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Nancy Fung

Nancy Fung

Subtracting Rational Numbers

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Table of Contents

Section 1: Variables and Algebraic Expressions
Numerical Expressions

13m 41s

Intro
0:00
What You'll Learn and Why
0:08
Topics Overview
0:09
Vocabulary
0:22
Order of Operations
0:26
Numerical Expression
1:03
Simplify
1:27
Simplifying an Expression
1:44
Example 1: Simplify the Expression
1:45
Simplifying an Expression
3:26
Example 2: Simplify the Expression
3:27
Using an Expression to Solve a Problem
4:29
Example 3: Babysitting
4:33
Using an Expression to Solve a Problem
6:14
Example 4: Shopping
6:17
Extra Example 1: Simplify the Expression
7:35
Extra Example 2: Simplify the Expression
8:55
Extra Example 3: Finding Total Cost
10:02
Extra Example 4: Finding Total Cost
11:44
Algebraic Expressions

9m 11s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Variable
0:19
Algebraic Expression
0:30
Evaluate
0:51
Modeling an Algebraic Expression
1:16
Model the Expression 2x + 4
1:17
Evaluating an Algebraic Expression
1:47
Evaluate 3x - 7 for x = 8.2
1:48
Evaluating an Algebraic Expression
2:45
Evaluate (3.7 + x) ÷ 2 for x = 9.6
2:46
Using a Table to Evaluate an Expression
4:10
Example: Pairs of Shoes
4:13
Extra Example 1: Evaluate the Expression
5:46
Extra Example 2: Evaluate the Expression
6:06
Extra Example 3: Perimeter of a Rectangle
6:46
Extra Example 4: Finding Income
7:40
Writing Expressions

8m 24s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Addition
0:26
Subtraction
1:04
Multiplication
2:06
Division
2:31
Translating Words to Expressions
3:02
Example: 9 Less than Twice a Number
3:08
Writing an Algebraic Expression
3:58
Example: Cost of Bowling
4:07
Extra Example 1: Writing Expressions
5:14
Extra Example 2: Writing Expressions
6:06
Extra Example 3: Writing Expressions
7:11
Extra Example 4: Writing Expressions
7:58
Estimating for Reasonableness

10m 20s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Compatible Numbers
0:17
Estimating by Rounding
1:08
Estimate 36 + 6 + 58
1:30
Estimate 94 - 35 - 42
2:29
Estimating with Compatible Numbers
3:02
Estimate 297 ÷ 17
3:17
Estimate 9 Times 38
3:39
Estimating for Reasonableness
4:13
Example: Total Cost of the Items
4:15
Extra Example 1: Estimating with Compatible Numbers
6:02
Extra Example 2: Estimating by Rounding
7:05
Extra Example 3: Estimating for Reasonableness
7:27
Extra Example 4: Estimating for Reasonableness
9:15
Properties of Numbers

12m 1s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Commutative Properties: Addition and Multiplication
0:21
Associative Properties: Addition and Multiplication
1:46
Vocabulary Cont.
3:08
Identity Properties: Addition and Multiplication
3:09
Recognizing Properties
3:55
Examples: Which Property is Illustrated?
3:58
Using Properties of Numbers
5:07
Using Mental Math to Find the Total Cost
5:18
Using Properties of Numbers
6:29
Using Mental Math to Simplify
6:30
Extra Example 1: Using Properties of Numbers
8:29
Extra Example 2: Using Properties of Numbers
9:06
Extra Example 3: Using Properties of Numbers
10:02
Extra Example 4: Using Properties of Numbers
10:32
Distributive Property

9m 40s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Distributive Property
0:16
Using the Distributive Property
1:32
Example: 8 ( 9 + 11 )
1:35
Using the Distributive Property
2:58
Example: 7 ( 12 - h )
2:59
Example: ( m + 2 ) 5
3:20
Distributive Property in Mental Math
3:34
Example: Finding Total Cost
3:38
Extra Example 1: Summer Job
4:55
Extra Example 2: Total Cost
6:03
Extra Example 3: Fundraiser
7:36
Extra Example 4: Tomato Plants
8:24
Section 2: Integers and Exponents
Integers and Absolute Value

11m 35s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:10
Vocabulary
0:21
Opposites
0:27
Integers
1:03
Absolute Value
1:23
Vocabulary
2:21
Number Line
2:23
Finding Absolute Value
2:35
Example: Absolute Value
2:36
More Examples
4:05
Example: Absolute Value of 5
4:06
Example: Absolute Value of Negative 2
4:15
Comparing Integers
4:29
Boiling Points of Elements
4:34
Comparing Integer Examples
6:00
Example 1: Comparing Integers
6:04
Example 2: Comparing Integers
6:17
Example 3: Comparing Integers
6:30
Comparing Integer Examples
6:49
Comparing Temperature
6:53
Extra Example 1: Simplify Absolute Value
8:13
Extra Example 2: Simplify Absolute Value
9:01
Extra Example 3: Simplify Absolute Value
9:29
Extra Example 4: Simplify Absolute Value
10:49
Adding Integers

10m 20s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:26
Integers
0:30
Adding Positive Integers
0:55
Example : -3 + -7
1:01
Example : +11 + 8
1:06
Example : 2 + (+6)
1:21
Adding Negative Integers
1:43
Example: -3 + -7
1:48
Example: -21 + -3
2:05
Example: -11 + (-4)
2:41
Adding Integers with Opposite Signs
3:01
Using a Number Line: -8 + 10
3:52
Using a Number Line: 4 + (-6)
4:36
Adding Integers with Opposite Signs
5:39
Using Absolute Value: -18 + 7
5:48
Extra Example 1: Adding Integers
6:33
Extra Example 2: Adding Integers
7:23
Extra Example 3: Money Problem
8:46
Extra Example 4: Measurement Problem
9:15
Subtracting Integers

12m 1s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:21
Integers
0:25
Opposites
0:47
Rules for Multiplying Signs
1:18
Using a Number Line
2:00
Example: 2 - 5
2:25
Other Examples
2:52
Using Number Line: 10 - (-13)
3:02
Rewriting Absolute Value
4:51
Extra Example 1: Subtracting Integers
5:48
Extra Example 2: Temperature
7:26
Extra Example 3: Depth
8:51
Extra Example 4: Change in Yards
11:09
Multiplying Integers

