Estimating for Reasonableness, Pre Algebra

Estimating for Reasonableness

I. Variables and Algebraic Expressions: Lecture 4 | 10:20 min

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Estimating for Reasonableness

Estimation is used when an exact answer is not needed.
Most estimation techniques involve replacing numbers and with ones that are close and easy to compute mentally.
Compatible numbers do not always follow the rules of estimating. For example, 310 ÷ 65 by using compatible numbers is 300 ÷ 60 = 5 compared to estimating which would be 300 ÷ 70.

Estimate 273 ÷ 28 using compatible numbers.

273 is close to 270.28 is close to 30.
270 ÷ 30 =

9

Estimate 37 × 3 using compatible numbers.

37 is close to 40.
40 × 3 =

120

Estimate 694.3 - 125.5 to the nearest ones place.

694.3 rounds to 694
125.5 rounds to 126
694 - 126 =

568

Estimate 1,927.5638 + 52,934.56 to the nearest hundreds place.

1,927.5638 rounds to 1,930.
52,934.56 rounds to 52,930
1,930 + 52,930 =

54,860

Estimate 56.783 - 5.477 to the nearest hundredths place.

56.783 rounds to 56.78.
5.477 rounds to 5.48.
56.78 - 5.48 =

51.30

What is 129 × 52 using compatible numbers?

129 is close to 130
52 is close to 50.
130 × 50 =

6500

You go out to eat and order a salad for $ 4.95, soup for $ 3.65, and steak for $ 11.99. What is the estimated total cost of your meal?

$ 4.95 is close to $ 5
$ 3.65 is close to $ 3.50
$ 11.99 is close to $ 12
$ 5 + $ 3.50 + $ 12 =

$ 20.50

Margaret is saving money to buy a new jacket that costs $ 29.78. She has already saved $ 12.43. Around how much more money does she still need to save buy the jacket?

The word Around tells us we need to estimate the amount
$ 29.78 - $ 12.43 = the exact amount of money Margaret still needs
$ 29.78 rounds to $ 29.75
$ 12.43 rounds to $ 12.45
$ 29.75 - $ 12.45 = the estimated amount of money Margaret still needs

$ 17.30

You buy shoes for $ 14.56, socks for $ 3.21, and pants for $ 29.07. The total comes to $ 46.84. Is this reasonable?

$ 14.56 rounds to $ 14.60
$ 3.21 rounds to $ 3.20
$ 29.07 rounds to $ 29.10
$ 14.60 + $ 3.20 + $ 29.10 =
$ 46.90, which is indeed close to the total of $ 46.85

Yes

Derrick buys a book for $ 10.92, a backpack for $ 37.89, and a calculator for $ 12.53. The total comes to $ 80.34. Is this reasonable?

$ 10.92 rounds to $ 11
$ 37.89 rounds to $ 38
$ 12.53 rounds to $ 12.50
$ 11 + $ 38 + $ 12.50 =
$ 61.50, which is not close to the total of $ 80.34

