Chapter 2: Integers and Exponents Regular Math. Section 2.1: Adding Integers Integers are the set of whole numbers, including 0, and their opposites

Chapter 2: Integers and Chapter 2: Integers and ExponentsExponents

Regular MathRegular Math

Section 2.1: Adding IntegersSection 2.1: Adding Integers

IntegersIntegers are the set of whole numbers, are the set of whole numbers, including 0, and their including 0, and their oppositesopposites. .

The The absolute valueabsolute value of a number is its distance of a number is its distance from 0.from 0.

Example 1: Using a Number Line to Example 1: Using a Number Line to Add IntegersAdd Integers

4 + (-6)4 + (-6)

Try this one on your Try this one on your own…own… (-6) + 2(-6) + 2

-4-4

Example 2: Using Absolute Value to Example 2: Using Absolute Value to Add IntegersAdd Integers

Add…Add… -3 + (-5)-3 + (-5)

4 + (-7)4 + (-7)

-3 + 6-3 + 6

Try these on your Try these on your own…own… 1 + (-2)1 + (-2)

-1-1

(-8) + 5(-8) + 5 -3-3

(-2) + (-4)(-2) + (-4) -6-6

7 + (-1)7 + (-1) 66

Example 3: Evaluating Expressions Example 3: Evaluating Expressions with Integerswith Integers

Evaluate b + 12 for b = -5Evaluate b + 12 for b = -5 -5 + 12-5 + 12 77

Try this one on your own…Try this one on your own… Evaluate c + 4 for c = -8Evaluate c + 4 for c = -8

-8 + 4-8 + 4 -4-4

Example 4: Health ApplicationExample 4: Health Application

Monday MorningMonday Morning

CaloriesCaloriesOatmeal 145Oatmeal 145

Toast with Jam 62Toast with Jam 62

8 fl oz juice 1118 fl oz juice 111

Calories BurnedCalories BurnedWalked six laps 110Walked six laps 110

Swam six laps 40Swam six laps 40

Katrina wants to check Katrina wants to check her calorie count after her calorie count after breakfast and exercise. breakfast and exercise. Use information from Use information from the journal entry to find the journal entry to find her total.her total.

145 + 62 + 111 – 110 – 40145 + 62 + 111 – 110 – 40 168 calories168 calories

Try this one on your own…Try this one on your own…

Katrina opened a bank account. Find her Katrina opened a bank account. Find her account balance after the four transactions, account balance after the four transactions, listed below.listed below. Deposits: $200 and $20Deposits: $200 and $20 Withdrawals: $166 and $38Withdrawals: $166 and $38

200 + 20 -166 – 38 = $16200 + 20 -166 – 38 = $16

Section 2.2: Subtracting IntegersSection 2.2: Subtracting Integers

Example 1: Subtracting IntegersExample 1: Subtracting Integers

-5 – 5-5 – 5

2 – (-4)2 – (-4)

-11 – (-8)-11 – (-8)

Try these on your Try these on your own…own… -7 – 4-7 – 4

-11-11

8 – (-5)8 – (-5) 1313

-6 – (-3) -6 – (-3) -3-3

Example 2: Evaluating Expressions Example 2: Evaluating Expressions with Integerswith Integers

4 – t for t = -34 – t for t = -3 4 – (-3)4 – (-3) 4 + 34 + 3 77

-5 – s for s = -7-5 – s for s = -7 -5 – (-7)-5 – (-7) -5 + 7-5 + 7 22

-1 – x for x = 8-1 – x for x = 8 -1 – 8-1 – 8 - 1 + (-8)- 1 + (-8) -9-9

Try these on your own…Try these on your own… 8 – j for j = -68 – j for j = -6

1414

-9 – y for y = -4-9 – y for y = -4 -5-5

n – 6 for n = -2n – 6 for n = -2 -8-8

Example 3: Architecture ApplicationExample 3: Architecture Application

The roller coaster Desperado has a maximum The roller coaster Desperado has a maximum height of 209 feet and maximum drop of 225 height of 209 feet and maximum drop of 225 feet. How far underground does the roller feet. How far underground does the roller coaster go?coaster go?


The top of Sears Tower, in Chicago, is 1454 The top of Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level feet above street level, while the lowest level is 43 feet below street level. How far is it from is 43 feet below street level. How far is it from the lowest level to the top?the lowest level to the top? 1454 – (-43)1454 – (-43) 1497 feet1497 feet

Section 2.3: Multiplying and Section 2.3: Multiplying and Dividing IntegersDividing Integers

Example 1: Multiplying and Example 1: Multiplying and Dividing IntegersDividing Integers

Multiply or Divide.Multiply or Divide. 6(-7)6(-7)

-42-42

-45 / 9-45 / 9 -5-5

-12 (-4)-12 (-4) 4848

18 / -618 / -6 -3-3

Try these on your Try these on your own…own… -6(4)-6(4)

