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

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Chapter 2: Integers and Exponents Regular Math

Section 2.1: Adding Integers Integers are the set of whole numbers, including 0, and their opposites. Integers are the set of whole numbers, including 0, and their opposites. The absolute value of a number is its distance from 0. The absolute value of a number is its distance from 0.

Example 1: Using a Number Line to Add Integers 4 + (-6) Try this one on your own… Try this one on your own… (-6) + 2 -4

Example 2: Using Absolute Value to Add Integers Add… Add… -3 + (-5) -3 + (-5) 4 + (-7) 4 + (-7) -3 + 6 -3 + 6 Try these on your own… Try these on your own… 1 + (-2) (-8) + 5 -3 (-2) + (-4) -6 7 + (-1) 6

Example 3: Evaluating Expressions with Integers Evaluate b + 12 for b = -5 Evaluate b + 12 for b = -5 -5 + 12 -5 + 12 7 Try this one on your own… Try this one on your own… Evaluate c + 4 for c = -8 -8 + 4 -4

Example 4: Health Application Monday Morning Calories Oatmeal 145 Toast with Jam 62 8 fl oz juice 111 Calories Burned Walked six laps 110 Swam six laps 40 Katrina wants to check her calorie count after breakfast and exercise. Use information from the journal entry to find her total. Katrina wants to check her calorie count after breakfast and exercise. Use information from the journal entry to find her total. 145 + 62 + 111 – 110 – 40 168 calories

Try this one on your own… Katrina opened a bank account. Find her account balance after the four transactions, listed below. