  Mary Pyo

Writing 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

• ## Related Books 1 answer Last reply by: Mary PyoFri Feb 3, 2012 11:54 PMPost by jeffrey breci on December 7, 201180/60 is 1.33, 1and 1/3 when you switch to an improper fraction is 4/3 and again switch to a decimal is 1.33. how do you get 1 min, and 20 seconds? 0 answersPost by Siddharth Gupta on August 14, 2011great video! you can learn a lot from this. she explains it nicely. she is amazing

### Writing Proportions

• When writing proportions, first create a ratio that you can base your proportion on

### Writing Proportions

Write a proportion and solve
8 pounds for \$ 24, find the cost for 2 pounds
• [24/8] = [x/2]
• 2 ·24 = 8x
• 48 = 8x
• [48/8] = [8x/8]
• [48/8] = x
x = \$ 6
Write a proportion and solve
21 feet for every 5 minutes, find how many feet in 10 minutes
• [21/5] = [x/10]
• [(21 ×2)/(5 ×2)] = [x/10]
x = 42 feet
Write a proportion and solve
10 chocolate bars cost \$ 20.50. Find the cost of 4 chocolate bars
• [10/20.50] = [4/x]
• 10x = 4 ·20.50
• 10x = 82
• [10x/10] = [82/10]
• x = [(82 ÷2)/(10 ÷2)] = [41/5] = 8.20
\$ 8.20
Write a proportion and solve
Sharon types 80 words per minute. Find how long it will take for her to type 120 words
• [80/1] = [120/x]
• 80x = 120
• x = [(120 ÷40)/(80 ÷40)] = [3/2] = 1[1/2]
1[1/2] min
Susanna estimates that it will take 8 hours to drive 1200 km. After 4 hours, she has driven 600 km. Write a proportion to see if she is on schedule.
• [8/1200] and [4/600]
• [(8 ÷8)/(1200 ÷8)] = [1/150]
• [(4 ÷4)/(600 ÷4)] = [1/150]
• [1/150] = [1/150]
Yes
Write a proportion and solve
2 pounds for \$ 30, find the cost of 15 pounds
• [2/30] = [15/x]
• 2x = 30 ·15
• 2x = 450
• [2x/2] = [450/2]
x = 2
Write a proportion and solve
12 feet for every 3 minutes, find how many feet in 9 minutes
• [12/3] = [x/9]
• 3x = 12 ·9
• 3x = 108
• [3x/3] = [108/3]
• x = [108/3]
36 feet
Write a proportion and solve
6 chocolate bars cost \$ 8.50. Find the cost of 3 chocolate bars
• [6/8.50] = [3/x]
• 6x = 3 ·8.50
• 6x = 25.50
• [6x/6] = [25.50/6]
• x = [25.50/6]
\$ 4.25
Sharon types 80 words per minute. Find how long it will take for her to type 200 words
[80/1] = [200/x]
• 80x = 200
• [80x/80] = [200/80]
• x = [(200 ÷40)/(80 ÷40)] = [5/2] = 2[1/2]
2[1/2] min
12 chocolate bars cost \$ 15.00. Find the cost of 20 chocolate bars.
• [12/15] = [20/x]
• 12x = 20 ·15
• 12x = 300
• [12x/12] = [300/12]
• x = [300/12] = 25
\$ 25

*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.

### Writing 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
• Writing Proportions 0:08
• Introduction to Writing Proportions and Example
• 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

### Transcription: Writing Proportions

Welcome back to Educator.com; for the next lesson, we are going to continue proportions.0001

We are going to actually write proportions and then solve them.0005

When we write proportions, it is easier if you first create a ratio that you can base your proportion on.0011

I like to call it a word ratio because you are going to look at what you have0022

and then create a word ratio meaning a part to a part.0033

You are going to find out what you are going to leave on the top0039

and what you are going to put on the bottom of your ratio.0043

Here I have my example, 2 miles in 20 minutes.0048

I want to find out how many miles it will be in 30 minutes.0053

I want to create my word ratio; for example, I could put miles over minutes.0059

That means all the numbers that have to do with miles is going to go on the top.0071

All the numbers that have to do with minutes is going to go on the bottom0077

because when we write a proportion, remember a proportion has to be two ratios that equal each other.0081

The first ratio I am going to write is going to have to do with this part right here.0091

2 miles in 20 minutes; remember ratio, I am comparing two things.0096

I am comparing the miles and I am comparing the number of minutes.0103

All the miles is going to go on the top.0106

That means I am going to write 2 miles... mi for miles0109

Over 20 minutes because that is on the bottom; 2 miles in 20 minutes.0116

Then I have to create my next ratio.0126

Remember I am making a proportion; I am making this ratio equal to this ratio.0131

That way I have a proportion, I can solve for whatever is missing, my X, my variable.0138

Again the miles is going to go on the top because that is what I set.0147

That is my word ratio; it is going to be X miles over... 30 minutes.0154

That is minutes; that is going to go on the bottom.0162

As long as I keep all the miles on the top and all the minutes on the bottom, I can create my proportion.0169

