction,0831

you are not changing it; you are just simplifying it.0835

33 divided by 3 is 11; 30 divided by 3 is 10.0839

This is your new improper fraction, 11/10.0850

Since it is an improper fraction, we can change it to a mixed number.0854

Or we can just leave it like that; that is fine too.0858

But if I do want to change it to a mixed number,0861

then this 10 fits into the top number 11 only one time.0864

10 fits into 11 only one time.0873

How many left over do I have?--only one.0877

My denominator always has to stay the same.0881

11/10 is the same thing as 1 and 1/10.0884

Another example, we are going to take 11/20 and subtract it to 11/30.0896

My denominators are different; I have to find the common denominator.0903

I can take 20; 5 is a prime number; I am going to circle it.0910

4, 2, and 2; I circle those; and then 30.0918

For this one, I can either do 3 and 10 or I can do 15 and 2, any factor pair.0927

Let's do 3 and 10; here 3 is a prime number; I am going to circle it.0933

10 is 5 and 2; they are both prime.0939

I am going to look for any numbers they have in common.0945

Here; I have a 2 here; and I have a 2 here.0949

I am going to cancel one of them out.0954

Here I have a 5; and I have a 5 here.0957

I am going to cancel just one of them out.0960

Any others?--nope, that is it.0963

My LCD or my LCM is going to be 2 times 2 times 5 times 3.0967

This is going to be 4 times 5 which is 20, times 3 which is 60; my LCD is 60.0981

Then my next step is going to be to change each fraction so that their denominator will become 60.0993

20, to figure out what you have to multiply to 20 to get 60,1004

I can just take 60 and divide it by 20.1009

This is going to be 3; 20 times 3 was 60.1014

Again you have to multiply the top number by the same number.1019

11 times 3 is 33.1022

For the second fraction, 11/30, 30 times 2 is 60.1028

Multiply the top number by that number; 22.1040

11/20 is the same thing as 33/60; I am going to subtract.1047

Then 11/30 is the same thing as 22/60.1055

Again double check your denominators; make sure that they are the same.1061

Since they are, now I can subtract; 33 minus 22 which is 11 over...1068

11/20 minus 11/30 became 11/60.1085

Let's do another example; this example, 23/95 plus 4/5.1093

In order for me to add these two fractions, I have to make sure they have a common denominator.1104

In this case, they don't; 95 is this denominator; 5 is the other one.1108

I have to look for the common denominator.1115

For 95, I can either look for the LCM, the least common denominator or least common multiple, between 95 and 5.1122

Or I can list all the multiples out and see the smallest common multiple.1134

I know that 95 is divisible by 5 because any number that ends in a 5 or 0 is divisible by 5.1143

In this case, a 5, if this number is divisible by this number,1156

then this becomes the new common denominator, the least common denominator.1162

Or if you want to just do the factor tree to find the least common denominator, then you can do that too.1167

95 is going to be 5 times 19; these are both prime numbers.1175

I am going to circle them; 5 is just 5 and 1.1189

To find the LCD, I am going to look for any factors they have in common.1197

Here, there is a 5 here and a 5 here.1207

I am going to cancel only one of them out.1210

Whenever they have something in common, just cancel only one of them out.1212

Then I am going to write all the circled numbers again; 5 times 19.1217

This is just a 1 so I don't have to write that.1225

5 times 19 I know is 95.1227

My LCD, my least common denominator, is going to be 95.1232

For this fraction here, since the denominator is already 95, I don't have to change it.1239

This one can stay as it is.1246

This one however, I have to change that 5 to make it a 95 so they will have a common denominator1250

because that is the only way I can add these fractions, if their denominators are the same.1256

For this fraction right here, I need to change it so that the denominator will become 95.1260

I am going to take this 95, divide it by 5 to see what I have to multiply this by.1271

That is 19; here I am going to take this and multiply it by 19.1281

This will become 76; 4/5 became 76/95.1296

Make sure you multiply it by the same number.1311

You have to multiply the top and the bottom number by the same number.1314

That way you are not changing the fraction.1318

You are just changing the numbers; but they are still equal fractions.1321

Now I am going to do 23/95 plus 76/95.1326

Again I have to make sure the denominators are the same.1340

If they are not the same at this point, then there is something wrong.1344

Go back and check your work.1347

But since they are the same, I can go ahead and add the fractions.1350

23 plus 76, I am going to add the numerators together.1354

If I add them, it is going to be 99.1358

Here denominator stays the same; it is 95 here; 95 here.1365

My denominator is going to become 95; 23/95 plus 4/5 is 99/95.1372

That is it for this lesson; thank you for watching Educator.com.1385

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