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Lecture Comments (6)

1 answer

Last reply by: Peter Spicer
Wed Jun 18, 2014 1:47 PM

Post by Milan Ray on April 15, 2014

2 plus -5
Equals -
7  right so when it was 2 plus -5 why did you put -3

0 answers

Post by Daniel Eckert on April 11, 2014

a few of the practice questions are done incorrectly. wrong order of operations and they add a division sign to a question in step 2 but its not in the original question.

0 answers

Post by Crystal Curry on September 25, 2012

nice

0 answers

Post by Arpana Duggal on June 15, 2012

really good video. my favorite one so far.

0 answers

Post by earl west on January 19, 2011

Your basic math instruction is excellent. I love your teaching style.

Integers and Order of Operations

Related Links

  • Remember to solve using the order of operations:
    • Parenthesis
    • Exponents
    • Multiplication/Division
    • Addition/Subtraction

Integers and Order of Operations

Evaluate:
- 5 + 9 · - 2 ÷ 3 - 4
  • − 5 + − 18 ÷3 − 4
  • − 5 + − 6 − 4
  • − 11 − 4
  • − 11 + − 4
- 15
Evaluate:
- 10 + 5 · - 6 ÷ 2 - 4
  • − 10 + − 30 ÷2 − 4
  • − 10 + − 15 − 4
  • − 25 − 4
  • − 25 + − 4
- 29
Evaluate:
42 + (5 − 6) ·2
  • 16 + (5 − 6) ·2
  • 16 + − 1 ·2
  • 16 − 2
14
Evaluate:
22 + ( − 19 − 2) ÷3
  • 4 + ( − 19 − 2) ÷3
  • 4 + ( − 21) ÷3
  • 4 + − 7
- 3
Evaluate:
32 + 12 − 3 ·4
  • 9 + 12 − 3 ·4
  • 9 + 12 − 12
  • 21 − 12
9
Evaluate:
( - 16 + 5) · ( - 5 - 1)
  • − 11 ·( − 5 − 1)
  • − 11 ·− 6
66
Evaluate:
( - 15 + 5) ÷ (4 - 6)
  • − 10 ÷− 2
5
Evaluate:
( - 10 + 5) · ( - 3 + 6)
  • − 5 ·( − 3 + 6)
  • − 5 ·3
- 15
Evaluate:
− (33) |−9| − 8
  • − (3 ·3 ·3) ÷|− 9| − 8
  • − 27 ÷|−9| − 8
  • − 27 ÷9 − 8
  • − 3 − 8
- 11
Evaluate:
− (23) ·|−3| + 5
  • − (2 ·2 ·2) ·|−3| + 5
  • − 8 ·|−3| + 5
  • − 8 ·3 + 5
  • − 24 + 5
- 19

*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

Integers and Order of Operations

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.

Transcription: Integers and Order of Operations

Welcome back to Educator.com.0000

For this next lesson on integers and order of operation,0002

now that we went over all the different ways we can solve integers,0007

we are going to put them together into the same problem and solve it by using order of operations.0012

Remember that when you solve, you have to solve in this order.0023

Parentheses is always, always first; then it is exponents.0029

Then after that, it is multiplication and division.0035

This is the same; you don't multiply before you divide.0039

You just do it in order from left to right.0045

If you have multiplication and division, then you would just solve it in that order.0049

You don't solve one over the other; same thing for addition and subtraction.0053

If you have something to subtract before you add, then you would just do that0059

in order from left to right instead of adding first and then subtracting.0064

Again parentheses; then exponents; then multiplication and division; then addition and subtraction.0070

The first problem is going to be -4 plus 8 times -3 divided by 6 minus 2.0080

Within all these operations, I have to multiply and divide first.0091

Multiplication and division, there is no order between those two.0099

I just have to solve it out whichever comes left to right.0103

I am going to solve this first right here; 8 times -3.0107

When you multiply integers, you have to look at how many negative signs there are.0114

There is only one negative sign; only this one has a negative.0122

My answer is going to be -24.0126

After you solve one thing out, write out the rest.0133

-4 plus the 8 divided by 6 minus 2.0138

I rewrote the whole problem with only this solved.0146

From here, my next step will be to divide these.0150

This is going to be -24 divided by 6.0155

Again the same rule applies for the negatives; negative sign here; positive here.0159

My answer is going to become a negative; that is going to be a -4.0166

This is not a divide; don't get confused with that.0175

-4; rewrite the whole problem again; plus that, minus that.0178

Don't forget to include these signs; this sign was included when we solved it.0184

This was part of this answer; but this wasn't.0190

You are going to write out that sign here when you rewrite the whole problem.0194

-4 plus a -4, I have the same sign.0200

When you add integers, if they have the same sign, then you are just going to add up the numbers.0207

Then you are going to give the same sign.0213

For this one, -4 plus -4 is -8.0216

I am going to write out this right here, -8 minus 2.0223

I have a minus; I am going to use the two-dash rule; one, two.0227

-8 plus -2 is -10; all of this became -10.0234

I know it looks like a lot of work.0243

But it is only a lot of work because you are doing one little step at a time.0245

But just remember, you are multiplying integers, then dividing, then adding, and then subtracting integers.0249

The next one, 32 plus 2 minus 5 times 6.0261

I have parentheses; parentheses always, always, always comes first.0270

I am going to solve this first; I have a minus problem, 2 minus 5.0276

I am going to use the two-dash rule to make this minus to a plus, the subtraction problem to an addition problem.0282

It would be one, two.0289

They have different signs; I am going to find the difference of their absolute values.0293

This is a 2; the absolute value of -5 is 5.0298

The difference will be 3.0303

I am going to give it the same sign as the 5.0306

That is a negative so this is a negative.0308

Then I am going to rewrite the whole problem.0312

This is 32; don't forget this plus; then times 6.0316

The next step on the order of operations is exponents.0325

I have to solve this exponent next; 32 is 9; plus -3 times 6.0330

Then after that, I have adding and I have multiplying; multiplying comes first.0339

That will be again one negative sign here; my answer will be -18.0346

Write everything else out; you don't have to write everything out.0355

But that is the best way to do it because that prevents any mistakes that you might make.0358

9 plus -18; again we are adding integers.0368

They have different signs; you find the difference.0372

This is a 9; absolute value of this is 18.0376

If you find the difference of those, you get 9.0380

Give it the sign of the 18; that will be your answer, -9.0383

This next problem, I have parentheses that I have to solve out first, -15 plus 4.0397

Again we are adding integers; they have different signs.0406

Find the difference of their absolute values.0410

Absolute value of -15 is 15; absolute value of 4 is 4.0413

If you find the difference of those, it is 11 with a negative sign.0419

Then times another parentheses that I have to solve out.0429

Here is a minus problem; use the two-dash rule; one, two.0433

Again two-dash rule, do not apply it to any other negative signs.0438

This negative sign, you are not going to touch that.0441

The two-dash rule only changes the minus to a plus.0444

Then this number to either a negative or a positive.0449

-2 plus -8; they have the same sign; -2 and -8.0454

You are going to add the numbers, their absolute values; then give it that same sign.0459

-2 plus -8 is going to be -10.0464

-11 times -10; I have two negative signs.0472

That is going to make my answer a positive; 11 times 10 is 110.0479

That is it for this problem; that is the answer.0488

The fourth example, let's see, I have a negative.0494

This, divided by absolute value of that minus a -7.0501

The first thing I want to solve out is the parentheses which is right here.0507

23; 23, be careful, 23 is not 2 times 3.0513

This is 2 times 2 times 2; I can just rewrite the whole thing.0519

Absolute value of -8 minus a -7; I have to solve this out first.0530

2 times 2 is 4; 4 times 2 is 8.0536

I am going to make this an 8.0541

-8 divided by absolute value of -8 minus a -7.0544

I want to solve this out too because absolute value is like parentheses.0555

Just solve that out first before you divide and do anything else.0560

Absolute value of -8 is 8 because the distance from 0 is 8.0567

I am going to write everything else out; don't forget these signs.0580

Minus a -7; write everything else out exactly the way it is.0584

-8 divided by 8 minus -7; I have to divide before I subtract.0590

Do this next; -8 divided by 8 is -1.0597

Because I have one negative sign, that is going to make my quotient a negative.0602

Then I am going to write all this out again; minus a -7.0608

I am subtracting integers; I am going to apply the two-dash rule.0612

Make this a plus; make that a plus; -1 plus a 7 here.0617

Again I have different signs so I am going to find the difference of their absolute values.0625

The absolute value of -1 is 1; absolute value of 7 is 7.0630

That is 6; then I am going to give it the sign of the 7.0635

That is it; that is your answer.0642

If any of these problems were confusing to you, if you forgot how to do some of these0646

