# Pre Algebra Dividing Rational Numbers

Section 5: Rational Number Operations: Lecture 4 | 12:08 min

In this lesson our instructor talks about dividing rational numbers. The vocabulary for this lesson is reciprocal. She talks about finding the reciprocal and dividing rational numbers. She also talks about dividing rational numbers in word problems an does an example on chocolate peanuts. Four complete extra example videos round up this lesson.

Nancy Fung

Dividing Rational Numbers

Slide Duration:Table of Contents

13m 41s

- Intro0:00
- What You'll Learn and Why0:08
- Topics Overview0:09
- Vocabulary0:22
- Order of Operations0:26
- Numerical Expression1:03
- Simplify1:27
- Simplifying an Expression1:44
- Example 1: Simplify the Expression1:45
- Simplifying an Expression3:26
- Example 2: Simplify the Expression3:27
- Using an Expression to Solve a Problem4:29
- Example 3: Babysitting4:33
- Using an Expression to Solve a Problem6:14
- Example 4: Shopping6:17
- Extra Example 1: Simplify the Expression7:35
- Extra Example 2: Simplify the Expression8:55
- Extra Example 3: Finding Total Cost10:02
- Extra Example 4: Finding Total Cost11:44

9m 11s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:16
- Variable0:19
- Algebraic Expression0:30
- Evaluate0:51
- Modeling an Algebraic Expression1:16
- Model the Expression 2x + 41:17
- Evaluating an Algebraic Expression1:47
- Evaluate 3x - 7 for x = 8.21:48
- Evaluating an Algebraic Expression2:45
- Evaluate (3.7 + x) ÷ 2 for x = 9.62:46
- Using a Table to Evaluate an Expression4:10
- Example: Pairs of Shoes4:13
- Extra Example 1: Evaluate the Expression5:46
- Extra Example 2: Evaluate the Expression6:06
- Extra Example 3: Perimeter of a Rectangle6:46
- Extra Example 4: Finding Income7:40

8m 24s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Addition0:26
- Subtraction1:04
- Multiplication2:06
- Division2:31
- Translating Words to Expressions3:02
- Example: 9 Less than Twice a Number3:08
- Writing an Algebraic Expression3:58
- Example: Cost of Bowling4:07
- Extra Example 1: Writing Expressions5:14
- Extra Example 2: Writing Expressions6:06
- Extra Example 3: Writing Expressions7:11
- Extra Example 4: Writing Expressions7:58

10m 20s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:16
- Compatible Numbers0:17
- Estimating by Rounding1:08
- Estimate 36 + 6 + 581:30
- Estimate 94 - 35 - 422:29
- Estimating with Compatible Numbers3:02
- Estimate 297 ÷ 173:17
- Estimate 9 Times 383:39
- Estimating for Reasonableness4:13
- Example: Total Cost of the Items4:15
- Extra Example 1: Estimating with Compatible Numbers6:02
- Extra Example 2: Estimating by Rounding7:05
- Extra Example 3: Estimating for Reasonableness7:27
- Extra Example 4: Estimating for Reasonableness9:15

12m 1s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:16
- Commutative Properties: Addition and Multiplication0:21
- Associative Properties: Addition and Multiplication1:46
- Vocabulary Cont.3:08
- Identity Properties: Addition and Multiplication3:09
- Recognizing Properties3:55
- Examples: Which Property is Illustrated?3:58
- Using Properties of Numbers5:07
- Using Mental Math to Find the Total Cost5:18
- Using Properties of Numbers6:29
- Using Mental Math to Simplify6:30
- Extra Example 1: Using Properties of Numbers8:29
- Extra Example 2: Using Properties of Numbers9:06
- Extra Example 3: Using Properties of Numbers10:02
- Extra Example 4: Using Properties of Numbers10:32

9m 40s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Distributive Property0:16
- Using the Distributive Property1:32
- Example: 8 ( 9 + 11 )1:35
- Using the Distributive Property2:58
- Example: 7 ( 12 - h )2:59
- Example: ( m + 2 ) 53:20
- Distributive Property in Mental Math3:34
- Example: Finding Total Cost3:38
- Extra Example 1: Summer Job4:55
- Extra Example 2: Total Cost6:03
- Extra Example 3: Fundraiser7:36
- Extra Example 4: Tomato Plants8:24

11m 35s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:10
- Vocabulary0:21
- Opposites0:27
- Integers1:03
- Absolute Value1:23
- Vocabulary2:21
- Number Line2:23
- Finding Absolute Value2:35
- Example: Absolute Value2:36
- More Examples4:05
- Example: Absolute Value of 54:06
- Example: Absolute Value of Negative 24:15
- Comparing Integers4:29
- Boiling Points of Elements4:34
- Comparing Integer Examples6:00
- Example 1: Comparing Integers6:04
- Example 2: Comparing Integers6:17
- Example 3: Comparing Integers6:30
- Comparing Integer Examples6:49
- Comparing Temperature6:53
- Extra Example 1: Simplify Absolute Value8:13
- Extra Example 2: Simplify Absolute Value9:01
- Extra Example 3: Simplify Absolute Value9:29
- Extra Example 4: Simplify Absolute Value10:49

10m 20s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:26
- Integers0:30
- Adding Positive Integers0:55
- Example : -3 + -71:01
- Example : +11 + 81:06
- Example : 2 + (+6)1:21
- Adding Negative Integers1:43
- Example: -3 + -71:48
- Example: -21 + -32:05
- Example: -11 + (-4)2:41
- Adding Integers with Opposite Signs3:01
- Using a Number Line: -8 + 103:52
- Using a Number Line: 4 + (-6)4:36
- Adding Integers with Opposite Signs5:39
- Using Absolute Value: -18 + 75:48
- Extra Example 1: Adding Integers6:33
- Extra Example 2: Adding Integers7:23
- Extra Example 3: Money Problem8:46
- Extra Example 4: Measurement Problem9:15