14m 28s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:43
Integers
0:47
Opposites
1:03
Repeated Addition
1:41
Example 1: Using a Number Line
1:43
More Examples
3:28
Example 2: Using a Number Line
3:30
Using a Number Line
4:45
Example 3: Using a Number Line
4:46
Example 4: Using a Number Line
5:59
Rules for Multiplying Same Sign Integers
7:20
Arithmetic
7:35
Algebra
8:00
Rules for Multiplying Different Signs Integers
8:17
Arithmetic
8:29
Algebra
8:58
Multiplying Integer Examples
9:20
Examples of Multiplying Integers
9:21
Using Multiplication of Integers to Solve a Problem
10:07
Elevation
10:12
Temperature
11:21
Determine the Sign of the Product
12:19
Example 5: Determine the Sign
12:20
Example 6: Determine the Sign
12:50
Extra Example 1: Product of Three Negative Numbers
13:07
Extra Example 2: Product of Four Negative Numbers
13:45
Extra Example 3: Product of Five Negative Numbers
13:58
Extra Example 4: Product of 103 Negative Numbers
14:13
Dividing Integers

20m 18s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:27
Quotient
0:30
Rules for Dividing Integers
0:49
Arithmetic (Same Sign Integers)
1:03
Algebraic (Same Sign Integers)
1:36
Rules for Dividing Integers, cont.
2:06
Arithmetic (Different Signs Integers)
2:14
Algebraic (Different Signs Integers)
2:41
Dividing Integer Examples
3:24
Dividing Integers: 14 ÷ 7
3:30
Dividing Integers: 45 ÷ (-9)
3:37
Dividing Integer Examples
3:51
Dividing Integers: (-105) ÷ (-15)
3:55
Dividing Integers: (-42) ÷ 6
5:07
Average Rate of Change
5:17
Using Integers to Represent the Situation
5:25
Example: Spend $360 in 6 Days
5:40
Example: Runs 1000 Feet in 4 Minutes
6:30
Average Rate of Change Word Problems
7:27
Example: Average Decrease in Value
7:32
Average Rate of Change Word Problems
9:19
Example: Average Increase in Stock
9:23
Average Rate of Change Word Problems
10:46
Example: Average Increase in Speed
10:51
Dividing Integers
12:00
Odd Number of Negatives
12:03
Even Number of Negatives
12:49
Order of Operations and Sign of Final Answer
13:50
Example: -120 ÷ (-5) ÷ -4
13:56
Extra Example 1: Order of Operations
14:48
Extra Example 2: Evaluate the Expression
15:29
Extra Example 3: Rate of Change
17:18
Extra Example 4: Rate of Evaporation
19:22
Positive Exponents

20m 5s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:26
Factor
0:32
Exponent
1:16
Vocabulary
1:57
Base
1:58
Power
2:18
Writing Expressions with Exponents
2:31
Example 1: Writing Expressions with Exponents
2:36
Example 2: Writing Expressions with Exponents
3:00
Writing Expressions with Exponents
3:20
Example 3: Writing Expressions with Exponents
3:25
Example 4: Writing Expressions with Exponents
3:53
Simplifying Power
4:06
Example 5: Simplifying Power
4:14
Example 6: Simplifying Power
5:03
Simplifying Power
6:06
Example 7: Simplifying Power
6:09
Example 8: Simplifying Power
6:50
Order of Operations
7:24
PEMDAS
7:26
Order of Operations
8:32
Multiplying/Dividing and Adding/Subtracting
8:34
Evaluating Expressions with Exponents
10:07
Example 9: Evaluating Expressions with Exponents
10:11
Example 10: Evaluating Expressions with Exponents
11:07
Extra Example 1: Evaluate
12:33
Extra Example 2: Evaluate
13:42
Extra Example 3: Height of the Rocket
15:00
Extra Example 4: Number of Cells
16:38
Section 3: Equations and Applications
Solving Addition Equations

21m 47s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:18
Equation
0:21
Isolate
1:00
Inverse Operations
1:18
Subtraction Property of Equality
1:59
Arithmetic
2:12
Algebraic
2:53
Inverse Operations
3:32
Example: 38 + x = 42
3:40
Using Substitution to Check Answer
4:43
Inverse Operations
5:19
Example: y + 7.3 = 9.1
5:22
Using Substitution to Check Answer
5:53
Draw a Model
6:26
Weight Gain
6:42
Draw a Model
8:20
Mountain Climber
8:23
Examples by Writing Equations
10:25
Calculating Profit: Sweat Shirt
10:30
Examples by Writing Equations
11:37
Calculating Profit: Car Dealer
11:38
Extra Example 1: Inverse Operation
14:21
Extra Example 2: Inverse Operation
15:37
Extra Example 3: Real Estate
17:23
Extra Example 4: Birth Date
20:06
Solving Subtraction Equations

19m 34s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:07
Vocabulary
0:23
Addition Property of Equality: Arithmetic
0:31
Addition Property of Equality: Algebraic
1:14
Subtraction Property of Equality: Arithmetic
1:54
Subtraction Property of Equality: Algebraic
2:19
Solving an Equation by Adding
3:05
Example: b - 2 = 2
3:22
Example: 23 - j = 12
4:00
Solving an Equation by Adding
5:29
Example: a - 7.9 = 17.9
5:32
Example: -5.6 + x = 10.2
6:33
Solving an Equation by Writing an Equation
7:42
Example: Bank Withdrawal
7:48
Solving an Equation by Writing an Equation
9:21
Example: Temperature
9:23
Extra Example 1: Solving Subtraction Equations
11:50
Extra Example 2: Solving Subtraction Equations
12:46
Extra Example 3: Money
13:40
Extra Example 4: Selling Price
16:01
Solving Multiplication and Division Equations

26m 11s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:19
Division Property of Equality: Arithmetic
0:27
Division Property of Equality: Algebraic
1:05
Multiplication Property of Equality: Arithmetic
1:38
Multiplication Property of Equality: Algebraic
2:07
Vocabulary
2:49
Inverse Operations
2:53
Solve the Equation Using Division
3:09
Example: 8x = 56
3:12
Example: -6y = 42
3:59
Solve the Equation Using Division
4:47
Example: 0.9c = 1.89
4:53
Solve the Equation Using Division
6:11
Example: Saving Money
6:17
Example: Soccer Team
8:14
Solve the Equation Using Multiplication
9:56
Example: a/7 = 9
10:04
Example: t/1.7 = 6
10:52
Solve the Equation Using Multiplication
12:09
Example: y/-45 = 3.2
12:17
Example: -p = 14
13:13
Solve the Equation Using Multiplication
14:10
Example: Distant
14:16
Extra Example 1: Solve the Equation
15:58
Extra Example 2: Solve the Equation
17:25
Extra Example 3: Height of an Elephant
20:55
Extra Example 4: Money
23:07
Solving Two-Step Equations

19m 10s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Two-Step Equation Involvement
0:19
Solving Two-Step Equations
0:41
Example: 8y - 11 = 32
0:45
Example: 32 = t/5 + 8
2:55
Solving Two-Step Equations
4:49
Example: Recommended Daily Intake
4:59
Solving Two-Step Equations
7:01
Example: Cost of Each Ride
7:02
Extra Example 1: Solving Two-Step Equations
10:13
Extra Example 2: Solving Two-Step Equations
12:54
Extra Example 3: Length of Phone Call
13:56
Extra Example 4: Cost of Owning a Pet
16:40
Square Roots

12m 16s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Perfect Square
0:20
Square Root
0:46
Square Roots
1:13
Every Positive Number has Two Square Roots
1:14
Square Roots of a Number are Opposites
1:40
Square Root Symbol
1:54
Positive Square Root of a Number
1:56
Compare: √25 and -√25
2:08
Find the Square Root
2:50
Example: Square Root of 81
2:52
Example: Square Root of 121
3:13
Estimating Square Roots
3:29
Example: Square Root of 23
3:35
Example: Square Root of 390
4:13
Example: Negative Square Root of 125
4:50
Estimating Square Roots
5:27
Estimating Length
5:31
Simplifying Square Roots
7:05
Example: Square Root of 36
7:08
Example: Simplifying Square Roots
7:47
Extra Example 1: Estimate the Length
8:21
Extra Example 2: Simplify the Expression
9:05
Extra Example 3: Estimate the Length
9:50
Extra Example 4: Simplify the Expression
10:34
Pythagorean Theorem

14m 49s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:36
Right Triangle
0:39
Legs
0:57
Hypotenuse
1:02
Pythagorean Theorem
1:11
Arithmetic Example
1:12
Algebra Example
2:41
Find the Length of the Hypotenuse
3:04
Example 1: Hypotenuse of a Triangle
3:07
Example 2: Hypotenuse of a Triangle
4:30
Find the Length of the Hypotenuse
6:18
Example 3: Hypotenuse of a Right Triangle
6:19
Extra Example 1: Square Roots
8:41
Extra Example 2: Perimeter
9:43
Extra Example 3: Length of Screen
11:58
Extra Example 4: Length of Wire
13:14
Using the Pythagorean Theorem

16m 15s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:30
The Pythagorean Theorem
0:32
Find the Length of a Leg
1:14
Example 1: Length of Ramp
1:19
Example: 2 Length of Platform
4:22
Identifying a Right Triangle
6:13
Example 3: Determine Right Triangle
6:14
Example 4: Determine Right Triangle
8:08
Extra Example 1: Find the Missing Leg Length
10:04
Extra Example 2: Length of Ladder
11:39
Extra Example 3: Determine Given Lengths
13:04
Extra Example 4: Length of Pole
14:20
Section 4: Rational Numbers
Prime Factorization

16m 40s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:23
Factor
0:24
Composite Number
1:04
Vocabulary
1:17
Prime Number
1:18
Prime Factorization
1:57
Divisibility Rules
2:54
Divisibility Rules for 2, 3, 4 ,5 ,6, 9 and 10
2:55
Finding Factors
4:56
Possible Arrangements
4:59
Finding Factors
6:06
How Many Oranges?
6:07
Prime or Composite
6:43
Prime or Composite: 48
6:47
Prime or Composite: 53
7:09
Prime or Composite: 57
7:35
Prime Factorization
8:16
Prime Factorization of 42
8:23
Prime Factorization of 84
8:47
Find the Number
9:23
Find the Number with the Given Prime Factorization
9:24
Extra Example 1: Prime or Composite
11:04
Extra Example 2: Prime Factorization of 72
12:23
Extra Example 3: Marching Arrangements
12:56
Extra Example 4: Flowers Arrangements
14:50
Greatest Common Divisor

14m 16s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:41
Factor
0:43
Common Divisor
1:00
Greatest Common Divisor (GCD)/ Greatest Common Factor (GCF)
1:16
Find the GCD by Listing Divisors
1:34
GCD of 27 and 36
1:46
GCD of 18 and 49
2:52
Prime Factorization to Find GCD
3:30
GCD of 42 and 72
3:42
GCD of 21 and 63
4:46
GCD in Word Problems
5:30
Greatest Number of Police Officers
5:32
GCD in Word Problems
7:15
Cutting Two Pipes
7:16
Extra Example 1: GCD of 32, -24, 40
8:08
Extra Example 2: How Many Groups?
9:41
Extra Example 3: GCD of Two Prime Numbers
11:34
Extra Example 4: How Many Children?
12:26
Equivalent Fractions

11m 22s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:21
Equivalent Fractions
0:23
Simplest Form
1:15
Creating Equivalent Fractions
1:59
Method to Create Equivalent Fractions
2:00
Equivalent Fractions
2:18
Write Two Fractions Equivalent to 5/8
2:22
Write Two Fractions Equivalent to 2/14
3:12
GCD to Simplify
3:51
Find the GCD of 24 and 32
4:03
Write 24/32 in Simplest Form
4:43
Write -27/45 in Simplest Form
5:08
Writing a Fraction
6:04
Example: What Fraction of the Vehicles are Trucks?
6:11
Writing a Fraction
7:45
Example: What Fraction of the Seats are Empty?
7:55
Extra Example 1: Pizza
9:00
Extra Example 2: Driving Time
9:28
Extra Example 3: Simplest Form
10:29
Extra Example 4: Basketball Team
10:52
Equivalent Forms of Rational Numbers

20m 47s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:08
Vocabulary
0:30
Rational Number
0:31
Terminating Decimal
0:53
Repeating Decimal
1:04
Converting Decimals to Fractions
1:22
Write 0.47 as a Fraction
1:26
Write 0.48 as a Fraction
2:03
Write 0.245 as a Fraction
3:21
Converting Decimals to Fractions
4:20
Write 0.08 as a Fraction
4:30
Write 0.8 as a Fraction
4:53
Converting Fractions to Decimals
5:26
Write 1/2 as a Decimal
5:30
Write 6/33 as a Decimal
6:12
Write -9/5 as a Decimal
7:39
Converting Fractions to Decimals in Word Problems
8:19
Batting Average
8:23
Converting Fractions to Decimals in Word Problems
11:22
Cooking Festival
11:26
Extra Example 1: Write 0.038 as a Fraction
14:45
Extra Example 2: Write -13/7 as a Decimal
15:35
Extra Example 3: Batting Average
16:38
Extra Example 4: Rational Number
19:55
Comparing and Ordering Rational Numbers

20m 21s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:29
Least Common Multiple (LCM)
0:30
Least Common Denominator (LCD)
1:50
Ordering Rational Numbers
2:45
Numbers as Decimals
2:46
Numbers as Fractions
5:36
Compare Each Pair of Numbers
8:10
Compare 3/4 and 4/5
8:11
Compare 3/11 and 1/6
8:44
Comparing rational Numbers in Word Problems
9:19
Cookies or French Fries?
9:22
Extra Example 1: Least to Greatest (Decimals)
11:32
Extra Example 2: Least to Greatest (Fractions)
13:35
Extra Example 3: Music Notes
15:54
Extra Example 4: Chocolate or Fruit
17:16
Section 5: Rational Number Operations
Adding Rational Numbers

15m 4s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:19
Least Common Multiple (LCM)
0:20
Least Common Denominator (LCD)
0:28
Adding Fractions with Unlike Denominators
1:22
Example: 3/4 + 2/5
1:28
Example: -3/5 + 1/7
2:29
Adding Different Forms of Rational Numbers
3:23
Example: Change to Fractions
3:31
Example: Change to Decimals
5:14
Extra Example 1: Adding Different Forms of Numbers
7:02
Extra Example 2: Exercising
10:06
Extra Example 3: Adding Different Forms of Numbers
11:20
Extra Example 4: Cooking Recipe
13:47
Subtracting Rational Numbers

14m 40s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:19
Least Common Denominator (LCD)
0:20
Subtracting with Unlike Denominators
0:41
Example: 5/9 - 3/5
0:44
Example: 3/4 - 7/8
1:23
Subtracting Rational Numbers
1:59
Example: 23/4 - 3.5
2:05
Example: 11.7 - 3/4
3:39
Subtracting Rational Numbers in Word Problems
4:37
Puppy's Weight
4:41
Extra Example 1: Subtracting with Unlike Denominators
6:48
Extra Example 2: Subtracting Rational Numbers
7:27
Extra Example 3: Rainfall
10:32
Extra Example 4: Decorating Your House
12:06
Multiplying Rational Numbers

11m 2s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:17
Rational Number
0:18
Exponent
0:30
Power
0:35
Multiplying Decimals
0:47
Example 1: Multiplying Decimals
0:50
Example 2: Multiplying Decimals
1:18
Multiplying Rational Numbers in Word Problems
1:51
Example: Length of Pipes
1:56
Raising a Fraction to a Power
2:58
Examples: Raising Fractions to Power
2:59
Extra Example 1: Multiplying Fractions
4:45
Extra Example 2: Compare Fractions
5:34
Extra Example 3: Flour
7:28
Extra Example 4: Income
8:50
Dividing Rational Numbers

12m 8s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:22
Reciprocal
0:26
Finding the Reciprocal
0:56
Example: Reciprocal of 2/3
1:00
Example: Reciprocal of 8
1:04
Example: Reciprocal of -1/2
1:10
Dividing Rational Numbers
1:28
Example 1: Dividing Rational Numbers
1:35
Example 2: Dividing Rational Numbers
2:09
Example 3: Dividing Rational Numbers
2:35
Dividing Rational Numbers in Word Problems
3:56
Example: Chocolate Peanuts
4:00
Extra Example 1: Dividing Decimals
5:17
Extra Example 2: Dividing Fractions
7:09
Extra Example 3: Search Committee
8:34
Extra Example 4: Stake
10:18
Solving Equations by Adding or Subtracting

13m 43s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
What You'll Learn and Why
0:23
Isolate
0:24
Solving Equations with Fractions
0:41
Example: n + 1/2 = 11/12
0:44
Example: 3/5 - a = 13/20
1:34
Writing Equations with Fractions
3:08
Example: Thickness
3:11
Extra Example 1: Solving Equations
6:01
Extra Example 2: Solving Equations
6:58
Extra Example 3: School Lunches
8:23
Extra Example 4: Fashion Designer
10:44
Solving Equations by Multiplying

11m 10s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:20
Multiplicative Inverse
0:21
Solve Each Equation
0:51
Example 1: Solve the Equation
0:57
Example 2: Solve the Equation
2:39
Writing Multiplication Equations
3:30
Example: Water Level
3:34
Extra Example 1: Solve the Equation
5:15
Extra Example 2: Solve the Equation
6:28
Extra Example 3:Money
7:26
Extra Example 4: Solve the Equation
9:45
Zero and Negative Exponents

6m 41s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:22
Zero Exponents: Arithmetic Definition
0:27
Zero Exponents: Algebra Definition
0:39
Negative Exponents: Arithmetic Definition
0:46
Negative Exponents: Algebra Definition
1:03
Simplifying Exponents
1:18
Examples: Simplifying Exponents
1:21
Fractions and Negative Exponents
2:41
Examples: Fractions and Negative Exponents
2:45
Extra Example 1: Negative Exponent
3:58
Extra Example 2: Zero Exponent
4:30
Extra Example 3: Fraction and Negative Exponent
4:40
Extra Example 4: Subtracting Numbers with Exponents
5:00
Section 6: Rates and Proportions
Ratios

7m 5s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:22
Ratio
0:23
Equivalent Ratios
0:40
Writing a Ratio
1:18
Write the Ratio in Three Ways
1:21
Writing an Equivalent Ratio
2:07
Different Ratios Equivalent to 10:12
2:08
Writing a Ratio in Simplest Form
2:47
Write the Ratio in Simplest Form
2:50
Extra Example 1: Write the Ratio
3:32
Extra Example 2: Ratio in Simplest Form
4:38
Extra Example 3: Write the Ratio
5:08
Extra Example 4: Ratio in Simplest Form
5:48
Rates