like either dividing or multiplying, maybe adding and subtracting integers,0653

then just go back to the previous lessons and review over it.0657

Then try to come back here and figure out these problems too.0660

That is it for this lesson; thank you for watching Educator.com.0665

I. Algebra and Decimals
  Expressions and Variables 5:57
   Intro 0:00 
   Vocabulary 0:06 
    Variable 0:09 
    Expression 0:48 
    Numerical Expression 1:08 
    Algebraic Expression 1:35 
    Word Expression 2:04 
   Extra Example 1: Evaluate the Expression 2:27 
   Extra Example 2: Evaluate the Expression 3:16 
   Extra Example 3: Evaluate the Expression 4:04 
   Extra Example 4: Evaluate the Expression 4:59 
  Exponents 5:34
   Intro 0:00 
   What Exponents Mean 0:07 
    Example: Ten Squared 0:08 
   Extra Example 1: Exponents 0:50 
   Extra Example 2: Write in Exponent Form 1:58 
   Extra Example 3: Using Exponent and Base 2:37 
   Extra Example 4: Write the Equal Factors 4:26 
  Order of Operations 8:40
   Intro 0:00 
   Please Excuse My Dear Aunt Sally 0:07 
    Step 1: Parenthesis 1:16 
    Step 2: Exponent 1:25 
    Step 3: Multiply and Divide 1:30 
    Step 4: Add and Subtract 2:00 
    Example: Please Excuse My Dear Aunt Sally 2:26 
   Extra Example 1: Evaluating Expression 3:37 
   Extra Example 2: Evaluating Expression 4:59 
   Extra Example 3: Evaluating Expression 5:34 
   Extra Example 4: Evaluating Expression 6:25 
  Comparing and Ordering Decimals 13:37
   Intro 0:00 
   Place Value 0:13 
    Examples: 1,234,567.89 0:19 
   Which is the Larger Value? 1:33 
    Which is Larger: 10.5 or 100.5 1:46 
    Which is Larger: 1.01 or 1.10 2:24 
    Which is Larger: 44.40 or 44.4 4:20 
    Which is Larger: 18.6 or 16.8 5:18 
   Extra Example 1: Order from Least to Greatest 5:55 
   Extra Example 2: Order from Least to Greatest 7:56 
   Extra Example 3: Order from Least to Greatest 9:16 
   Extra Example 4: Order from Least to Greatest 10:42 
  Rounding Decimals 12:31
   Intro 0:00 
   Decimal Place Value 0:06 
    Example: 12,3454.6789 0:07 
   How to Round Decimals 1:17 
    Example: Rounding 1,234.567 1:18 
   Extra Example 1: Rounding Decimals 3:47 
   Extra Example 2: Rounding Decimals 6:10 
   Extra Example 3: Rounding Decimals 7:45 
   Extra Example 4: Rounding Decimals 9:56 
  Adding and Subtracting Decimals 11:30
   Intro 0:00 
   When Adding and Subtracting 0:06 
    Align the Decimal Point First 0:12 
    Add or Subtract the Digits 0:47 
    Place the Decimal Point in the Same Place 0:55 
    Check by Estimating 1:09 
   Examples 1:28 
    Add: 3.45 + 7 + 0.835 1:30 
    Find the Difference: 351.4 - 65.25 3:34 
   Extra Example 1: Adding Decimals 5:32 
   Extra Example 2: How Much Money? 6:09 
   Extra Example 3: Subtracting Decimals 7:20 
   Extra Example 4: Adding Decimals 9:32 
  Multiplying Decimals 10:30
   Intro 0:00 
   Multiply the Decimals 0:05 
    Methods for Multiplying Decimals 0:06 
    Example: 1.1 x 6 0:38 
   Extra Example 1: Multiplying Decimals 1:51 
   Extra Example 2: Work Money 2:49 
   Extra Example 3: Multiplying Decimals 5:45 
   Extra Example 4: Multiplying Decimals 7:46 
  Dividing Decimals 17:49
   Intro 0:00 
   When Dividing Decimals 0:06 
    Methods for Dividing Decimals 0:07 
     Divisor and Dividend 0:37 
    Example: 0.2 Divided by 10 1:35 
   Extra Example 1 : Dividing Decimals 5:24 
   Extra Example 2: How Much Does Each CD Cost? 8:22 
   Extra Example 3: Dividing Decimals 10:59 
   Extra Example 4: Dividing Decimals 12:08 
II. Number Relationships and Fractions
  Prime Factorization 7:00
   Intro 0:00 
   Terms to Review 0:07 
    Prime vs. Composite 0:12 
    Factor 0:54 
    Product 1:15 
   Factor Tree 1:39 
    Example: Prime Factorization 2:01 
    Example: Prime Factorization 2:43 
   Extra Example 1: Prime Factorization 4:08 
   Extra Example 2: Prime Factorization 5:05 
   Extra Example 3: Prime Factorization 5:33 
   Extra Example 4: Prime Factorization 6:13 
  Greatest Common Factor 12:47
   Intro 0:00 
   Terms to Review 0:05 
    Factor 0:07 
    Example: Factor of 20 0:18 
   Two Methods 0:59 
    Greatest Common Factor 1:00 
    Method 1: GCF of 15 and 30 1:37 
    Method 2: GCF of 15 and 30 2:58 
   Extra Example 1: Find the GCF of 6 and 18 5:16 
   Extra Example 2: Find the GCF of 36 and 27 7:43 
   Extra Example 3: Find the GCF of 6 and 18 9:18 
   Extra Example 4: Find the GCF of 54 and 36 10:30 
  Fraction Concepts and Simplest Form 10:03
   Intro 0:00 
   Fraction Concept 0:10 