-24-24

-8(-5)-8(-5) 4040

-18/2-18/2 -9-9

-25/-5-25/-5 55

Example 2: Using the Order of Example 2: Using the Order of Operations with IntegersOperations with Integers

Simplify…Simplify… -2(3 - 9)-2(3 - 9)

4(-7 - 2)4(-7 - 2)

-3(16 - 8)-3(16 - 8)

Try these on your own…Try these on your own…

Simplify…Simplify… 3(-6 - 12)3(-6 - 12)

-54-54 -5(-5 + 2)-5(-5 + 2)

1515 -2(14 – 5)-2(14 – 5)

-18-18

Example 3: Plotting Integer Example 3: Plotting Integer Solutions of Equations.Solutions of Equations.

x -2x – 1 y (x,y)

-2 -2(-2) – 1 3 (-2,3)

-1 -2(-1) – 1 1 (-1,1)

0 -2(0) – 1 -1 (0,-1)

1 -2(1) – 1 -3 (1, -3)

2 -2(2) - 1 -5 (2, -5)

Complete a table of Complete a table of solutions for y = -2x – 1 solutions for y = -2x – 1 for x = -2, -1, 0, 1, 2. for x = -2, -1, 0, 1, 2. Plot the points on a Plot the points on a coordinate plane.coordinate plane.


Complete a table of Complete a table of solutions for y =3x – 1 solutions for y =3x – 1 for x = -2, -1, 0, 1, and for x = -2, -1, 0, 1, and 2. Plot the points on a 2. Plot the points on a coordinate grid.coordinate grid.

x 3x-1 y (x,y)

-2 3(-2) – 1 -7 (-2,-7)

-1 3(-1) – 1 -4 (-1,-4)

0 3(0) – 1 -1 (0,-1)

1 3(1) – 1 2 (1,2)

2 3(2) - 1 5 (2,5)

Section 2.4: Solving Equations Section 2.4: Solving Equations Containing IntegersContaining Integers

Example 1: Adding and Subtracting to Solve EquationsExample 1: Adding and Subtracting to Solve Equations Solve…Solve…

y + 8 = 6y + 8 = 6

-5 + t = -25-5 + t = -25

x = -7 + 13x = -7 + 13


x – 3 = -6x – 3 = -6 x = -3x = -3

-5 + r = 9-5 + r = 9 r = 14r = 14

-6 + 8 = n-6 + 8 = n n = 2n = 2

Z + 6 = -3Z + 6 = -3 z = -9z = -9

Example 2: Multiplying and Example 2: Multiplying and Dividing to Solve EquationsDividing to Solve Equations

Try these on your Try these on your own…own… -5x = 35-5x = 35

x = -7x = -7

z / -4 = 5z / -4 = 5 z = -20z = -20

Solve…Solve… k / -7 = -1k / -7 = -1

-51 = 17b-51 = 17b

Example 3: Problem Solving Example 3: Problem Solving ApplicationApplication

Net force is the sum of all forces acting on an Net force is the sum of all forces acting on an object. Expressed in newtons (N), it tells you object. Expressed in newtons (N), it tells you in which direction and how quickly the object in which direction and how quickly the object will move. If two dogs are playing tug-of-war, will move. If two dogs are playing tug-of-war, and the dog on the right pulls with a force of and the dog on the right pulls with a force of 12 N, what force is the dog on the left exerting 12 N, what force is the dog on the left exerting on the rope if the new force is 2N?on the rope if the new force is 2N?


Sarah heard on the morning news that the Sarah heard on the morning news that the temperature had dropped 26 degrees since temperature had dropped 26 degrees since midnight. In the morning, the temperature was midnight. In the morning, the temperature was -8 degrees. What was the temperature at -8 degrees. What was the temperature at midnight?midnight? -8 = x – 26-8 = x – 26 x = 18 degreesx = 18 degrees

Section 2.5: Solving Inequalities Section 2.5: Solving Inequalities Containing IntegersContaining Integers

Solve and Graph…Solve and Graph… w + 3 < -1w + 3 < -1

n – 6 > -5n – 6 > -5

Try these on your Try these on your own…own… k + 3 > -2k + 3 > -2

k > -5k > -5

r – 9 > 12r – 9 > 12 r > 21r > 21

u – 5 < 3u – 5 < 3 u < 8u < 8

c + 6 < 2c + 6 < 2 c < -4c < -4

Example 2: Multiplying and Example 2: Multiplying and Dividing to Solve InequalitiesDividing to Solve Inequalities

Solve and Graph…Solve and Graph… Try these on your Try these on your own…own… Solve and Graph.Solve and Graph.