No

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Answer

Estimating for Reasonableness

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

What You'll Learn and Why

Topics Overview

Vocabulary

Compatible Numbers

Estimating by Rounding

Estimating with Compatible Numbers

Estimating for Reasonableness

Example: Total Cost of the Items

Extra Example 1: Estimating with Compatible Numbers

Extra Example 2: Estimating by Rounding

Extra Example 3: Estimating for Reasonableness

Extra Example 4: Estimating for Reasonableness

I. Variables and Algebraic Expressions
	Numerical Expressions	13:41
	Algebraic Expressions	9:11
	Writing Expressions	8:24
	Estimating for Reasonableness	10:20
	Properties of Numbers	12:01
	Distributive Property	9:40
II. Integers and Exponents
	Integers and Absolute Value	11:35
	Adding Integers	10:20
	Subtracting Integers	12:01
	Multiplying Integers	14:28
	Dividing Integers	20:18
	Positive Exponents	20:05
III. Equations and Applications
	Solving Addition Equations	21:47
	Solving Subtraction Equations	19:34
	Solving Multiplication and Division Equations	26:11
	Solving Two-Step Equations	19:10
	Square Roots	12:16
	Pythagorean Theorem	14:49
	Using the Pythagorean Theorem	16:15
IV. Rational Numbers
	Prime Factorization	16:40
	Greatest Common Divisor	14:16
	Equivalent Fractions	11:22
	Equivalent Forms of Rational Numbers	20:47
	Comparing and Ordering Rational Numbers	20:21
V. Rational Number Operations
	Adding Rational Numbers	15:04
	Subtracting Rational Numbers	14:40
	Multiplying Rational Numbers	11:02
	Dividing Rational Numbers	12:08
	Solving Equations by Adding or Subtracting	13:43
	Solving Equations by Multiplying	11:10
	Zero and Negative Exponents	6:41
VI. Rates and Proportions
	Ratios	7:05
	Rates	12:45
	Dimensional Analysis	16:19
	Application of Rates	17:42
	Proportions	14:36
VII. Applications of Percent
	Fractions, Decimals, and Percents	10:13
	Finding a Percent of a Number	8:39
	Percents and Proportions	15:38
	Percent of Change	11:27
	Applications of a Percent	12:55
VIII. Linear Functions and Graphing
	Graphing in the Coordinate Plane	15:13
	Length in the Coordinate Plane	18:36
	Functions	14:29
	Graphing Linear Functions	16:02
	Slope	17:53
	Slope and Direct Variation	13:50
IX. Inequalities
	Writing Inequalities	17:32
	Solving Inequalities by Adding or Subtracting	9:16
	Solving Inequalities by Dividing	12:15
	Solving Inequalities by Multiplying	14:33
	Solving Two-Step Inequalities	14:15
X. Exponents and Equations
	Properties of Exponents	12:07
	Power Rules	11:58
	Exploring Roots	9:39
	Simplifying Algebraic Expressions	12:43
	Solving Multi-Step Equations	18:35
	Solving Equations with Variables on Both Sides	18:50
XI. Test-Taking Strategies
	Test Taking Strategy Part 1	12:55
	Test Taking Strategy Part 2	11:24
	Test Taking Strategy Part 3	11:36
	Test Taking Strategy Part 4	20:13

Mathematics: Pre Algebra

I. Variables and Algebraic Expressions
	Numerical Expressions			13:41
		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			9:11
		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			8:24
		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			10:20
		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			12:01
		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			9:40
		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
II. Integers and Exponents
	Integers and Absolute Value			11:35
		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			10:20
		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			12:01
		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			14:28
		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			20:18
		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			20:05
		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
III. Equations and Applications
	Solving Addition Equations			21:47
		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			19:34
		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			26:11
		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			19:10
		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			12:16
		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			14:49
		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			16:15
		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
IV. Rational Numbers
	Prime Factorization			16:40
		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			14:16
		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			11:22
		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			20:47
		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			20:21
		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
V. Rational Number Operations
	Adding Rational Numbers			15:04
		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			14:40
		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			11:02
		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			12:08
		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			13:43
		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			11:10
		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			6:41
		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
VI. Rates and Proportions
	Ratios			7:05
		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			12:45
		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			16:19
		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			17:42
		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			14:36
		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
VII. Applications of Percent
	Fractions, Decimals, and Percents			10:13
		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			8:39
		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			15:38
		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			11:27
		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			12:55
		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
VIII. Linear Functions and Graphing
	Graphing in the Coordinate Plane			15:13
		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			18:36
		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			14:29
		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			16:02
		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			17:53
		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			13:50
		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
IX. Inequalities
	Writing Inequalities			17:32
		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			9:16
		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			12:15
		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			14:33
		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			14:15
		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
X. Exponents and Equations
	Properties of Exponents			12:07
		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			11:58
		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			9:39
		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			12:43
		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			18:35
		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			18:50
		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
XI. Test-Taking Strategies
	Test Taking Strategy Part 1			12:55
		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			11:24
		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			11:36
		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			20:13
		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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Estimating for Reasonableness

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Features Overview

Estimating for Reasonableness

Estimate 273 ÷ 28 using compatible numbers.

9

Estimate 37 × 3 using compatible numbers.

120

Estimate 694.3 - 125.5 to the nearest ones place.

568

Estimate 1,927.5638 + 52,934.56 to the nearest hundreds place.

54,860

Estimate 56.783 - 5.477 to the nearest hundredths place.

51.30

What is 129 × 52 using compatible numbers?

6500

You go out to eat and order a salad for $ 4.95, soup for $ 3.65, and steak for $ 11.99. What is the estimated total cost of your meal?

$ 20.50

Margaret is saving money to buy a new jacket that costs $ 29.78. She has already saved $ 12.43. Around how much more money does she still need to save buy the jacket?

$ 17.30

You buy shoes for $ 14.56, socks for $ 3.21, and pants for $ 29.07. The total comes to $ 46.84. Is this reasonable?

Yes

Derrick buys a book for $ 10.92, a backpack for $ 37.89, and a calculator for $ 12.53. The total comes to $ 80.34. Is this reasonable?

No

Answer

Estimating for Reasonableness

Mathematics: Pre Algebra

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