    Example: Birthday Cake 0:28 
    Example: Chocolate Bar 2:10 
   Simples Form 3:38 
    Example: Simplifying 4 out of 8 3:46 
   Extra Example 1: Graphically Show 4 out of 10 4:41 
   Extra Example 2: Finding Fraction Shown by Illustration 5:10 
   Extra Example 3: Simplest Form of 5 over 25 7:02 
   Extra Example 4: Simplest Form of 14 over 49 8:30 
  Least Common Multiple 14:16
   Intro 0:00 
   Term to Review 0:06 
    Multiple 0:07 
    Example: Multiples of 4 0:15 
   Two Methods 0:41 
    Least Common Multiples 0:44 
    Method 1: LCM of 6 and 10 1:09 
    Method 2: LCM of 6 and 10 2:56 
   Extra Example 1: LCM of 12 and 15 5:09 
   Extra Example 2: LCM of 16 and 20 7:36 
   Extra Example 3 : LCM of 15 and 25 10:00 
   Extra Example 4 : LCM of 12 and 18 11:27 
  Comparing and Ordering Fractions 13:10
   Intro 0:00 
   Terms Review 0:14 
    Greater Than 0:16 
    Less Than 0:40 
   Compare the Fractions 1:00 
    Example: Comparing 2/4 and 3/4 1:08 
    Example: Comparing 5/8 and 2/5 2:04 
   Extra Example 1: Compare the Fractions 3:28 
   Extra Example 2: Compare the Fractions 6:06 
   Extra Example 3: Compare the Fractions 8:01 
   Extra Example 4: Least to Greatest 9:37 
  Mixed Numbers and Improper Fractions 12:49
   Intro 0:00 
   Fractions 0:10 
    Mixed Number 0:21 
    Proper Fraction 0:47 
    Improper Fraction 1:30 
   Switching Between 2:47 
    Mixed Number to Improper Fraction 2:53 
    Improper Fraction to Mixed Number 4:41 
   Examples: Switching Fractions 6:37 
   Extra Example 1: Mixed Number to Improper Fraction 8:57 
   Extra Example 2: Improper Fraction to Mixed Number 9:37 
   Extra Example 3: Improper Fraction to Mixed Number 10:21 
   Extra Example 4: Mixed Number to Improper Fraction 11:31 
  Connecting Decimals and Fractions 15:01
   Intro 0:00 
   Examples: Decimals and Fractions 0:06 
   More Examples: Decimals and Fractions 2:48 
   Extra Example 1: Converting Decimal to Fraction 6:55 
   Extra Example 2: Converting Fraction to Decimal 8:45 
   Extra Example 3: Converting Decimal to Fraction 10:28 
   Extra Example 4: Converting Fraction to Decimal 11:42 
III. Fractions and Their Operations
  Adding and Subtracting Fractions with Same Denominators 5:17
   Intro 0:00 
   Same Denominator 0:11 
    Numerator and Denominator 0:18 
    Example: 2/6 + 5/6 0:41 
   Extra Example 1: Add or Subtract the Fractions 2:02 
   Extra Example 2: Add or Subtract the Fractions 2:45 
   Extra Example 3: Add or Subtract the Fractions 3:17 
   Extra Example 4: Add or Subtract the Fractions 4:05 
  Adding and Subtracting Fractions with Different Denominators 23:08
   Intro 0:00 
   Least Common Multiple 0:12 
    LCM of 6 and 4 0:31 
   From LCM to LCD 2:25 
    Example: Adding 1/6 with 3/4 3:12 
   Extra Example 1: Add or Subtract 6:23 
   Extra Example 2: Add or Subtract 9:49 
   Extra Example 3: Add or Subtract 14:54 
   Extra Example 4: Add or Subtract 18:14 
  Adding and Subtracting Mixed Numbers 19:44
   Intro 0:00 
   Example 0:05 
    Adding Mixed Numbers 0:17 
   Extra Example 1: Adding Mixed Numbers 1:57 
   Extra Example 2: Subtracting Mixed Numbers 8:13 
   Extra Example 3: Adding Mixed Numbers 12:01 
   Extra Example 4: Subtracting Mixed Numbers 14:54 
  Multiplying Fractions and Mixed Numbers 21:32
   Intro 0:00 
   Multiplying Fractions 0:07 
    Step 1: Change Mixed Numbers to Improper Fractions 0:08 
    Step2: Multiply the Numerators Together 0:56 
    Step3: Multiply the Denominators Together 1:03 
   Extra Example 1: Multiplying Fractions 1:37 
   Extra Example 2: Multiplying Fractions 6:39 
   Extra Example 3: Multiplying Fractions 10:20 
   Extra Example 4: Multiplying Fractions 13:47 
  Dividing Fractions and Mixed Numbers 18:00
   Intro 0:00 
   Dividing Fractions 0:09 
    Step 1: Change Mixed Numbers to Improper Fractions 0:15 
    Step 2: Flip the Second Fraction 0:27 
    Step 3: Multiply the Fractions 0:52 
   Extra Example 1: Dividing Fractions 1:23 
   Extra Example 2: Dividing Fractions 5:06 
   Extra Example 3: Dividing Fractions 9:34 
   Extra Example 4: Dividing Fractions 12:06 
  Distributive Property 11:05
   Intro 0:00 
   Distributive Property 0:06 
    Methods of Distributive Property 0:07 
    Example: a(b) 0:35 
    Example: a(b+c) 0:49 
    Example: a(b+c+d) 1:22 
   Extra Example 1: Using Distributive Property 1:56 
   Extra Example 2: Using Distributive Property 4:36 
   Extra Example 3: Using Distributive Property 6:39 
   Extra Example 4: Using Distributive Property 8:19 
  Units of Measure 16:36
   Intro 0:00 
   Length 0:05 
    Feet, Inches, Yard, and Mile 0:20 
    Millimeters, Centimeters, and Meters 0:43 
   Mass 2:57 
    Pounds, Ounces, and Tons 3:03 
    Grams and Kilograms 3:38 
   Liquid 4:11 
    Gallons, Quarts, Pints, and Cups 4:14 
   Extra Example 1: Converting Units 7:02 
   Extra Example 2: Converting Units 9:31 
   Extra Example 3: Converting Units 12:21 
   Extra Example 4: Converting Units 14:05 
IV. Positive and Negative Numbers
  Integers and the Number Line 13:24
   Intro 0:00 
   What are Integers 0:06 
    Integers are all Whole Numbers and Their Opposites 0:09 
    Absolute Value 2:35 
   Extra Example 1: Compare the Integers 4:36 
   Extra Example 2: Writing Integers 9:24 
   Extra Example 3: Opposite Integer 10:38 
   Extra Example 4: Absolute Value 11:27 
  Adding Integers 16:05
   Intro 0:00 
   Using a Number Line 0:04 
    Example: 4 + (-2) 0:14 
    Example: 5 + (-8) 1:50 
   How to Add Integers 3:00 
    Opposites Add to Zero 3:10 
    Adding Same Sign Numbers 3:37 
    Adding Opposite Signs Numbers 4:44 
   Extra Example 1: Add the Integers 8:21 
   Extra Example 2: Find the Sum 10:33 
   Extra Example 3: Find the Value 11:37 
   Extra Example 4: Add the Integers 13:10 
  Subtracting Integers 15:25
   Intro 0:00 
   How to Subtract Integers 0:06 
    Two-dash Rule 0:16 
    Example: 3 - 5 0:44 
    Example: 3 - (-5) 1:12 
    Example: -3 - 5 1:39 
   Extra Example 1: Rewrite Subtraction to Addition 4:43 
   Extra Example 2: Find the Difference 7:59 
   Extra Example 3: Find the Difference 9:08 
   Extra Example 4: Evaluate 10:38 
  Multiplying Integers 7:33
   Intro 0:00 
   When Multiplying Integers 0:05 
    If One Number is Negative 0:06 
    If Both Numbers are Negative 0:18 
    Examples: Multiplying Integers 0:53 
   Extra Example 1: Multiplying Integers 1:27 
   Extra Example 2: Multiplying Integers 2:43 
   Extra Example 3: Multiplying Integers 3:13 
   Extra Example 4: Multiplying Integers 3:51 
  Dividing Integers 6:42
   Intro 0:00 
   When Dividing Integers 0:05 
    Rules for Dividing Integers 0:41 
   Extra Example 1: Dividing Integers 1:01 
   Extra Example 2: Dividing Integers 1:51 
   Extra Example 3: Dividing Integers 2:21 
   Extra Example 4: Dividing Integers 3:18 
  Integers and Order of Operations 11:09
   Intro 0:00 
   Combining Operations 0:21 
    Solve Using the Order of Operations 0:22 
   Extra Example 1: Evaluate 1:18 
   Extra Example 2: Evaluate 4:20 
   Extra Example 3: Evaluate 6:33 
   Extra Example 4: Evaluate 8:13 
V. Solving Equations
  Writing Expressions 9:15
   Intro 0:00 
   Operation as Words 0:05 
    Operation as Words 0:06 
   Extra Example 1: Write Each as an Expression 2:09 
   Extra Example 2: Write Each as an Expression 4:27 
   Extra Example 3: Write Each Expression Using Words 6:45 
  Writing Equations 18:03
   Intro 0:00 
   Equation 0:05 
    Definition of Equation 0:06 
    Examples of Equation 0:58 
   Operations as Words 1:39 
    Operations as Words 1:40 
   Extra Example 1: Write Each as an Equation 3:07 
   Extra Example 2: Write Each as an Equation 6:19 
   Extra Example 3: Write Each as an Equation 10:08 
   Extra Example 4: Determine if the Equation is True or False 13:38 
  Solving Addition and Subtraction Equations 24:53
   Intro 0:00 
   Solving Equations 0:08 
    inverse Operation of Addition and Subtraction 0:09 
   Extra Example 1: Solve Each Equation Using Mental Math 4:15 
   Extra Example 2: Use Inverse Operations to Solve Each Equation 5:44 
   Extra Example 3: Solve Each Equation 14:51 
   Extra Example 4: Translate Each to an Equation and Solve 19:57 
  Solving Multiplication Equation 19:46
   Intro 0:00 
   Multiplication Equations 0:08 
    Inverse Operation of Multiplication 0:09 
   Extra Example 1: Use Mental Math to Solve Each Equation 3:54 
   Extra Example 2: Use Inverse Operations to Solve Each Equation 5:55 
   Extra Example 3: Is -2 a Solution of Each Equation? 12:48 
   Extra Example 4: Solve Each Equation 15:42 
  Solving Division Equation 17:58
   Intro 0:00 
   Division Equations 0:05 
    Inverse Operation of Division 0:06 
   Extra Example 1: Use Mental Math to Solve Each Equation 0:39 
   Extra Example 2: Use Inverse Operations to Solve Each Equation 2:14 
   Extra Example 3: Is -6 a Solution of Each Equation? 9:53 
   Extra Example 4: Solve Each Equation 11:50 
VI. Ratios and Proportions
  Ratio 40:21
   Intro 0:00 
   Ratio 0:05 
    Definition of Ratio 0:06 
    Examples of Ratio 0:18 
   Rate 2:19 
    Definition of Rate 2:20 
    Unit Rate 3:38 
    Example: $10 / 20 pieces 5:05 
   Converting Rates 6:46 
    Example: Converting Rates 6:47 
   Extra Example 1: Write in Simplest Form 16:22 
   Extra Example 2: Find the Ratio 20:53 
   Extra Example 3: Find the Unit Rate 22:56 
   Extra Example 4: Convert the Unit 26:34 
  Solving Proportions 17:22
   Intro 0:00 
   Proportions 0:05 
    An Equality of Two Ratios 0:06 
    Cross Products 1:00 
   Extra Example 1: Find Two Equivalent Ratios for Each 3:21 
   Extra Example 2: Use Mental Math to Solve the Proportion 5:52 
   Extra Example 3: Tell Whether the Two Ratios Form a Proportion 8:21 
   Extra Example 4: Solve the Proportion 13:26 
  Writing Proportions 22:01
   Intro 0:00 
   Writing Proportions 0:08 
    Introduction to Writing Proportions and Example 0:10 
   Extra Example 1: Write a Proportion and Solve 5:54 
   Extra Example 2: Write a Proportion and Solve 11:19 
   Extra Example 3: Write a Proportion for Word Problem 17:29 
  Similar Polygons 16:31
   Intro 0:00 
   Similar Polygons 0:05 
    Definition of Similar Polygons 0:06 
    Corresponding Sides are Proportional 2:14 
   Extra Example 1: Write a Proportion and Find the Value of Similar Triangles 4:26 
   Extra Example 2: Write a Proportional to Find the Value of x 7:04 
   Extra Example 3: Write a Proportion for the Similar Polygons and Solve 9:04 
   Extra Example 4: Word Problem and Similar Polygons 11:03 
  Scale Drawings 13:43
   Intro 0:00 
   Scale Drawing 0:05 
    Definition of a Scale Drawing 0:06 
    Example: Scale Drawings 1:00 
   Extra Example 1: Scale Drawing 4:50 
   Extra Example 2: Scale Drawing 7:02 
   Extra Example 3: Scale Drawing 9:34 
  Probability 11:51
   Intro 0:00 
   Probability 0:05 
    Introduction to Probability 0:06 
    Example: Probability 1:22 
   Extra Example 1: What is the Probability of Landing on Orange? 3:26 
   Extra Example 2: What is the Probability of Rolling a 5? 5:02 
   Extra Example 3: What is the Probability that the Marble will be Red? 7:40 
   Extra Example 4: What is the Probability that the Student will be a Girl? 9:43 
VII. Percents
  Percents, Fractions, and Decimals 35:05
   Intro 0:00 
   Percents 0:06 
    Changing Percent to a Fraction 0:07 
    Changing Percent to a Decimal 1:54 
   Fractions 4:17 
    Changing Fraction to Decimal 4:18 
    Changing Fraction to Percent 7:50 
   Decimals 10:10 
    Changing Decimal to Fraction 10:11 
    Changing Decimal to Percent 12:07 
   Extra Example 1: Write Each Percent as a Fraction in Simplest Form 13:29 
   Extra Example 2: Write Each as a Decimal 17:09 
   Extra Example 3: Write Each Fraction as a Percent 22:45 
   Extra Example 4: Complete the Table 29:17 
  Finding a Percent of a Number 28:18
   Intro 0:00 
   Percent of a Number 0:06 
    Translate Sentence into an Equation 0:07 
    Example: 30% of 100 is What Number? 1:05 
   Extra Example 1: Finding a Percent of a Number 7:12 
   Extra Example 2: Finding a Percent of a Number 15:56 
   Extra Example 3: Finding a Percent of a Number 19:14 
   Extra Example 4: Finding a Percent of a Number 24:26 
  Solving Percent Problems 32:31
   Intro 0:00 
   Solving Percent Problems 0:06 
    Translate the Sentence into an Equation 0:07 
   Extra Example 1: Solving Percent Problems 0:56 
   Extra Example 2: Solving Percent Problems 14:49 
   Extra Example 3: Solving Percent Problems 23:44 
  Simple Interest 27:09
   Intro 0:00 
   Simple Interest 0:05 
    Principal 0:06 
    Interest & Interest Rate 0:41 
    Simple Interest 1:43 
   Simple Interest Formula 2:23 
    Simple Interest Formula: I = prt 2:24 
   Extra Example 1: Finding Simple Interest 3:53 
   Extra Example 2: Finding Simple Interest 8:08 
   Extra Example 3: Finding Simple Interest 12:02 
   Extra Example 4: Finding Simple Interest 17:46 
  Discount and Sales Tax 17:15
   Intro 0:00 
   Discount 0:19 
    Discount 0:20 
    Sale Price 1:22 
   Sales Tax 2:24 
    Sales Tax 2:25 
    Total Due 2:59 
   Extra Example 1: Finding the Discount 3:43 
   Extra Example 2: Finding the Sale Price 6:28 
   Extra Example 3: Finding the Sale Tax 11:14 
   Extra Example 4: Finding the Total Due 14:08 
VIII. Geometry in a Plane
  Intersecting Lines and Angle Measures 24:17
   Intro 0:00 
   Intersecting Lines 0:07 
    Properties of Lines 0:08 
    When Two Lines Cross Each Other 1:55 
   Angles 2:56 
    Properties of Angles: Sides, Vertex, and Measure 2:57 
   Classifying Angles 7:18 
    Acute Angle 7:19 
    Right Angle 7:54 
    Obtuse Angle 8:03 
   Angle Relationships 8:56 
    Vertical Angles 8:57 
    Adjacent Angles 10:38 
    Complementary Angles 11:52 
    Supplementary Angles 12:54 
   Extra Example 1: Lines 16:00 
   Extra Example 2: Angles 18:22 
   Extra Example 3: Angle Relationships 20:05 
   Extra Example 4: Name the Measure of Angles 21:11 
  Angles of a Triangle 13:35
   Intro 0:00 
   Angles of a Triangle 0:05 
    All Triangles Have Three Angles 0:06 
    Measure of Angles 2:16 
   Extra Example 1: Find the Missing Angle Measure 5:39 
   Extra Example 2: Angles of a Triangle 7:18 
   Extra Example 3: Angles of a Triangle 9:24 
  Classifying Triangles 15:10
   Intro 0:00 
   Types of Triangles by Angles 0:05 
    Acute Triangle 0:06 
    Right Triangle 1:14 
    Obtuse Triangle 2:22 
   Classifying Triangles by Sides 4:18 
    Equilateral Triangle 4:20 
    Isosceles Triangle 5:21 
    Scalene Triangle 5:53 
   Extra Example 1: Classify the Triangle by Its Angles and Sides 6:34 
   Extra Example 2: Sketch the Figures 8:10 
   Extra Example 3: Classify the Triangle by Its Angles and Sides 9:55 
   Extra Example 4: Classify the Triangle by Its Angles and Sides 11:35 
  Quadrilaterals 17:41
   Intro 0:00 
   Quadrilaterals 0:05 
    Definition of Quadrilaterals 0:06 
    Parallelogram 0:45 
    Rectangle 2:28 
    Rhombus 3:13 
    Square 3:53 
    Trapezoid 4:38 
   Parallelograms 5:33 
    Parallelogram, Rectangle, Rhombus, Trapezoid, and Square 5:35 
   Extra Example 1: Give the Most Exact Name for the Figure 11:37 
   Extra Example 2: Fill in the Blanks 13:31 
   Extra Example 3: Complete Each Statement with Always, Sometimes, or Never 14:37 
  Area of a Parallelogram 12:44
   Intro 0:00 
   Area 0:06 
    Definition of Area 0:07 
   Area of a Parallelogram 2:00 
    Area of a Parallelogram 2:01 
   Extra Example 1: Find the Area of the Rectangle 4:30 
   Extra Example 2: Find the Area of the Parallelogram 5:29 
   Extra Example 3: Find the Area of the Parallelogram 7:22 
   Extra Example 4: Find the Area of the Shaded Region 8:55 
  Area of a Triangle 11:29
   Intro 0:00 
   Area of a Triangle 0:05 
    Area of a Triangle: Equation and Example 0:06 
   Extra Example 1: Find the Area of the Triangles 1:31 
   Extra Example 2: Find the Area of the Figure 4:09 
   Extra Example 3: Find the Area of the Shaded Region 7:45 
  Circumference of a Circle 15:04
   Intro 0:00 
   Segments in Circles 0:05 
    Radius 0:06 
    Diameter 1:08 
    Chord 1:49 
   Circumference 2:53 
    Circumference of a Circle 2:54 
   Extra Example 1: Name the Given Parts of the Circle 6:26 
   Extra Example 2: Find the Circumference of the Circle 7:54 
   Extra Example 3: Find the Circumference of Each Circle with the Given Measure 11:04 
  Area of a Circle 14:43
   Intro 0:00 
   Area of a Circle 0:05 
    Area of a Circle: Equation and Example 0:06 
   Extra Example 1: Find the Area of the Circle 2:17 
   Extra Example 2: Find the Area of the Circle 5:47 
   Extra Example 3: Find the Area of the Shaded Region 9:24 
XI. Geometry in Space
  Prisms and Cylinders 21:49
   Intro 0:00 
   Prisms 0:06 
    Polyhedron 0:07 
    Regular Prism, Bases, and Lateral Faces 1:44 
   Cylinders 9:37 
    Bases and Altitude 9:38 
   Extra Example 1: Classify Each Prism by the Shape of Its Bases 11:16 
   Extra Example 2: Name Two Different Edges, Faces, and Vertices of the Prism 15:44 
   Extra Example 3: Name the Solid of Each Object 17:58 
   Extra Example 4: Write True or False for Each Statement 19:47 
  Volume of a Rectangular Prism 8:59
   Intro 0:00 
   Volume of a Rectangular Prism 0:06 
    Volume of a Rectangular Prism: Formula 0:07 
    Volume of a Rectangular Prism: Example 1:46 
   Extra Example 1: Find the Volume of the Rectangular Prism 3:39 
   Extra Example 2: Find the Volume of the Cube 5:00 
   Extra Example 3: Find the Volume of the Solid 5:56 
  Volume of a Triangular Prism 16:15
   Intro 0:00 
   Volume of a Triangular Prism 0:06 
    Volume of a Triangular Prism: Formula 0:07 
   Extra Example 1: Find the Volume of the Triangular Prism 2:42 
   Extra Example 2: Find the Volume of the Triangular Prism 7:21 
   Extra Example 3: Find the Volume of the Solid 10:38 
  Volume of a Cylinder 15:55
   Intro 0:00 
   Volume of a Cylinder 0:05 
    Volume of a Cylinder: Formula 0:06 
   Extra Example 1: Find the Volume of the Cylinder 1:52 
   Extra Example 2: Find the Volume of the Cylinder 7:38 