12m 1s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:21
- Integers0:25
- Opposites0:47
- Rules for Multiplying Signs1:18
- Using a Number Line2:00
- Example: 2 - 52:25
- Other Examples2:52
- Using Number Line: 10 - (-13)3:02
- Rewriting Absolute Value4:51
- Extra Example 1: Subtracting Integers5:48
- Extra Example 2: Temperature7:26
- Extra Example 3: Depth8:51
- Extra Example 4: Change in Yards11:09

14m 28s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:43
- Integers0:47
- Opposites1:03
- Repeated Addition1:41
- Example 1: Using a Number Line1:43
- More Examples3:28
- Example 2: Using a Number Line3:30
- Using a Number Line4:45
- Example 3: Using a Number Line4:46
- Example 4: Using a Number Line5:59
- Rules for Multiplying Same Sign Integers7:20
- Arithmetic7:35
- Algebra8:00
- Rules for Multiplying Different Signs Integers8:17
- Arithmetic8:29
- Algebra8:58
- Multiplying Integer Examples9:20
- Examples of Multiplying Integers9:21
- Using Multiplication of Integers to Solve a Problem10:07
- Elevation10:12
- Temperature11:21
- Determine the Sign of the Product12:19
- Example 5: Determine the Sign12:20
- Example 6: Determine the Sign12:50
- Extra Example 1: Product of Three Negative Numbers13:07
- Extra Example 2: Product of Four Negative Numbers13:45
- Extra Example 3: Product of Five Negative Numbers13:58
- Extra Example 4: Product of 103 Negative Numbers14:13

20m 18s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:27
- Quotient0:30
- Rules for Dividing Integers0:49
- 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 Examples3:24
- Dividing Integers: 14 ÷ 73:30
- Dividing Integers: 45 ÷ (-9)3:37
- Dividing Integer Examples3:51
- Dividing Integers: (-105) ÷ (-15)3:55
- Dividing Integers: (-42) ÷ 65:07
- Average Rate of Change5:17
- Using Integers to Represent the Situation5:25
- Example: Spend $360 in 6 Days5:40
- Example: Runs 1000 Feet in 4 Minutes6:30
- Average Rate of Change Word Problems7:27
- Example: Average Decrease in Value7:32
- Average Rate of Change Word Problems9:19
- Example: Average Increase in Stock9:23
- Average Rate of Change Word Problems10:46
- Example: Average Increase in Speed10:51
- Dividing Integers12:00
- Odd Number of Negatives12:03
- Even Number of Negatives12:49
- Order of Operations and Sign of Final Answer13:50
- Example: -120 ÷ (-5) ÷ -413:56
- Extra Example 1: Order of Operations14:48
- Extra Example 2: Evaluate the Expression15:29
- Extra Example 3: Rate of Change17:18
- Extra Example 4: Rate of Evaporation19:22

20m 5s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:26
- Factor0:32
- Exponent1:16
- Vocabulary1:57
- Base1:58
- Power2:18
- Writing Expressions with Exponents2:31
- Example 1: Writing Expressions with Exponents2:36
- Example 2: Writing Expressions with Exponents3:00
- Writing Expressions with Exponents3:20
- Example 3: Writing Expressions with Exponents3:25
- Example 4: Writing Expressions with Exponents3:53
- Simplifying Power4:06
- Example 5: Simplifying Power4:14
- Example 6: Simplifying Power5:03
- Simplifying Power6:06
- Example 7: Simplifying Power6:09
- Example 8: Simplifying Power6:50
- Order of Operations7:24
- PEMDAS7:26
- Order of Operations8:32
- Multiplying/Dividing and Adding/Subtracting8:34
- Evaluating Expressions with Exponents10:07
- Example 9: Evaluating Expressions with Exponents10:11
- Example 10: Evaluating Expressions with Exponents11:07
- Extra Example 1: Evaluate12:33
- Extra Example 2: Evaluate13:42
- Extra Example 3: Height of the Rocket15:00
- Extra Example 4: Number of Cells16:38

21m 47s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:18
- Equation0:21
- Isolate1:00
- Inverse Operations1:18
- Subtraction Property of Equality1:59
- Arithmetic2:12
- Algebraic2:53
- Inverse Operations3:32
- Example: 38 + x = 423:40
- Using Substitution to Check Answer4:43
- Inverse Operations5:19
- Example: y + 7.3 = 9.15:22
- Using Substitution to Check Answer5:53
- Draw a Model6:26
- Weight Gain6:42
- Draw a Model8:20
- Mountain Climber8:23
- Examples by Writing Equations10:25
- Calculating Profit: Sweat Shirt10:30
- Examples by Writing Equations11:37
- Calculating Profit: Car Dealer11:38
- Extra Example 1: Inverse Operation14:21
- Extra Example 2: Inverse Operation15:37
- Extra Example 3: Real Estate17:23
- Extra Example 4: Birth Date20:06

19m 34s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:07
- Vocabulary0:23
- Addition Property of Equality: Arithmetic0:31
- Addition Property of Equality: Algebraic1:14
- Subtraction Property of Equality: Arithmetic1:54
- Subtraction Property of Equality: Algebraic2:19
- Solving an Equation by Adding3:05
- Example: b - 2 = 23:22
- Example: 23 - j = 124:00
- Solving an Equation by Adding5:29
- Example: a - 7.9 = 17.95:32
- Example: -5.6 + x = 10.26:33
- Solving an Equation by Writing an Equation7:42
- Example: Bank Withdrawal7:48
- Solving an Equation by Writing an Equation9:21
- Example: Temperature9:23
- Extra Example 1: Solving Subtraction Equations11:50
- Extra Example 2: Solving Subtraction Equations12:46
- Extra Example 3: Money13:40
- Extra Example 4: Selling Price16:01

26m 11s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:19
- Division Property of Equality: Arithmetic0:27
- Division Property of Equality: Algebraic1:05
- Multiplication Property of Equality: Arithmetic1:38
- Multiplication Property of Equality: Algebraic2:07
- Vocabulary2:49
- Inverse Operations2:53
- Solve the Equation Using Division3:09
- Example: 8x = 563:12
- Example: -6y = 423:59
- Solve the Equation Using Division4:47
- Example: 0.9c = 1.894:53
- Solve the Equation Using Division6:11
- Example: Saving Money6:17
- Example: Soccer Team8:14
- Solve the Equation Using Multiplication9:56
- Example: a/7 = 910:04
- Example: t/1.7 = 610:52
- Solve the Equation Using Multiplication12:09
- Example: y/-45 = 3.212:17
- Example: -p = 1413:13
- Solve the Equation Using Multiplication14:10
- Example: Distant14:16
- Extra Example 1: Solve the Equation15:58
- Extra Example 2: Solve the Equation17:25
- Extra Example 3: Height of an Elephant20:55
- Extra Example 4: Money23:07

19m 10s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Two-Step Equation Involvement0:19
- Solving Two-Step Equations0:41
- Example: 8y - 11 = 320:45
- Example: 32 = t/5 + 82:55
- Solving Two-Step Equations4:49
- Example: Recommended Daily Intake4:59
- Solving Two-Step Equations7:01
- Example: Cost of Each Ride7:02
- Extra Example 1: Solving Two-Step Equations10:13
- Extra Example 2: Solving Two-Step Equations12:54
- Extra Example 3: Length of Phone Call13:56
- Extra Example 4: Cost of Owning a Pet16:40

12m 16s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:16
- Perfect Square0:20
- Square Root0:46
- Square Roots1:13
- Every Positive Number has Two Square Roots1:14
- Square Roots of a Number are Opposites1:40
- Square Root Symbol1:54
- Positive Square Root of a Number1:56
- Compare: √25 and -√252:08
- Find the Square Root2:50
- Example: Square Root of 812:52
- Example: Square Root of 1213:13
- Estimating Square Roots3:29
- Example: Square Root of 233:35
- Example: Square Root of 3904:13
- Example: Negative Square Root of 1254:50
- Estimating Square Roots5:27
- Estimating Length5:31
- Simplifying Square Roots7:05
- Example: Square Root of 367:08
- Example: Simplifying Square Roots7:47
- Extra Example 1: Estimate the Length8:21
- Extra Example 2: Simplify the Expression9:05
- Extra Example 3: Estimate the Length9:50
- Extra Example 4: Simplify the Expression10:34

14m 49s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:36
- Right Triangle0:39
- Legs0:57
- Hypotenuse1:02
- Pythagorean Theorem1:11
- Arithmetic Example1:12
- Algebra Example2:41
- Find the Length of the Hypotenuse3:04
- Example 1: Hypotenuse of a Triangle3:07
- Example 2: Hypotenuse of a Triangle4:30
- Find the Length of the Hypotenuse6:18
- Example 3: Hypotenuse of a Right Triangle6:19
- Extra Example 1: Square Roots8:41
- Extra Example 2: Perimeter9:43
- Extra Example 3: Length of Screen11:58
- Extra Example 4: Length of Wire13:14

16m 15s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:30
- The Pythagorean Theorem0:32
- Find the Length of a Leg1:14
- Example 1: Length of Ramp1:19
- Example: 2 Length of Platform4:22
- Identifying a Right Triangle6:13
- Example 3: Determine Right Triangle6:14
- Example 4: Determine Right Triangle8:08
- Extra Example 1: Find the Missing Leg Length10:04
- Extra Example 2: Length of Ladder11:39
- Extra Example 3: Determine Given Lengths13:04
- Extra Example 4: Length of Pole14:20

16m 40s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:23
- Factor0:24
- Composite Number1:04
- Vocabulary1:17
- Prime Number1:18
- Prime Factorization1:57
- Divisibility Rules2:54
- Divisibility Rules for 2, 3, 4 ,5 ,6, 9 and 102:55
- Finding Factors4:56
- Possible Arrangements4:59
- Finding Factors6:06
- How Many Oranges?6:07
- Prime or Composite6:43
- Prime or Composite: 486:47
- Prime or Composite: 537:09
- Prime or Composite: 577:35
- Prime Factorization8:16
- Prime Factorization of 428:23
- Prime Factorization of 848:47
- Find the Number9:23
- Find the Number with the Given Prime Factorization9:24
- Extra Example 1: Prime or Composite11:04
- Extra Example 2: Prime Factorization of 7212:23
- Extra Example 3: Marching Arrangements12:56
- Extra Example 4: Flowers Arrangements14:50

14m 16s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:41
- Factor0:43
- Common Divisor1:00
- Greatest Common Divisor (GCD)/ Greatest Common Factor (GCF)1:16
- Find the GCD by Listing Divisors1:34
- GCD of 27 and 361:46
- GCD of 18 and 492:52
- Prime Factorization to Find GCD3:30
- GCD of 42 and 723:42
- GCD of 21 and 634:46
- GCD in Word Problems5:30
- Greatest Number of Police Officers5:32
- GCD in Word Problems7:15
- Cutting Two Pipes7:16
- Extra Example 1: GCD of 32, -24, 408:08
- Extra Example 2: How Many Groups?9:41
- Extra Example 3: GCD of Two Prime Numbers11:34
- Extra Example 4: How Many Children?12:26