217

52

122

m

y

d

31

25

153

z

t

y

Section 2.6: ExponentsSection 2.6: Exponents

PowerPower

Exponential FormExponential Form

BaseBase

ExponentExponent

Example 1: Writing ExponentsExample 1: Writing Exponents

Write in exponential Write in exponential form.form. 3x3x3x3x3x33x3x3x3x3x3

(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)

NxNxNxNxNNxNxNxNxN

1212

Try these on your Try these on your own… own… 4x4x4x44x4x4x4

DxDxDxDxDDxDxDxDxD

(-6)(-6)(-6)(-6)(-6)(-6)

5x55x5

Example 2: Evaluating PowersExample 2: Evaluating Powers

Evaluate…Evaluate…


3

2

6

)5(

)8(

2

8

4

5

5

2

)4(

)3(

3

Example 3: Simplifying Expressions Example 3: Simplifying Expressions Containing ExponentsContaining Exponents

Try this one on your Try this one on your own…own…

Simplify…Simplify…

)23(250 3)4(6)32( 25

Example 4: Geometry ApplicationExample 4: Geometry Application

The number of diagonals of an n-sided figure The number of diagonals of an n-sided figure is is . Use the formula to find the . Use the formula to find the number of diagonals for a 5-sided figure.number of diagonals for a 5-sided figure.

)3(2

1 2 nn


Use the formulaUse the formula to find the number of to find the number of diagonals in a 7-sided figure.diagonals in a 7-sided figure.

)3(2

1 2 nn

Section 2.7: Properties of ExponentsSection 2.7: Properties of Exponents

Example 1: Multiplying Powers with Example 1: Multiplying Powers with the Same Basethe Same Base

Multiply. Write the Multiply. Write the product as one power.product as one power.

Try these on your Try these on your own…own…

44

1010

7

25

46

1616

33

aa

44

5

75

36

2424

22

66

nn

Example 2: Dividing Powers with Example 2: Dividing Powers with the Same Basethe Same Base

Divide. Write the Divide. Write the quotient as one power.quotient as one power.


5

8

3

9

100

100

y

x

9

10

3

5

7

7

x

x

Example 3: Physical Science Example 3: Physical Science ApplicationApplication

There are aboutThere are about molecules in a cubic meter of molecules in a cubic meter of air at sea level, but onlyair at sea level, but only molecules at a molecules at a high altitude (33km). How many times more high altitude (33km). How many times more molecules are there at sea level than at 33 km?molecules are there at sea level than at 33 km?

2510

2310


A light-year, or the distance light travels in A light-year, or the distance light travels in one year, is almostone year, is almost centimeters. To centimeters. To convert this number to kilometers, you must convert this number to kilometers, you must divide bydivide by . How many kilometers is a light . How many kilometers is a light year?year?

1810

510

153

18

1010

10

Section 2.8: Look for a Pattern in Section 2.8: Look for a Pattern in Integer ExponentsInteger Exponents

Example 1: Using a Pattern to Evaluate Example 1: Using a Pattern to Evaluate Negative ExponentsNegative Exponents Evaluate the powers of 10.Evaluate the powers of 10.

5

4

3

10

10

10


Evaluate the powers of 10.Evaluate the powers of 10.

6

1

2

10

10

10

Example 2: Evaluating Negative Example 2: Evaluating Negative NumbersNumbers

Evaluate…Evaluate… Try this one on your Try this one on your own…own…3)2(

3

3

)10(

5

Example 3: Evaluating Products and Example 3: Evaluating Products and Quotients of Negative ExponentsQuotients of Negative Exponents


Evaluate…Evaluate…

7

4

33

2

2

1010

54

8

5

35

33

6

6

22

Section 2.9: Scientific NotationSection 2.9: Scientific Notation

Scientific Notation Scientific Notation is a method of writing is a method of writing very large or very small numbers by using very large or very small numbers by using powers of 10.powers of 10.

Example 1: Translating Scientific Example 1: Translating Scientific Notation to Standard NotationNotation to Standard Notation

Write each number in Write each number in standard notation.standard notation.


6

4

7

108.5

1035.1

1064.2

4

3

5

1001.2

107.2

1035.1

Example 2: Translating Standard Example 2: Translating Standard Notation to Scientific NotationNotation to Scientific Notation

Write 0.000002 in Write 0.000002 in scientific notation.scientific notation.

Try this one on your Try this one on your own…own… Write 0.00709 in Write 0.00709 in

scientific notation.scientific notation.

31009.7

Example 3: Money ApplicationExample 3: Money Application

Suppose you have a million dollars in pennies. Suppose you have a million dollars in pennies. A penny is 1.55 mm thick. How tall would a A penny is 1.55 mm thick. How tall would a stack of all your pennies by? Write your stack of all your pennies by? Write your answer in scientific notation?answer in scientific notation?


A pencil is 18.7 cm long. If you were to lay A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to end, how many 10,000 pencils end to end, how many millimeters long would they be? Write the millimeters long would they be? Write the answer in scientific notation.answer in scientific notation.

51087.1

000,107.18

Documents

Chapter 2: Integers and Exponents Regular Math. Section 2.1: Adding Integers Integers are the set of whole numbers, including 0, and their opposites