12m 45s

Intro
0:00
What You'll Learn and Why
0:04
Topics Overview
0:05
Vocabulary
0:18
Rate
0:22
Unit Rate
0:40
Finding a Unit Rate
1:00
Example: Delivery Rate
1:03
Using a Unit Rate
1:46
Example: Miles and Gallon of Gas
1:49
Comparing Unit Rates
2:52
Example: Which is the Better Buy
2:58
Extra Example 1: Calories
6:30
Extra Example 2: Typing Speed
7:22
Extra Example 3: Which is the Better Buy
8:23
Extra Example 4: Wages
10:48
Dimensional Analysis

16m 19s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Conversion Factor
0:16
Dimensional Analysis
0:23
Conversion Chart: Length
0:32
Conversion Chart: in, ft, yd, and m
0:33
Conversion Chart: Weight
0:49
Conversion Chart: oz, lb, and t
0:50
Conversion Chart: Capacity
0:59
Conversion Chart: fl oz, cup, pt, qt, and gal
1:00
Converting Units
1:17
Example: Convert 1.3 Miles Into Feet
1:18
Converting Units
3:14
Example: Convert Pounds to Ounces
3:15
Example: Convert Cups to Fluid Ounces
3:52
Converting Units in a Rate
4:30
Unit Rate: 2,200 m in 17.2 min
4:31
Using Dimensional Analysis
8:06
Example: Planning Project
8:07
Extra Example 1: Converting Units
9:15
Extra Example 2: Unit Rate
10:31
Extra Example 3: Planning Project
12:15
Extra Example 4: Converting Units
13:45
Application of Rates

17m 42s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:18
Rate
0:22
Unit Rate
0:27
Finding Total Distance
0:32
Example: Total Distance
0:33
Finding Average Speed
2:49
Example: Car's Average Speed
2:53
Using a Unit Rate
6:31
Example: Weight and Spring
6:32
Extra Example 1: Total Distance
8:08
Extra Example 2: Bird's Average Speed
10:33
Extra Example 3: Cost of Shirts
13:37
Extra Example 4: Cost of Bottles
15:22
Proportions

14m 36s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Proportion
0:17
Cross Products
0:45
Identifying a Proportion
11:28
Example: Do the Ratios Form a Proportion?
11:29
Solving Proportions Using Two Methods
2:47
Example: x/4 = 12/21
3:03
Example: 20/y = 15/9
4:43
Solving Proportions in Word Problems
5:56
Example: Find the Unit Rate of Exchange
6:00
Extra Example 1: Does the Ratio Form a Proportion?
9:55
Extra Example 2: Solving Proportions
10:53
Extra Example 3: Find the Length of the Photo
11:33
Extra Example 4: Distance
12:59
Section 7: Applications of Percent
Fractions, Decimals, and Percents

10m 13s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:24
Percent
0:25
Compare a Fraction to a Decimal to a Percent
0:35
Example: 31 out of 100
0:39
Write a Percent as a Fraction
1:11
Example: Write 47% as a Fraction
1:12
Example: Write 25% as a Fraction
1:59
Write a Fraction as a Percent
2:38
Example: Write 2/10 as a Percent
2:39
Example: Write 57/100 as a Percent
3:22
Example: Write 3/25 as a Percent
3:57
Write a Decimal as a Percent
4:48
Example: Write 0.85 as a Percent
4:49
Example: Write 0.3 as a Percent
5:05
Example: Write 0.04 as a Percent
5:17
Extra Example 1: Write Percent as Decimal and Fraction
5:34
Extra Example 2: Write Fraction as Decimal and Percent
6:47
Extra Example 3: Write Percent as Fraction and Decimal
7:41
Extra Example 4: Fraction, Percent, and Decimal of Students
8:36
Finding a Percent of a Number

8m 39s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:20
Percent
0:21
Finding a Percent
0:26
Example: Find 15% of 100
0:27
Example: Find 10% of 135
1:08
Finding More Percents
2:23
Example: Find 8% of 65
2:25
Example: Find 120% of 50
2:45
Estimating a Percent
3:25
Example: Estimate 10% of 31.05
3:38
Example: Estimate 15% of 31.05
3:54
Example: Estimate 20% of 31.05
4:55
Extra Example 1: Find 7% of 120
5:35
Extra Example 2: Find 125% of 75
6:01
Extra Example 3: Estimate 15% Tip
7:02
Extra Example 4: Estimate 20% Tip
8:01
Percents and Proportions

15m 38s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:23
Proportion
0:33
Cross Products
0:38
Finding Part of a Whole
1:07
Method 1: Find 50% of 36
1:11
Method 2: Find 50% of 36
2:23
Finding Part of a Whole, cont.
3:06
Example: Find 65% of 143
3:07
Finding the Whole Amount
3:44
Example: How Many Students are in 8th Grade?
3:45
Finding the Whole Amount, cont.
5:18
Example: How Many Students are in the School?
5:19
Finding a Percent
6:38
Method 1: What Percent of 175 is 105
7:21
Method 2: What Percent of 175 is 105
8:49
Finding a Percent, cont.
9:57
What Percent of 115 is 46?
9:58
Extra Example 1: Find 8% of 48
11:09
Extra Example 2: 9 is 25% of What Number?
11:34
Extra Example 3: How Many Students are in the Class?
12:39
Extra Example 4: 66 is What Percent of 55?
14:25
Percent of Change

11m 27s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:17
Percent of Change
0:18
Amount of Change/ Original Amount
0:26
Finding a Percent of Increase
1:04
Example: Find the Percent of Increase
1:06
Converting Units
2:56
Example: Converting Units and Percent Increase
3:00
Finding a Percent of Decrease
5:08
Example: Find the Percent of Decrease
5:09
Extra Example 1: Find the Percent of Increase
6:32
Extra Example 2: Find the Percent of Decrease
7:30
Extra Example 3: Find the Percent of Increase
8:28
Extra Example 4: Find the Percent of Decrease
10:23
Applications of a Percent

12m 55s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:22
Markup
0:23
Selling Price
0:28
Formula of Markup
0:32
Formula for Discount
1:06
Finding a Percent of Markup
1:16
Example: Find the Percent of Markup
1:19
Finding a Percent of Discount
3:19
Example: Find the Percent of Discount
3:21
Finding a Sale Price
5:03
Example: Find the Sale Price of the Stereo System
5:10
Extra Example 1: Find the Percent of Markup
6:39
Extra Example 2: Find the Percent of Discount
8:57
Extra Example 3: Find the Percent of Discount
9:52
Extra Example 4: Find the Percent of Discount
10:44
Section 8: Linear Functions and Graphing
Graphing in the Coordinate Plane