   Extra Example 3: Find the Volume of the Cylinder 11:25 
  Surface Area of a Prism 23:28
   Intro 0:00 
   Surface Area of a Prism 0:06 
    Surface Area of a Prism 0:07 
   Lateral Area of a Prism 2:12 
    Lateral Area of a Prism 2:13 
   Extra Example 1: Find the Surface Area of the Rectangular Prism 7:08 
   Extra Example 2: Find the Lateral Area and the Surface Area of the Cube 12:05 
   Extra Example 3: Find the Surface Area of the Triangular Prism 17:13 
  Surface Area of a Cylinder 27:41
   Intro 0:00 
   Surface Area of a Cylinder 0:06 
    Introduction to Surface Area of a Cylinder 0:07 
   Surface Area of a Cylinder 1:33 
    Formula 1:34 
   Extra Example 1: Find the Surface Area of the Cylinder 5:51 
   Extra Example 2: Find the Surface Area of the Cylinder 13:51 
   Extra Example 3: Find the Surface Area of the Cylinder 20:57 
X. Data Analysis and Statistics
  Measures of Central Tendency 24:32
   Intro 0:00 
   Measures of Central Tendency 0:06 
    Mean 1:17 
    Median 2:42 
    Mode 5:41 
   Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data 6:24 
   Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data 11:14 
   Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data 15:13 
   Extra Example 4: Find the Three Measures of the Central Tendency 19:12 
  Histograms 19:43
   Intro 0:00 
   Histograms 0:05 
    Definition and Example 0:06 
   Extra Example 1: Draw a Histogram for the Frequency Table 6:14 
   Extra Example 2: Create a Histogram of the Data 8:48 
   Extra Example 3: Create a Histogram of the Following Test Scores 14:17 
  Box-and-Whisker Plot 17:54
   Intro 0:00 
   Box-and-Whisker Plot 0:05 
    Median, Lower & Upper Quartile, Lower & Upper Extreme 0:06 
   Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme 6:04 
   Extra Example 2: Draw a Box-and-Whisker Plot Given the Information 7:35 
   Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme 9:31 
   Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data 12:50 
  Stem-and-Leaf Plots 17:42
   Intro 0:00 
   Stem-and-Leaf Plots 0:05 
    Stem-and-Leaf Plots 0:06 
   Extra Example 1: Use the Data to Create a Stem-and-Leaf Plot 2:28 
   Extra Example 2: List All the Numbers in the Stem-and-Leaf Plot in Order From Least to Greatest 7:02 
   Extra Example 3: Create a Stem-and-Leaf Plot of the Data & Find the Median and the Mode. 8:59 
  The Coordinate Plane 19:59
   Intro 0:00 
   The Coordinate System 0:05 
    The Coordinate Plane 0:06 
    Quadrants, Origin, and Ordered Pair 0:50 
   The Coordinate Plane 7:02 
    Write the Coordinates for Points A, B, and C 7:03 
   Extra Example 1: Graph Each Point on the Coordinate Plane 9:03 
   Extra Example 2: Write the Coordinate and Quadrant for Each Point 11:05 
   Extra Example 3: Name Two Points From Each of the Four Quadrants 13:13 
   Extra Example 4: Graph Each Point on the Same Coordinate Plane 17:47 
XI. Probability and Discrete Mathematics
  Organizing Possible Outcomes 15:35
   Intro 0:00 
   Compound Events 0:08 
    Compound Events 0:09 
    Fundamental Counting Principle 3:35 
   Extra Example 1: Create a List of All the Possible Outcomes 4:47 
   Extra Example 2: Create a Tree Diagram For All the Possible Outcomes 6:34 
   Extra Example 3: Create a Tree Diagram For All the Possible Outcomes 10:00 
   Extra Example 4: Fundamental Counting Principle 12:41 
  Independent and Dependent Events 35:19
   Intro 0:00 
   Independent Events 0:11 
    Definition 0:12 
    Example 1: Independent Event 1:45 
    Example 2: Two Independent Events 4:48 
   Dependent Events 9:09 
    Definition 9:10 
    Example: Dependent Events 10:10 
   Extra Example 1: Determine If the Two Events are Independent or Dependent Events 13:38 
   Extra Example 2: Find the Probability of Each Pair of Events 18:11 
   Extra Example 3: Use the Spinner to Find Each Probability 21:42 
   Extra Example 4: Find the Probability of Each Pair of Events 25:49 
  Disjoint Events 12:13
   Intro 0:00 
   Disjoint Events 0:06 
    Definition and Example 0:07 
   Extra Example 1: Disjoint & Not Disjoint Events 3:08 
   Extra Example 2: Disjoint & Not Disjoint Events 4:23 
   Extra Example 3: Independent, Dependent, and Disjoint Events 6:30 
  Probability of an Event Not Occurring 20:05
   Intro 0:00 
   Event Not Occurring 0:07 
    Formula and Example 0:08 
   Extra Example 1: Use the Spinner to Find Each Probability 7:24 
   Extra Example 2: Probability of Event Not Occurring 11:21 
   Extra Example 3: Probability of Event Not Occurring 15:51