11m 22s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:21
- Equivalent Fractions0:23
- Simplest Form1:15
- Creating Equivalent Fractions1:59
- Method to Create Equivalent Fractions2:00
- Equivalent Fractions2:18
- Write Two Fractions Equivalent to 5/82:22
- Write Two Fractions Equivalent to 2/143:12
- GCD to Simplify3:51
- Find the GCD of 24 and 324:03
- Write 24/32 in Simplest Form4:43
- Write -27/45 in Simplest Form5:08
- Writing a Fraction6:04
- Example: What Fraction of the Vehicles are Trucks?6:11
- Writing a Fraction7:45
- Example: What Fraction of the Seats are Empty?7:55
- Extra Example 1: Pizza9:00
- Extra Example 2: Driving Time9:28
- Extra Example 3: Simplest Form10:29
- Extra Example 4: Basketball Team10:52

20m 47s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:08
- Vocabulary0:30
- Rational Number0:31
- Terminating Decimal0:53
- Repeating Decimal1:04
- Converting Decimals to Fractions1:22
- Write 0.47 as a Fraction1:26
- Write 0.48 as a Fraction2:03
- Write 0.245 as a Fraction3:21
- Converting Decimals to Fractions4:20
- Write 0.08 as a Fraction4:30
- Write 0.8 as a Fraction4:53
- Converting Fractions to Decimals5:26
- Write 1/2 as a Decimal5:30
- Write 6/33 as a Decimal6:12
- Write -9/5 as a Decimal7:39
- Converting Fractions to Decimals in Word Problems8:19
- Batting Average8:23
- Converting Fractions to Decimals in Word Problems11:22
- Cooking Festival11:26
- Extra Example 1: Write 0.038 as a Fraction14:45
- Extra Example 2: Write -13/7 as a Decimal15:35
- Extra Example 3: Batting Average16:38
- Extra Example 4: Rational Number19:55

20m 21s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:29
- Least Common Multiple (LCM)0:30
- Least Common Denominator (LCD)1:50
- Ordering Rational Numbers2:45
- Numbers as Decimals2:46
- Numbers as Fractions5:36
- Compare Each Pair of Numbers8:10
- Compare 3/4 and 4/58:11
- Compare 3/11 and 1/68:44
- Comparing rational Numbers in Word Problems9:19
- 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 Notes15:54
- Extra Example 4: Chocolate or Fruit17:16

15m 4s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:19
- Least Common Multiple (LCM)0:20
- Least Common Denominator (LCD)0:28
- Adding Fractions with Unlike Denominators1:22
- Example: 3/4 + 2/51:28
- Example: -3/5 + 1/72:29
- Adding Different Forms of Rational Numbers3:23
- Example: Change to Fractions3:31
- Example: Change to Decimals5:14
- Extra Example 1: Adding Different Forms of Numbers7:02
- Extra Example 2: Exercising10:06
- Extra Example 3: Adding Different Forms of Numbers11:20
- Extra Example 4: Cooking Recipe13:47

14m 40s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:19
- Least Common Denominator (LCD)0:20
- Subtracting with Unlike Denominators0:41
- Example: 5/9 - 3/50:44
- Example: 3/4 - 7/81:23
- Subtracting Rational Numbers1:59
- Example: 23/4 - 3.52:05
- Example: 11.7 - 3/43:39
- Subtracting Rational Numbers in Word Problems4:37
- Puppy's Weight4:41
- Extra Example 1: Subtracting with Unlike Denominators6:48
- Extra Example 2: Subtracting Rational Numbers7:27
- Extra Example 3: Rainfall10:32
- Extra Example 4: Decorating Your House12:06

11m 2s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:17
- Rational Number0:18
- Exponent0:30
- Power0:35
- Multiplying Decimals0:47
- Example 1: Multiplying Decimals0:50
- Example 2: Multiplying Decimals1:18
- Multiplying Rational Numbers in Word Problems1:51
- Example: Length of Pipes1:56
- Raising a Fraction to a Power2:58
- Examples: Raising Fractions to Power2:59
- Extra Example 1: Multiplying Fractions4:45
- Extra Example 2: Compare Fractions5:34
- Extra Example 3: Flour7:28
- Extra Example 4: Income8:50

12m 8s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:22
- Reciprocal0:26
- Finding the Reciprocal0:56
- Example: Reciprocal of 2/31:00
- Example: Reciprocal of 81:04
- Example: Reciprocal of -1/21:10
- Dividing Rational Numbers1:28
- Example 1: Dividing Rational Numbers1:35
- Example 2: Dividing Rational Numbers2:09
- Example 3: Dividing Rational Numbers2:35
- Dividing Rational Numbers in Word Problems3:56
- Example: Chocolate Peanuts4:00
- Extra Example 1: Dividing Decimals5:17
- Extra Example 2: Dividing Fractions7:09
- Extra Example 3: Search Committee8:34
- Extra Example 4: Stake10:18

13m 43s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- What You'll Learn and Why0:23
- Isolate0:24
- Solving Equations with Fractions0:41
- Example: n + 1/2 = 11/120:44
- Example: 3/5 - a = 13/201:34
- Writing Equations with Fractions3:08
- Example: Thickness3:11
- Extra Example 1: Solving Equations6:01
- Extra Example 2: Solving Equations6:58
- Extra Example 3: School Lunches8:23
- Extra Example 4: Fashion Designer10:44