15m 13s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:17
Coordinate Plane
0:23
y-axis
0:29
x-axis
0:33
Quadrants
0:37
More Vocabulary
0:49
Origin
0:50
Ordered Pair
0:53
x-coordinate
1:00
y-coordinate
1:08
Labeling Vocabulary
1:24
Example: Label the Vocabulary
1:25
Graphing Points on a Coordinate Plane
3:08
Example: Graph and Label the Locations
3:12
Quadrants
6:18
Example: Name the Quadrants of Each Ordered Pair
6:23
Extra Example 1: Draw and Label
10:18
Extra Example 2: Graph the Ordered Pair
11:20
Extra Example 3: Graph the Ordered Pair
12:42
Extra Example 4: Name the Quadrants of Each Ordered Pair
13:32
Length in the Coordinate Plane

18m 36s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:18
x-coordinate
0:21
y-coordinate
0:28
Pythagorean Theorem
0:34
Finding Lengths of Line Segments
1:02
Example: Find the Length of the Horizontal Line Segment
1:05
Finding Lengths of Line Segments
3:50
Example: Find the Length of the Vertical Line Segment
3:54
Finding Distance in the Coordinate Plane
5:59
Example: Find the Length of the Hypotenuse
6:02
Extra Example 1: Find the Distance Between Two Points
7:36
Extra Example 2: Find the Length of the Line Segment
10:13
Extra Example 3: Find the Length of the Line Segment
14:28
Extra Example 4: How Far is Your School from the Arcade?
16:02
Functions

14m 29s

Intro
0:00
What You'll Learn and Why
0:04
Topics Overview
0:05
Vocabulary
0:24
Function
0:25
Function Rule
0:51
Evaluating a Function Rule
0:59
Example: Table of Input and Output
1:00
Using Function Notation
2:56
Example: Write the Equation and Evaluate the Cost
2:59
Writing Functions
4:40
Example: Writing Function
4:41
Extra Example 1: Complete the Table
6:02
Extra Example 2: Complete the Table and Find the Function
7:38
Extra Example 3: Function Notation
9:39
Extra Example 4: Write a Function and Find the Total Cost
11:49
Graphing Linear Functions

16m 2s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:21
Solution
0:22
Linear Equation
0:29
Linear Function
0:44
Making a Graph from a Table
1:05
Example: Total Savings in Dollars
1:08
Graphing a Linear Function
3:03
Example: Graph the Linear Function
3:07
Extra Example 1: How Much Cereal is Left?
5:42
Extra Example 2: Graph the Value
7:45
Extra Example 3: Graph the Linear Function
10:17
Extra Example 4: Graph the Linear Function
12:28
Slope

17m 53s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Slope Definition 1
0:18
Slope Definition 2
0:40
Slope
1:20
Positive Slope
1:32
Negative Slope
1:39
Slope of 0
2:10
Undefined Slope
2:25
Finding the Slope of a Line
3:57
Example: Using Rise/Run to Find Slope
3:58
Finding the Slope of a Line
6:01
Example: Using Coordinates to Find Slope
6:02
Finding Slope of a Line With Given Coordinates
9:00
Example: Slope of (4,1) and (3, -2)
9:01
Extra Example 1: Find the Slope of the Line
10:17
Extra Example 2: Find the Slope of the Line
12:19
Extra Example 3: Find the Slope of the Line
14:54
Extra Example 4: Find the Slope of the Line
16:35
Slope and Direct Variation

13m 50s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:33
Direct Variation
0:34
Identifying a Direct Variation
0:47
Steps in Identifying a Direct Variation
0:56
Slope and Direct Variation
3:01
Example: Slope and Direct Variation
3:05
Extra Example 1: Direct Variation
6:16
Extra Example 2: Direct Variation
7:14
Extra Example 3: Graphing Direct Variation
8:10
Extra Example 4: Slope and Direct Variation
11:23
Section 9: Inequalities
Writing Inequalities

17m 32s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Inequality
0:18
System of Inequalities
1:31
Solution of an Inequality
1:50
Writing an Inequality
2:10
Example: Price p is More than $6
2:20
Writing an Inequality
3:53
Example: Wage w is at Least $8.25
3:54
Writing a System of Inequalities
5:24
Example: System of Inequalities for Wind Speed
5:32
Writing a System of Inequalities
9:03
Example: Price of a Room in Las Vegas
9:04
Identifying Solutions of an Inequality
10:33
Example: Driver's Permit
10:37
Extra Example 1: Writing Inequalities
12:03
Extra Example 2: Writing a System of Inequalities
13:24
Extra Example 3: Writing Inequalities
14:51
Extra Example 4: Using Inequality to Solve Word Problem
15:31
Solving Inequalities by Adding or Subtracting

9m 16s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:20
Addition Property of Equality
0:31
Subtraction Property of Equality
0:43
Example: x > 7
0:57
Solving an Inequality by Adding
1:33
Example: Solve x - 8 = 10
1:37
Example: Solve x - 8 < 10
2:05
Solving an Inequality by Adding
2:21
Example: 2 ≤ t - 5
2:22
Example: a - 8 > 15
2:59
Solving an Inequality by Subtracting
3:14
Example: How Many Students can Board the Bus?
3:22
Solving an Inequality by Subtracting
4:13
Example: How Many More Tickets can be Sold?
4:14
Extra Example 1: Solve the Inequality
5:16
Extra Example 2: Solve 8 ≥ 3 + m
5:52
Extra Example 3: MP3 Player
6:29
Extra Example 4: Write and Solve an Inequality
7:34
Solving Inequalities by Dividing

12m 15s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:22
Division Property of Inequality
0:23
Example: 3x > 6
0:37
Dividing by a Positive Number
1:08
Example: Hotel Elevator
1:11
Dividing by a Negative Number
2:29
Example: Solve -6x ≥ -18
2:32
Example: Suppose x = 2
3:13
Dividing by a Negative Number
4:58
Example: Solve -3t ≥ 51
5:05
Example: Solve -8m < -56
5:24
Extra Example 1: Photo Album
5:49
Extra Example 2: Banquet
8:05
Extra Example 3: Solve -0.5x > 18
9:24
Extra Example 4: How Many Crates can the Crane Lift?
10:30
Solving Inequalities by Multiplying

14m 33s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:17
Multiplication Property of Inequality
0:18
Multiplying by a Positive Number
1:25
Example: Write and Solve an Inequality
1:28
Multiplying by a Positive Number
3:38
Example: Write and Solve an Inequality
3:39
Multiplying by a Negative Number
5:42
Example: Solve x/-4 > 28
5:45
Example: Solve (-1/2)y < -8
6:10
Example: t/-7 < 5
6:42
Extra Example 1: Bowling League
7:12
Extra Example 2: Street Performers
8:27
Extra Example 3: Write and Solve the Inequality
9:52
Extra Example 4: Solve and Graph the System of Inequalities
11:26
Solving Two-Step Inequalities

14m 15s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Inequality
0:16
Properties of Inequality
0:27
Solving Two-Step Inequalities
0:37
Example: Solve -2x - 8 > -14
0:41
Example: Solve (x/4) - 7 > 25
1:40
Example: Solve -5y + 9 ≤ 54
2:12
Writing Two-Step Inequalities
3:16
Example: How Many Pairs of Socks?
3:21
Writing Two-Step Inequalities
5:49
Example: How Many Folders?
5:53
Extra Example 1: Solve 15 < -3 ( x + 1 )
7:32
Extra Example 2: Solve the Inequalities
8:43
Extra Example 3: Muffin
10:37
Extra Example 4: Birthday Party
11:51
Section 10: Exponents and Equations
Properties of Exponents

12m 7s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:26
Exponent
0:29
Power
0:44
Multiplying Powers with the Same Base
1:04
Example: Multiplying Powers with the Same Base
1:07
Multiplying Expressions with Exponents
2:25
Examples
2:26
Dividing Powers with the Same Base
3:24
Example: Dividing Powers with the Same Base
3:25
Dividing Expression with Exponents
3:59
Example: How Long Sunlight Takes to Reach the Comet
4:02
Dividing Expression with Exponents
6:44
Example: How Long Sunlight Takes to Reach Earth
6:45
Extra Example 1: Multiplying Expressions with Exponents
8:22
Extra Example 2: Dividing Expression with Exponents
8:46
Extra Example 3: How Long Sunlight Takes to Reach Saturn
9:12
Extra Example 4: Sun's Diameter and Earth's Diameter
10:34
Power Rules

11m 58s

Intro
0:00
What You'll Learn and Why
0:04
Topics Overview
0:05
Vocabulary
0:15
Exponent
0:18
Power
0:34
Raising a Power to a Power
0:44
Example: Raising a Power to a Power
0:47
Raising a Power to a Power
2:38
More Examples
2:42
Raising a Product to a Power
3:00
Example: Raising a Product to a Power
3:01
Raising a Product to a Power
4:00
Example: Surface Area of a Plant Cell
4:12
Example: Surface Area of the Moon
6:15
Extra Example 1: Raising Power to a Power
8:08
Extra Example 2: Complete the Inequality Statement
8:22
Extra Example 3: Find the Area of a Square
8:51
Extra Example 4: Find the Area of a Circle
10:28
Exploring Roots

9m 39s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:17
Square Root
0:21
Roots
1:13
The Root Symbol
2:10
Root Symbols
2:11
Finding Roots of a Number
2:41
Examples
2:42
Simplifying Expressions with Roots
4:41
Example: Simplify the Expression
4:42
Simplifying Expressions with Roots
5:42
Example: Simplify the Expression
5:43
Extra Example 1: Finding Roots of a Number
6:36
Extra Example 2: Simplifying Expressions with Roots
7:11
Extra Example 3: Simplifying Expressions with Roots
7:36
Extra Example 4: Simplifying Expressions with Roots
8:34
Simplifying Algebraic Expressions

12m 43s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:23
Term
0:28
Like Terms
0:35
Combining Like Terms
1:18
Example: 2y + y - 15y
1:20
Example: -x - 5x
2:16
Writing and Simplifying Expressions
2:57
Example: Total Cost of Drinks
2:58
Writing and Simplifying Expressions
4:48
Example: Total Cost of Apples
4:49
Distributing and Simplifying
5:42
Simplify: 4x - 2( x + 6 )
5:46
Simplify: 3( 2y + 2 ) - 4y
6:57
Extra Example 1: Simplify the Expression
7:52
Extra Example 2: Distributing and Simplifying
8:18
Extra Example 3: Writing and Simplifying Expressions
9:35
Extra Example 4: Distributing and Simplifying
10:50
Solving Multi-Step Equations

18m 35s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:17
Like Terms
0:21
Distributive Property
0:49
Simplifying Before Solving an Equation
1:37
Example: 8x + 45 - 12x = 9
1:40
Example: -15 = 6b + 12 - 3b + 6
3:25
Using the Distributive Property
4:50
Example: Haiti Relief Efforts
4:51
Using the Distributive Property
7:50
Example: Amusement Park
7:51
Extra Example 1: Simplify and Solve
11:34
Extra Example 2: Simplify and Solve
12:21
Extra Example 3: Simplify and Solve
13:18
Extra Example 4: Mailing Letters
14:53
Solving Equations with Variables on Both Sides

18m 50s

Intro
0:00
What You'll Learn and Why
0:07
Topics Overview
0:08
Vocabulary
0:26
Term
0:30
Like Terms
0:44
Variables on Both Sides
1:10
Example: 3x + 24 = 9x
1:11
Example: -7 - 3x = 1 + 5x
2:16
Using the Distributive Property
4:01
Example: Height of Two Plants
4:02
Using the Distributive Property
9:01
Example: Running Laps
9:02
Extra Example 1: Solving Equations with Variables on Both Sides
11:59
Extra Example 2: Solving Equations with Variables on Both Sides
12:46
Extra Example 3: Solving Equations with Variables on Both Sides
14:18
Extra Example 4: Cost of Renting Video
15:24
Section 11: Test-Taking Strategies
Test Taking Strategy Part 1

12m 55s

Intro
0:00
Finding Needed Information
1:02
Ask Yourself
1:07
Example: Finding Needed Information
1:25
Extra Example 1: Finding Needed Information
2:36
Extra Example 2: Finding Needed Information
4:10
Using Mental Math
6:10
Use Mental Math to Eliminate Unreasonable Answers
6:16
Example: Using Mental Math
6:47
Extra Example 1: Simplify Using Mental Math
8:54
Extra Example 2: Mental Math and Total Cost
9:36
Extra Example 3: Account Balance
11:15
Test Taking Strategy Part 2

