  Mary Pyo

Solving Proportions

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 2 answersLast reply by: Ana ChuSun Feb 1, 2015 11:21 AMPost by mohamed bulhan on July 3, 2014PROPORTIONS are confusing to me. what is the easiest way to solve proportions?

### Solving Proportions

• Portion: An equality of two ratios

### Solving Proportions

Find two equivalent ratios for each
[3/5]
• [(3 ×2)/(5 ×2)] = [6/10]
• [(6 ×2)/(10 ×2)] = [12/20]
[6/10],[12/20]
Find two equivalent ratios for each
[11/44]
• [(11 ÷11)/(44 ÷11)] = [1/4]
• [(1 ×2)/(4 ×2)] = [2/8]
[1/4],[2/8]
Use mental math to solve the proportion
[3/5] = [x/10]
• [(3 ·2)/(5 ·2)] = [x/10]
x = 6
Use mental math to solve the proportion
[1/8] = [x/24]
• [(1 ·3)/(8 ·3)] = [x/24]
x = 3
Use mental math to solve the proportion
[3/z] = [12/16]
• [(3 ·4)/(z ·4)] = [12/16]
z = 4
Tell whether the two ratios form a proportion
[4/40],[8/80]
• [(4 ×2)/(40 ×2)] = [8/40]
Yes
Tell whether the two ratios form a proportion
[12/24],[24/47]
• [(12 ×2)/(24 ×2)] = [24/48]
No
Tell whether the two ratios form a proportion
[13/26],[25/52]
• [(13 ×2)/(26 ×2)] = [26/52]
• [26/52] ≠ [25/52]
No
Solve the proportion
[5/x] = [2/20]
• 2x = 5 ·20
• 2x = 100
• [2x/2] = [100/2]
• x = [100/2]
x = 50
Solve the proportion
[2/4] = [y/16]
• 4y = 2 ·16
• 4y = 32
• [4y/4] = [32/4]
• y = [32/4]
y = 8

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

### Solving Proportions

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
• Proportions 0:05
• An Equality of Two Ratios
• Cross Products
• 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

### Transcription: Solving Proportions

Welcome back to Educator.com.0000

For the next lesson, we are going to be solving proportions.0002

A proportion is when we have two equal ratios.0008

A ratio is a comparison between two parts, A and B.0014

Here this is a ratio comparing A and B together.0022

You read it as A to B.0028

You can also write ratios A to B like that.0030

But when you are taking two ratios and you are comparing them0036

to each other and you are saying that they are equal,0039

the ratio of A to B is equal to the ratio of C to D, then you have a proportion.0042

You are actually going to have to write it A to B like a fraction.0049

Proportion is when you have ratio equaling another ratio.0056

To solve proportions, let's say you are missing one of these.0062

You are missing A; or you are missing B; one of these.0065

To solve a proportion, you are going to use what is called cross products.0069

Cross products is when you multiply across.0075

You are going to go A times D equal to B times C.0078

You have the proportion A over B equal to C over D.0089

Then you are going to find the products AD.0096

Cross products, that is A times D.0100

When you write two variables next to each other like that, that means multiply.0103

A times D equal to B times C.0107

Be careful, this is not the same thing as cross cancelling.0113

Cross cancelling is when you are multiplying fractions0117

and you can cancel out numbers if they have common factors.0120

But this is cross products; this is for proportions.0126

This is only when they are equal to each other.0129

Then you can multiply across and make it equal to this across.0132

AD, A times D is equal to B times C.0140

Let's do an example; if I have let's say 1/2 equal to X/ 4.0145

This one is easy; we know we can do this in our head.0156

One half, 1/2, is the same thing as 2/4.0158

I know that X has to be 2.0163

But to solve it, just to use cross products, it will be 2 times X.0167

2 times X is 2X; same thing as 2 times X.0174

It is equal to 1 times 4 which is 4.0178

Then to solve this out, we are going to... remember one-step equation.0183

This is 2 times X or 2 times what equals 4?0188

2 times 2 equals 4; X equals 2.0193

Let's do a few examples; the first example, find two equivalent ratios for each.0200

We know that proportions are when we have two equal ratios.0207

Let's find two other ratios that are equal to this.0214

3/4, I can say that if I multiply this by 2, then this is 6/8.0218

This ratio is equal to this ratio.0228

To find another one, how about if I multiply it by 3?0232

3 times 3 is 9; 4 times 3 is 12.0235

Here are my two equivalent ratios.0241

Here I can also divide.0248

If I divide by 10, divide this by 10, because I know 10 goes into both, this becomes 1/2.0250

That is one equivalent ratio.0261

I can multiply this by 2; multiplied by 2; multiplied by 2.0266

This can be 2/4.0272

This and this, they don't look like they are equivalent.0276

But they actually are because if you simplify this, this is 1/2.0279

If you simplify this, this is 1/2; it is the same; it is equivalent ratios.0284

This one, you can multiply it by 2; you can divide.0294

I know that 11 and 33 have factors of 11.0301

11 divided by 11 is 1 over... 33 divided by 11 is 3.0308

Again you can just base it on this for the next one.0315

Multiply it by 2; it will be 2.0318

Multiply this by 2; it will be 6.0321

There are actually many, many different ratios or fractions that you can write out to make them equivalent.0327

There is going to be many, many; these are not the only answers.0336

These are not the only fractions that are equal to this fraction.0339

If you want, you can multiply this by 10, multiply it by 20.0344

As long as you do it to both numbers, you are going to have equivalent ratios.0347

Let's solve these proportions; but we are going to use mental math.0354

Meaning we are going to try to solve these out in our head.0358

For the first one, I want to solve for X; 3/4 equals X/12.0362

If this fraction is going to have to equal this fraction, 4 times what is 12?0371