Let's say I created my word ratio so that it was minutes over miles.0175

That is OK.0180

As long as you keep all the minutes on the top and all the miles on the bottom,0181

you are still going to get the same answer.0186

You are still going to get the correct answer.0189

Again this ratio is equal to this ratio; that is how I get my proportion.0192

That is how I am going to write my proportion.0198

From here, I need to solve this out; I can cross multiply.0200

If I can solve it in my head, then I want to do that instead so I don't have to do all the work.0208

2/20 is going to equal X/30.0214

I just rewrote the proportion without all of the units so you can see it a little bit easier.0223

Here I can create an equivalent ratio; remember equivalent ratios from the previous lesson.0232

2/20 is the same thing as 1 over... because here I divided this by 2.0241

2 divided by 2 is 1.0250

If I want to do 20 divided by 2, then it is going to equal 10.0253

I can also do the same thing here.0260

I want to make this ratio the same as 1/10.0263

I can multiply this by 3 to get 30.0269

Then I have to multiply this top by 3 to get 3.0273

My X is going to be 3.0279

Here I just used mental math to solve for X.0285

I just made this equivalent ratio, 1/10, and then turned this into the same thing, 1/10.0289

If you want, you can use cross products instead; that is another method.0297

You are going to multiply all this together; make it equal to this.0302

2 times 30... actually let's go this way first.0309

It doesn't matter which way you go first.0311

20 times X is 20X; equal to... 2 times 30 is 60.0313

If I double 30, it is 60; 20 times what equals 60?0325

20 times 3 equals 60.0331

20, 40, 60; that is 3; X will become 3.0335

That is the same thing; it doesn't matter which way you solve.0340

As long as you make it so that this ratio is equal to this ratio.0347

Let's do a few examples.0354

We are going to write a proportion and then solve them out.0358

5 pounds for \$15; find the cost for 4 pounds.0362

I want to first create a word ratio; word ratio, what am I comparing?0369

Or what am I using?--I am using pounds and I am using money.0380

I can say money or dollars on the top.0385

Then I am going to keep the pounds on the bottom.0391

It doesn't matter if you do pounds over money; that is fine too.0395

Here is my word ratio; that means when I create my proportion,0398

I am going to keep all the dollars on the top and then all the number of pounds on the bottom.0402

5 pounds for \$15, here is my first ratio, comparing these two things.0410

\$15, that is the dollars; that is going to go on the top; 15.0415

Over 5 pounds; that is going to go on the bottom because that is what I made my word ratio.0420

Find the cost for 4 pounds.0429

4 pounds, does the 4 go on the top or the bottom?0432

It is pounds; it is going to go on the bottom.0435

I want to find the cost; that is what I am looking for.0440

I am going to make that my variable; I can say X.0442

That is the money part; find the cost; cost is money.0446

That is going to go on the top.0451

Here I am going to solve for X; again you can solve this two ways.0454

You can find the equivalent ratio; I am going to simplify this.0462

This is going to become... divide this by 5.0468

15 divided by 5 is going to be 3.0474

5 divided by 5 is going to be 1; there was my equivalent fraction.0478

Same thing here; I want to make this the same as 3/1.0487

How did I go from 1 to 4?--this was multiplied by 4.0498

Or I can just do 4 divided by 4 is 1.0502

Same thing here; 3 times... whatever I do to the bottom, I have to do to the top.0505

X becomes 12; or again you can just do cross multiplying.0511

You can do 15 times 4 equal to 5 times X.0520

Then you can see what you have to multiply by 5 to get this number.0524

My X is going to be 12 because 12/4 is going to be 3/1.0531

That is the same thing as 15/5.0538

I have to look back and see what am I looking for?0543

I know that X is 12; but it is asking for the cost.0546

We know cost is money.0551

How much is it going to cost for 4 pounds? \$12.0555

The next one, 15 feet for every 4 minutes; find how many feet in 10 minutes.0562

My word ratio, I am going to make it 50 over minutes.0570

My 16 feet is going to go on the top.0581

My 4 minutes is going to go on the bottom.0584

Equal it to how many feet?--find how many feet.0588

That is what we are looking for; feet, that is the top number.0591

That is X; over the number of minutes is 10.0595

Again you can look for equivalent fraction.0606

This is going to be the same... 16/4 is going to be the same as...0610

If you divide this by 4, divide this by 4, you are going to get 4/1.0615

I am going to use that fraction to help me solve for X.0626

1 times 10 equals 10; it is 4 times 10 is 40.0635

That means X has to be 40.0640

Again these two have to be equal; this is the same as 4/1.0647

That means this has to be the same as 4/1.0653

1 times 10 is 10; 4 times 10 has to be 40.0659

How many feet?--X is going to be 40 feet.0667

Example two, write a proportion and solve.0680

5 chocolate bars costs 7.50; find the cost of 2 chocolate bars.0684

My word ratio, chocolate bars; you can do money on the bottom.0689

Or you can just do money on the top and then the number of chocolate bars on the bottom.0698

It doesn't matter; there is my word ratio.0702

Chocolate bars; 5 chocolate bars; 5 on top; over money; 7.50 on the bottom.0708

Equal to chocolate bars... that is 2 on the top; over the amount of money on the bottom.0717

For this one, I can solve this proportionally.0730

You can also use this as a ratio.0739

Remember 7.50 for 5 chocolate bars; you can make that as a ratio.0746

Then find the unit rate; find how much it costs per chocolate bar.0751

If you remember from a couple of lessons ago, you can use unit rate also for the same problem.0758

Let's just go ahead and solve this using cross products.0766

I am going to multiply this and this; that is going to be 5X.0770

Again if you are multiplying number times variable, then you can just put it together like that.0776

Equals 7.50 times 2; 7.50 times 2.0782

If you want, you can just multiply it out like that.0790

0; 5 times 2 is 10; 2 times 7 is 14; add the 1; 15.0796

You know that this is 7.50; that is money; 7 times 2 is 14.0808

If you have 50 cents and you double it, that is a dollar.0815

You can think of it that way too; 5X equals \$15.0818

I am not going to put the 0.00 because that is just change.0825

This is my whole number, \$15; I can now find X.0829

5 times... I know 3 equals 15; X is going to be 3.0836

That means if for 5 chocolate bars, it costs 7.50,0845

for 2 chocolate bars, it is going to cost me \$3.0850

I need to write my dollar sign here to give me the answer.0855

The next one, Sharon types 60 words per minute.0864

Find how long it will take for her to type 80 words.0869

My word ratio could be words over minute; 60 words per minute.0874

That is over 1 because the number of minutes is 1.0886

How long will it take... they are asking how long it will take.0894

They are asking for words or minutes?--they are asking for minutes; how long.0899

This will be X down here; then they are asking for 80 words.0903

Again you can use proportions; you can use cross products.0911

60 times X is 60X; equal to 1 times 80 is 80.0919

Remember if you want to find what 60 times X is and what X is, then you can divide the 60.0929

Anytime you have a number times 60, you have a number times a variable,0939

you can just divide that number to find X.0942

X is going to equal... I am going to cross out these 0s.0947

I am going to have 8/6; but then here I can simplify that.0951

Divide this by 2; divide this by 2; it is going to be 4/3; 4/3.0957

If I want to change this to a mixed number, this will be... 3 goes into 4 one whole times.0971

How many do I have left over?--1; my denominator is 3.0982

It will be 1 and 1/3 of a minute.0988

If you have a problem like this on your homework or at school,1001

it depends on how your teacher wants it, but you can change this to a decimal.1008

Or since it is minutes, you can take this fraction.1012

It is 1 whole minute and then some seconds; 1/3 is part of a minute.1016

You can just figure out how many seconds that would be by doing 60 divided by 3.1022

60 divided by 3; that is going to give you 20.1030

That means this is going to be 1 minute and 20 seconds.1036

Or you can just leave it like this if your teacher doesn't mind.1040

Then it is 1 and 1/3 of a minute.1045

The third example, Susanna estimates that it will take 4 hours to drive 600 kilometers.1051

After 3 hours, she has driven 500 kilometers.1058

Write a proportion to see if she is on schedule.1064

Basically they are asking if you make a ratio of this and you make a ratio of the next part,1068

are they the same?--that is all it is asking.1076

My word ratio, hours over kilometers.1083

It is going to be 4 hours over 600 kilometers.1091

We are going to see if this equals the same as 3 hours over 500 kilometers.1102

Let's see here; let's simplify these.1117

Here I can say that if I simplify this, 4 goes into 600 how many times?1124

Here is 1, 4, 2; I am just dividing it.1141

That is 5; 20; bring down this 0; 150.1146

If I divide this by 4 and I divide this by 4, I am going to get 1/150.1155

That means every hour, Susanna should drive 150 kilometers.1167

If 4 hours, she estimates she is going to be driving 600 kilometers,1178

that means every 1 hour, she is going to be driving 150 kilometers.1184

Is that the same thing as this?1191

If 1 hour, 150 kilometers, does she get this in 3 hours?1193

This is 1 times 3 equals 3 hours; 1 hour times 3 is 3 hours.1203

Does that mean 150 times 3 is 500?--let's see.1210

This times 3; 0; 5 times 3 is 15; add that; that will be 450.1219

No, if she drives 150 kilometers for every hour,1234

then in 3 hours, she should be driving 450 kilometers.1240

But she drove 500 kilometers; that means she is not really on schedule.1246

I mean, she is a little bit faster.1252

But according to what she has estimated, it is not the same.1256

So this one is no; she is not on schedule.1260

She is actually a little bit early because she drove more than what she thought she would be at.1264

This is not the same ratio.1273

If it is 4 hours for 600 kilometers, then in 3 hours, she should be driving 450 kilometers.1276

Because 1 hour is 150 kilometers; this needs to have the same ratio also.1292

1 hour is 150; this has to equal this too.1304

This one is no; she is early.1311

That is it for this lesson; thank you for watching Educator.com.1318

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