11m 24s

Intro
0:00
Working Backward
0:06
Substitute Multiple Choice Answers
0:08
Example: Working Backward
0:38
Extra Example 1: Equivalent Expression
2:54
Extra Example 2: Miles Per Gallon
4:13
Extra Example 3: Miles Per Hour
5:14
Choosing the Process
6:12
Strategies for Choosing the Process
6:19
Example: Dimensions of the Fenced Area
6:48
Extra Example 1: Choosing the Process
8:28
Extra Example 2: Choosing the Process
10:01
Test Taking Strategy Part 3

11m 36s

Intro
0:00
Eliminating the Answer
0:06
Eliminate Wrong Answers
0:07
Example: Height of a Plant
0:49
Extra Example 1: Distance
2:36
Extra Example 2: Decimal
4:11
Using a Variable
4:50
Variables Represent the Unknown
4:51
Example: Company Logo
5:20
Extra Example 1: Road Trip
6:31
Extra Example 2: Proportion
9:03
Test Taking Strategy Part 4

20m 13s

Intro
0:00
Eliminating the Answer
0:06
Eliminate Answers and Educated Guess
0:07
Example: Election
0:28
Extra Example 1: Football Kicker
2:42
Extra Example 2: Percent
4:09
Answering the Question Asked
6:19
Answer the Question Correctly
6:20
Example: Inequality
6:43
Extra Example 1: Cost of Cheese
8:12
Extra Example 2: Inequality
9:40
Drawing a Diagram
11:35
Diagrams
11:36
Example: Drawing a Diagram to Show Distance
12:03
Extra Example 1: Drawing a Diagram to Show Distance
15:22
Extra Example 2: Height
17:48
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Lecture Comments (12)

0 answers

Post by Kyan Wang on August 28 at 10:20:11 AM

can i please get a response from teacher so many of your questions you got wrong!!!!!

0 answers

Post by Terrance Goins on July 24, 2015

why when subtracting fractions you borrow at times and sometimes you treat them as integers how do you know when to use the proper operation?

1 answer

Last reply by: Terry Tianrui Xie
Sun Jul 4, 2021 10:27 PM

Post by Mohammed Jaweed on July 22, 2015

3 times 9 doesn't equal 18 it equals 27.

0 answers

Post by Habida Popal on July 17, 2014

5/9-3/5=-2/45...not -1/8....please check your answers and work carefully. Otherwise, I really like following your examples.

0 answers

Post by Daniel Eckert on April 29, 2014

5/9 - 3/5 = 25/45 - 27/45= -2/45 right? I notice 95% of the questions don't get replies or it takes 2 years to get a response but I would like to know the right answer.

1 answer

Last reply by: Professor Fung
Mon Jul 8, 2013 1:21 AM

Post by Omar Arab on July 8, 2013

You are explaining a very fast.

0 answers

Post by denny beltre on October 8, 2012

you get the idea which is what's important.

0 answers

Post by RAFAEL MENDIVES on June 19, 2011

5/9 - 3/5 = 2/45. the video show wrong answer

1 answer

Last reply by: Jesse Ogwal
Fri Aug 31, 2012 9:21 AM

Post by earl west on February 1, 2011

in example 3/4-7/8 ; note that 3x9=27 not 18.

Subtracting Rational Numbers

  • To subtract fractions with different denominators, write equivalent fractions for each fraction so that have the same denominator. Then subtract the numerators and keep the denominators the same. Remember to always check if you can simplify the fraction as your last step.
  • Any common denominator can be used. If you are having trouble finding a common denominator you can multiply the denominators of the fractions with each other. However, using the Lowest Common Denominator may save steps and make simplifying the difference a lot easier.
  • To subtract rational numbers that are in different forms, either make all the numbers fractions or make all the numbers decimals.

Subtracting Rational Numbers

[7/9] − [3/5] =
  • [35/45] − [27/45] =
[8/45]
[6/7] − [1/3] =
  • [18/21] − [7/21] =
[11/21]
− [8/15] − [1/6] =
  • − [16/30] − [5/30] =
  • − [21/30] =
− [7/10]
[34/8] − 2.2 =
  • 4[2/8] − 2[2/10] =
  • 4[10/40] − 2[8/40] =
  • 2[2/40] =
2[1/20]
9.55 − 5[1/4] =
  • 9[55/100] − 5[1/4] =
  • 9[55/100] − 5[25/100] =
  • 4[30/100] =
4[3/10]
[67/25] − 2.1 =
  • 2[17/25] − 2[1/10] =
  • 2[34/50] − 2[5/50] =
2[29/50]
5.09 − 2[3/8] =
  • 5[9/100] − 2[3/8] =
  • 5[18/200] − 2[75/200] =
  • 4[218/200] − 2[75/200] =
2[143/200]
One watermelon weighs 10.4 pounds. Another watermelon weighs 10[7/9] pounds. How much more does the heavier watermelon weigh?
  • 10.4 = 10[4/10] = 10[36/90]
  • 10[7/9] = 10[70/90]
  • 10[70/90] − 10[36/90] =
[34/90] pounds
A plant was 5[1/12] inches tall last year. Now, the plant is 17.29 inches tall. How much did the plant grow in the past year?
  • Let g = inches the plant grew in the last year
  • 5[1/12] + g = 17.29
  • g = 17.29 − 5[1/12]
  • 17[29/100] − 5[1/12] =
  • 17[348/1200] − 5[100/1200] =
  • 12[248/1200] =
12[31/150] inches

*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.

Answer

Subtracting Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What You'll Learn and Why 0:06
    • Topics Overview
  • Vocabulary 0:19
    • Least Common Denominator (LCD)
  • Subtracting with Unlike Denominators 0:41
    • Example: 5/9 - 3/5
    • Example: 3/4 - 7/8
  • Subtracting Rational Numbers 1:59
    • Example: 23/4 - 3.5
    • Example: 11.7 - 3/4
  • Subtracting Rational Numbers in Word Problems 4:37
    • Puppy's Weight
  • Extra Example 1: Subtracting with Unlike Denominators 6:48
  • Extra Example 2: Subtracting Rational Numbers 7:27
  • Extra Example 3: Rainfall 10:32
  • Extra Example 4: Decorating Your House 12:06

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