11m 10s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:20
- Multiplicative Inverse0:21
- Solve Each Equation0:51
- Example 1: Solve the Equation0:57
- Example 2: Solve the Equation2:39
- Writing Multiplication Equations3:30
- Example: Water Level3:34
- Extra Example 1: Solve the Equation5:15
- Extra Example 2: Solve the Equation6:28
- Extra Example 3:Money7:26
- Extra Example 4: Solve the Equation9:45

6m 41s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:22
- Zero Exponents: Arithmetic Definition0:27
- Zero Exponents: Algebra Definition0:39
- Negative Exponents: Arithmetic Definition0:46
- Negative Exponents: Algebra Definition1:03
- Simplifying Exponents1:18
- Examples: Simplifying Exponents1:21
- Fractions and Negative Exponents2:41
- Examples: Fractions and Negative Exponents2:45
- Extra Example 1: Negative Exponent3:58
- Extra Example 2: Zero Exponent4:30
- Extra Example 3: Fraction and Negative Exponent4:40
- Extra Example 4: Subtracting Numbers with Exponents5:00

7m 5s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:22
- Ratio0:23
- Equivalent Ratios0:40
- Writing a Ratio1:18
- Write the Ratio in Three Ways1:21
- Writing an Equivalent Ratio2:07
- Different Ratios Equivalent to 10:122:08
- Writing a Ratio in Simplest Form2:47
- Write the Ratio in Simplest Form2:50
- Extra Example 1: Write the Ratio3:32
- Extra Example 2: Ratio in Simplest Form4:38
- Extra Example 3: Write the Ratio5:08
- Extra Example 4: Ratio in Simplest Form5:48

12m 45s

- Intro0:00
- What You'll Learn and Why0:04
- Topics Overview0:05
- Vocabulary0:18
- Rate0:22
- Unit Rate0:40
- Finding a Unit Rate1:00
- Example: Delivery Rate1:03
- Using a Unit Rate1:46
- Example: Miles and Gallon of Gas1:49
- Comparing Unit Rates2:52
- Example: Which is the Better Buy2:58
- Extra Example 1: Calories6:30
- Extra Example 2: Typing Speed7:22
- Extra Example 3: Which is the Better Buy8:23
- Extra Example 4: Wages10:48

16m 19s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Conversion Factor0:16
- Dimensional Analysis0:23
- Conversion Chart: Length0:32
- Conversion Chart: in, ft, yd, and m0:33
- Conversion Chart: Weight0:49
- Conversion Chart: oz, lb, and t0:50
- Conversion Chart: Capacity0:59
- Conversion Chart: fl oz, cup, pt, qt, and gal1:00
- Converting Units1:17
- Example: Convert 1.3 Miles Into Feet1:18
- Converting Units3:14
- Example: Convert Pounds to Ounces3:15
- Example: Convert Cups to Fluid Ounces3:52
- Converting Units in a Rate4:30
- Unit Rate: 2,200 m in 17.2 min4:31
- Using Dimensional Analysis8:06
- Example: Planning Project8:07
- Extra Example 1: Converting Units9:15
- Extra Example 2: Unit Rate10:31
- Extra Example 3: Planning Project12:15
- Extra Example 4: Converting Units13:45

17m 42s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:18
- Rate0:22
- Unit Rate0:27
- Finding Total Distance0:32
- Example: Total Distance0:33
- Finding Average Speed2:49
- Example: Car's Average Speed2:53
- Using a Unit Rate6:31
- Example: Weight and Spring6:32
- Extra Example 1: Total Distance8:08
- Extra Example 2: Bird's Average Speed10:33
- Extra Example 3: Cost of Shirts13:37
- Extra Example 4: Cost of Bottles15:22

14m 36s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:16
- Proportion0:17
- Cross Products0:45
- Identifying a Proportion11:28
- Example: Do the Ratios Form a Proportion?11:29
- Solving Proportions Using Two Methods2:47
- Example: x/4 = 12/213:03
- Example: 20/y = 15/94:43
- Solving Proportions in Word Problems5:56
- Example: Find the Unit Rate of Exchange6:00
- Extra Example 1: Does the Ratio Form a Proportion?9:55
- Extra Example 2: Solving Proportions10:53
- Extra Example 3: Find the Length of the Photo11:33
- Extra Example 4: Distance12:59

10m 13s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:24
- Percent0:25
- Compare a Fraction to a Decimal to a Percent0:35
- Example: 31 out of 1000:39
- Write a Percent as a Fraction1:11
- Example: Write 47% as a Fraction1:12
- Example: Write 25% as a Fraction1:59
- Write a Fraction as a Percent2:38
- Example: Write 2/10 as a Percent2:39
- Example: Write 57/100 as a Percent3:22
- Example: Write 3/25 as a Percent3:57
- Write a Decimal as a Percent4:48
- Example: Write 0.85 as a Percent4:49
- Example: Write 0.3 as a Percent5:05
- Example: Write 0.04 as a Percent5:17
- Extra Example 1: Write Percent as Decimal and Fraction5:34
- Extra Example 2: Write Fraction as Decimal and Percent6:47
- Extra Example 3: Write Percent as Fraction and Decimal7:41
- Extra Example 4: Fraction, Percent, and Decimal of Students8:36

8m 39s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:20
- Percent0:21
- Finding a Percent0:26
- Example: Find 15% of 1000:27
- Example: Find 10% of 1351:08
- Finding More Percents2:23
- Example: Find 8% of 652:25
- Example: Find 120% of 502:45
- Estimating a Percent3:25
- Example: Estimate 10% of 31.053:38
- Example: Estimate 15% of 31.053:54
- Example: Estimate 20% of 31.054:55
- Extra Example 1: Find 7% of 1205:35
- Extra Example 2: Find 125% of 756:01
- Extra Example 3: Estimate 15% Tip7:02
- Extra Example 4: Estimate 20% Tip8:01

15m 38s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:23
- Proportion0:33
- Cross Products0:38
- Finding Part of a Whole1:07
- Method 1: Find 50% of 361:11
- Method 2: Find 50% of 362:23
- Finding Part of a Whole, cont.3:06
- Example: Find 65% of 1433:07
- Finding the Whole Amount3:44
- 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 Percent6:38
- Method 1: What Percent of 175 is 1057:21
- Method 2: What Percent of 175 is 1058:49
- Finding a Percent, cont.9:57
- What Percent of 115 is 46?9:58
- Extra Example 1: Find 8% of 4811:09
- 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

11m 27s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:17
- Percent of Change0:18
- Amount of Change/ Original Amount0:26
- Finding a Percent of Increase1:04
- Example: Find the Percent of Increase1:06
- Converting Units2:56
- Example: Converting Units and Percent Increase3:00
- Finding a Percent of Decrease5:08
- Example: Find the Percent of Decrease5:09
- Extra Example 1: Find the Percent of Increase6:32
- Extra Example 2: Find the Percent of Decrease7:30
- Extra Example 3: Find the Percent of Increase8:28
- Extra Example 4: Find the Percent of Decrease10:23

12m 55s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:22
- Markup0:23
- Selling Price0:28
- Formula of Markup0:32
- Formula for Discount1:06
- Finding a Percent of Markup1:16
- Example: Find the Percent of Markup1:19
- Finding a Percent of Discount3:19
- Example: Find the Percent of Discount3:21
- Finding a Sale Price5:03
- Example: Find the Sale Price of the Stereo System5:10
- Extra Example 1: Find the Percent of Markup6:39
- Extra Example 2: Find the Percent of Discount8:57
- Extra Example 3: Find the Percent of Discount9:52
- Extra Example 4: Find the Percent of Discount10:44

15m 13s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:17
- Coordinate Plane0:23
- y-axis0:29
- x-axis0:33
- Quadrants0:37
- More Vocabulary0:49
- Origin0:50
- Ordered Pair0:53
- x-coordinate1:00
- y-coordinate1:08
- Labeling Vocabulary1:24
- Example: Label the Vocabulary1:25
- Graphing Points on a Coordinate Plane3:08
- Example: Graph and Label the Locations3:12
- Quadrants6:18
- Example: Name the Quadrants of Each Ordered Pair6:23
- Extra Example 1: Draw and Label10:18
- Extra Example 2: Graph the Ordered Pair11:20
- Extra Example 3: Graph the Ordered Pair12:42
- Extra Example 4: Name the Quadrants of Each Ordered Pair13:32

18m 36s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:18
- x-coordinate0:21
- y-coordinate0:28
- Pythagorean Theorem0:34
- Finding Lengths of Line Segments1:02
- Example: Find the Length of the Horizontal Line Segment1:05
- Finding Lengths of Line Segments3:50
- Example: Find the Length of the Vertical Line Segment3:54
- Finding Distance in the Coordinate Plane5:59
- Example: Find the Length of the Hypotenuse6:02
- Extra Example 1: Find the Distance Between Two Points7:36
- Extra Example 2: Find the Length of the Line Segment10:13
- Extra Example 3: Find the Length of the Line Segment14:28
- Extra Example 4: How Far is Your School from the Arcade?16:02

14m 29s

- Intro0:00
- What You'll Learn and Why0:04
- Topics Overview0:05
- Vocabulary0:24
- Function0:25
- Function Rule0:51
- Evaluating a Function Rule0:59
- Example: Table of Input and Output1:00
- Using Function Notation2:56
- Example: Write the Equation and Evaluate the Cost2:59
- Writing Functions4:40
- Example: Writing Function4:41
- Extra Example 1: Complete the Table6:02
- Extra Example 2: Complete the Table and Find the Function7:38
- Extra Example 3: Function Notation9:39
- Extra Example 4: Write a Function and Find the Total Cost11:49

16m 2s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:21
- Solution0:22
- Linear Equation0:29
- Linear Function0:44
- Making a Graph from a Table1:05
- Example: Total Savings in Dollars1:08
- Graphing a Linear Function3:03
- Example: Graph the Linear Function3:07
- Extra Example 1: How Much Cereal is Left?5:42
- Extra Example 2: Graph the Value7:45
- Extra Example 3: Graph the Linear Function10:17
- Extra Example 4: Graph the Linear Function12:28

17m 53s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Slope Definition 10:18
- Slope Definition 20:40
- Slope1:20
- Positive Slope1:32
- Negative Slope1:39
- Slope of 02:10
- Undefined Slope2:25
- Finding the Slope of a Line3:57
- Example: Using Rise/Run to Find Slope3:58
- Finding the Slope of a Line6:01
- Example: Using Coordinates to Find Slope6:02
- Finding Slope of a Line With Given Coordinates9:00
- Example: Slope of (4,1) and (3, -2)9:01
- Extra Example 1: Find the Slope of the Line10:17
- Extra Example 2: Find the Slope of the Line12:19
- Extra Example 3: Find the Slope of the Line14:54
- Extra Example 4: Find the Slope of the Line16:35

13m 50s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:33
- Direct Variation0:34
- Identifying a Direct Variation0:47
- Steps in Identifying a Direct Variation0:56
- Slope and Direct Variation3:01
- Example: Slope and Direct Variation3:05
- Extra Example 1: Direct Variation6:16
- Extra Example 2: Direct Variation7:14
- Extra Example 3: Graphing Direct Variation8:10
- Extra Example 4: Slope and Direct Variation11:23

17m 32s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Inequality0:18
- System of Inequalities1:31
- Solution of an Inequality1:50
- Writing an Inequality2:10
- Example: Price p is More than $62:20
- Writing an Inequality3:53
- Example: Wage w is at Least $8.253:54
- Writing a System of Inequalities5:24
- Example: System of Inequalities for Wind Speed5:32
- Writing a System of Inequalities9:03
- Example: Price of a Room in Las Vegas9:04
- Identifying Solutions of an Inequality10:33
- Example: Driver's Permit10:37
- Extra Example 1: Writing Inequalities12:03
- Extra Example 2: Writing a System of Inequalities13:24
- Extra Example 3: Writing Inequalities14:51
- Extra Example 4: Using Inequality to Solve Word Problem15:31

9m 16s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:20
- Addition Property of Equality0:31
- Subtraction Property of Equality0:43
- Example: x > 70:57
- Solving an Inequality by Adding1:33
- Example: Solve x - 8 = 101:37
- Example: Solve x - 8 < 102:05
- Solving an Inequality by Adding2:21
- Example: 2 ≤ t - 52:22
- Example: a - 8 > 152:59
- Solving an Inequality by Subtracting3:14
- Example: How Many Students can Board the Bus?3:22
- Solving an Inequality by Subtracting4:13
- Example: How Many More Tickets can be Sold?4:14
- Extra Example 1: Solve the Inequality5:16
- Extra Example 2: Solve 8 ≥ 3 + m5:52
- Extra Example 3: MP3 Player6:29
- Extra Example 4: Write and Solve an Inequality7:34

12m 15s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:22
- Division Property of Inequality0:23
- Example: 3x > 60:37
- Dividing by a Positive Number1:08
- Example: Hotel Elevator1:11
- Dividing by a Negative Number2:29
- Example: Solve -6x ≥ -182:32
- Example: Suppose x = 23:13
- Dividing by a Negative Number4:58
- Example: Solve -3t ≥ 515:05
- Example: Solve -8m < -565:24
- Extra Example 1: Photo Album5:49
- Extra Example 2: Banquet8:05
- Extra Example 3: Solve -0.5x > 189:24
- Extra Example 4: How Many Crates can the Crane Lift?10:30

14m 33s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:17
- Multiplication Property of Inequality0:18
- Multiplying by a Positive Number1:25
- Example: Write and Solve an Inequality1:28
- Multiplying by a Positive Number3:38
- Example: Write and Solve an Inequality3:39
- Multiplying by a Negative Number5:42
- Example: Solve x/-4 > 285:45
- Example: Solve (-1/2)y < -86:10
- Example: t/-7 < 56:42
- Extra Example 1: Bowling League7:12
- Extra Example 2: Street Performers8:27
- Extra Example 3: Write and Solve the Inequality9:52
- Extra Example 4: Solve and Graph the System of Inequalities11:26

14m 15s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:15
- Inequality0:16
- Properties of Inequality0:27
- Solving Two-Step Inequalities0:37
- Example: Solve -2x - 8 > -140:41
- Example: Solve (x/4) - 7 > 251:40
- Example: Solve -5y + 9 ≤ 542:12
- Writing Two-Step Inequalities3:16
- Example: How Many Pairs of Socks?3:21
- Writing Two-Step Inequalities5:49
- Example: How Many Folders?5:53
- Extra Example 1: Solve 15 < -3 ( x + 1 )7:32
- Extra Example 2: Solve the Inequalities8:43
- Extra Example 3: Muffin10:37
- Extra Example 4: Birthday Party11:51

12m 7s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:26
- Exponent0:29
- Power0:44
- Multiplying Powers with the Same Base1:04
- Example: Multiplying Powers with the Same Base1:07
- Multiplying Expressions with Exponents2:25
- Examples2:26
- Dividing Powers with the Same Base3:24
- Example: Dividing Powers with the Same Base3:25
- Dividing Expression with Exponents3:59
- Example: How Long Sunlight Takes to Reach the Comet4:02
- Dividing Expression with Exponents6:44
- Example: How Long Sunlight Takes to Reach Earth6:45
- Extra Example 1: Multiplying Expressions with Exponents8:22
- Extra Example 2: Dividing Expression with Exponents8:46
- Extra Example 3: How Long Sunlight Takes to Reach Saturn9:12
- Extra Example 4: Sun's Diameter and Earth's Diameter10:34

11m 58s

- Intro0:00
- What You'll Learn and Why0:04
- Topics Overview0:05
- Vocabulary0:15
- Exponent0:18
- Power0:34
- Raising a Power to a Power0:44
- Example: Raising a Power to a Power0:47
- Raising a Power to a Power2:38
- More Examples2:42
- Raising a Product to a Power3:00
- Example: Raising a Product to a Power3:01
- Raising a Product to a Power4:00
- Example: Surface Area of a Plant Cell4:12
- Example: Surface Area of the Moon6:15
- Extra Example 1: Raising Power to a Power8:08
- Extra Example 2: Complete the Inequality Statement8:22
- Extra Example 3: Find the Area of a Square8:51
- Extra Example 4: Find the Area of a Circle10:28

9m 39s

- Intro0:00
- What You'll Learn and Why0:05
- Topics Overview0:06
- Vocabulary0:17
- Square Root0:21
- Roots1:13
- The Root Symbol2:10
- Root Symbols2:11
- Finding Roots of a Number2:41
- Examples2:42
- Simplifying Expressions with Roots4:41
- Example: Simplify the Expression4:42
- Simplifying Expressions with Roots5:42
- Example: Simplify the Expression5:43
- Extra Example 1: Finding Roots of a Number6:36
- Extra Example 2: Simplifying Expressions with Roots7:11
- Extra Example 3: Simplifying Expressions with Roots7:36
- Extra Example 4: Simplifying Expressions with Roots8:34