4 times 3 is 12; that means I have to multiply the top number by 3.0376

X has to be 9; X equals 9.0382

Same thing here; this is 1 times 5 which gave me 5.0388

Then I have to multiply 5 to this; A is going to be 25.0394

Same thing here.0404

If you look at the bottom numbers, this is 6 times 1 equals 6.0406

Something times 1 is going to equal 4; isn't this 4 times 1?0414

This is going to be the same fraction; 4/6 has to equal 4/6.0418

D is going to be 4.0424

The next one, this one is a little bit different0428

because I can't divide and multiply a number 15 to give me 12.0433

What I can do is I can just simplify this ratio because I have both the top and bottom number.0441

I want to simplify this ratio to help me solve for this ratio.0449

If I simplify this, I know that 4 goes into both numbers.0454

Divide this by 4; this is 3/2; this ratio is equivalent to that ratio.0459

I just have to base this one on this then.0473

3 times 5 is 15; to go from here to here, it is times 5.0480

To go from here to here then, it will be times 5.0489

Z has to be 10.0493

Tell whether the two ratios form a proportion.0503

That just means that they have to be equal.0508

It is just a yes or no.0511

Are they equal or are they not equal?--because proportions have to be two equal ratios.0512

Is this ratio equal to this ratio?0519

2/3, multiply this by 10 to get 20; multiply this to 10 to get 30.0525

Is it equal?--yes, this one is equal.0533

The next one, are these equal ratios?0539

This one, you had to multiply this by 7 to get 35.0543

If you multiply this by 7, you have to multiply it by the same number.0549

Does it give you that?--this one is yes.0552

This one here, again I can't multiply or divide this number to get this number.0560

I can find another equivalent ratio to base both of these on.0566

I know that 5 goes into both of these.0572

5 goes into 25 five times; I am dividing by 5.0577

70 divided by 5 is going to be...0584

Again if you want to just divide it out, it is going to be 70 divided by 5.0589

Otherwise it is going to be 14.0594

I know that because... I will just solve it out.0598

Let's do it right here; 70 divided by 5.0602

1 is going to give you 5; subtract it; 2; 5 times 4 is 20.0608

That means to get from 5 to 35, I have to multiply this by 7.0617

What is 14 times 5?--it is 70; I know it is not 70.0626

This has to be 70; so I am going to say no.0636

The next one, here 42/21, this also is going to be equivalent fraction.0651

This will be 2/1 because 42/21... 21 is half of 42.0666

Again I can just divide this by 21 to get 2; and then 21 to get 1.0680

To get from here to here... or see if this one equals the same thing.0687

This one, divide this by common factor; is this 12?0693

This becomes 2; this becomes 1.0703

See how this was equal to this?--and then this also equal to this?0707

That means these are the same; so this one is yes.0712

You can do the same thing for this one.0716

I know that this simplified to get that.0720

Here 35 divided by 5 because a common factor between this one and this one is 5.0724

This one is 7 over... 75 divided by 5.0740

75 divided by 5 is going to be 15.0751

That will just be 5, 2; bring down the 5; this is 15.0757

Automatically because these are different, I know that it is a no.0765

Again if you want to figure out if two ratios are equal, you can either multiply, see if it is the same factor.0772

Or can just simplify each one of them and see if those simplified fractions are the same.0783

Like the bottom one right here, this last one, you simplify this; it became 2/1.0791

You simplify this; it became 2/1.0796

Since they simplify to become the same fraction, you know that these are the same.0798

So that is yes.0804

For the next example, we are going to solve the proportion using cross products.0807

Just practice using these cross products.0814

You are going to multiply these across.0816

You are going to make it equal to those two multiplied.0822

This becomes 2 times X; I am just going to write that as 2X.0828

Remember whenever you multiply a number with a variable, you can write it together like that.0832

Then equals 5 times 10 which is 50.0838

Again be careful, cross products is not the same thing as cross cancel.0843

You are not cancelling anything out.0849

This 5 and this 10, they have a common factor of 5.0850

But you are not cross cancelling out.0856

You only cross cancel when you are multiplying the fractions.0858

But here you are solving proportions where it is an equal, not a multiplication.0863

You are going to multiply them together and you are going to make it this side.0867

From here, I have to find out what X is; 2 times something equals 50.0874

2 times 25 equals 50; think of 50 cents.0880

2 times 2 quarters... that is 25 cents... equals 50 cents.0888

Or you can also just divide this 2; X is going to equal 25.0895

If you want, you can just use division like this.0906

2 goes into 5 two times; 4; subtract it; you bring down the 1.0910

Bring down the 0; 2 times 10 is 6; X is 25.0917

Same thing here; let's cross multiply; cross products.0927

3 times M would be 3M; just write them together like that.0939

Make sure you don't do it with numbers.0945

If it was 3 times 4, then you can't put 34 because it looks like the number 34.0946

This means 3 times M; then 4 times 21; 4 times 21 is 84.0952

21 times 4; 1 times 4 is 4; 4 times 2 is 8.0968

From here, 3 times something equals 84.0976

That means I have to divide this 3.0979

I need to divide the 3 to get my answer; 84 divided by 3.0984

How many times does 3 go into 8?--two times; that becomes 6.0993

I am going to subtract and get 2; bring down the 4.0998

3 times 8 equals 24; 24, 0; my M is 28.1002

Make sure you write what the variable is; the variable equals 28.1018

Don't forget, when you are solving proportions, if you can do it mentally, then go ahead and do that using mental math.1023

Otherwise you are going to just multiply this.1030

These two across equal these two across; then solve for your variable.1032

That is it for this lesson; thank you for watching Educator.com.1038

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