12m 43s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:23
- Term0:28
- Like Terms0:35
- Combining Like Terms1:18
- Example: 2y + y - 15y1:20
- Example: -x - 5x2:16
- Writing and Simplifying Expressions2:57
- Example: Total Cost of Drinks2:58
- Writing and Simplifying Expressions4:48
- Example: Total Cost of Apples4:49
- Distributing and Simplifying5:42
- Simplify: 4x - 2( x + 6 )5:46
- Simplify: 3( 2y + 2 ) - 4y6:57
- Extra Example 1: Simplify the Expression7:52
- Extra Example 2: Distributing and Simplifying8:18
- Extra Example 3: Writing and Simplifying Expressions9:35
- Extra Example 4: Distributing and Simplifying10:50

18m 35s

- Intro0:00
- What You'll Learn and Why0:06
- Topics Overview0:07
- Vocabulary0:17
- Like Terms0:21
- Distributive Property0:49
- Simplifying Before Solving an Equation1:37
- Example: 8x + 45 - 12x = 91:40
- Example: -15 = 6b + 12 - 3b + 63:25
- Using the Distributive Property4:50
- Example: Haiti Relief Efforts4:51
- Using the Distributive Property7:50
- Example: Amusement Park7:51
- Extra Example 1: Simplify and Solve11:34
- Extra Example 2: Simplify and Solve12:21
- Extra Example 3: Simplify and Solve13:18
- Extra Example 4: Mailing Letters14:53

18m 50s

- Intro0:00
- What You'll Learn and Why0:07
- Topics Overview0:08
- Vocabulary0:26
- Term0:30
- Like Terms0:44
- Variables on Both Sides1:10
- Example: 3x + 24 = 9x1:11
- Example: -7 - 3x = 1 + 5x2:16
- Using the Distributive Property4:01
- Example: Height of Two Plants4:02
- Using the Distributive Property9:01
- Example: Running Laps9:02
- Extra Example 1: Solving Equations with Variables on Both Sides11:59
- Extra Example 2: Solving Equations with Variables on Both Sides12:46
- Extra Example 3: Solving Equations with Variables on Both Sides14:18
- Extra Example 4: Cost of Renting Video15:24

12m 55s

- Intro0:00
- Finding Needed Information1:02
- Ask Yourself1:07
- Example: Finding Needed Information1:25
- Extra Example 1: Finding Needed Information2:36
- Extra Example 2: Finding Needed Information4:10
- Using Mental Math6:10
- Use Mental Math to Eliminate Unreasonable Answers6:16
- Example: Using Mental Math6:47
- Extra Example 1: Simplify Using Mental Math8:54
- Extra Example 2: Mental Math and Total Cost9:36
- Extra Example 3: Account Balance11:15

11m 24s

- Intro0:00
- Working Backward0:06
- Substitute Multiple Choice Answers0:08
- Example: Working Backward0:38
- Extra Example 1: Equivalent Expression2:54
- Extra Example 2: Miles Per Gallon4:13
- Extra Example 3: Miles Per Hour5:14
- Choosing the Process6:12
- Strategies for Choosing the Process6:19
- Example: Dimensions of the Fenced Area6:48
- Extra Example 1: Choosing the Process8:28
- Extra Example 2: Choosing the Process10:01

11m 36s

- Intro0:00
- Eliminating the Answer0:06
- Eliminate Wrong Answers0:07
- Example: Height of a Plant0:49
- Extra Example 1: Distance2:36
- Extra Example 2: Decimal4:11
- Using a Variable4:50
- Variables Represent the Unknown4:51
- Example: Company Logo5:20
- Extra Example 1: Road Trip6:31
- Extra Example 2: Proportion9:03

20m 13s

- Intro0:00
- Eliminating the Answer0:06
- Eliminate Answers and Educated Guess0:07
- Example: Election0:28
- Extra Example 1: Football Kicker2:42
- Extra Example 2: Percent4:09
- Answering the Question Asked6:19
- Answer the Question Correctly6:20
- Example: Inequality6:43
- Extra Example 1: Cost of Cheese8:12
- Extra Example 2: Inequality9:40
- Drawing a Diagram11:35
- Diagrams11:36
- Example: Drawing a Diagram to Show Distance12:03
- Extra Example 1: Drawing a Diagram to Show Distance15:22
- Extra Example 2: Height17:48

For more information, please see full course syllabus of Pre Algebra

1 answer

Last reply by: SIMON XENITELLIS

Thu Jul 4, 2019 4:24 PM

Post by Genevieve Carisse on August 17, 2017

How do you know which fraction goes first/second? I flipped the 24/1 and got 19/96 as my answer.

0 answers

Post by Aaron Dhaemers on February 25, 2013

Department stores sometimes advertise a clearance sale: â€œTake Â½ of Â½â€â€¦ In practice, this means a 75% discount off the original price. But mathematically, half of half works out to 1. What's up with this?

1 answer

Last reply by: Professor Fung

Mon Sep 24, 2012 4:53 AM

Post by Michael Trow on September 22, 2012

75 / 2.25 is 33.3 recurring so it should be 34, right?

1 answer

Last reply by: mickaole walden

Sat Mar 9, 2013 12:18 PM

Post by Michael Trow on September 22, 2012

31 multiplied by 2.25 = 69.75 not 75 !

0 answers

Post by Samvel Karapetyan on May 20, 2012

31 stakes to build the fence!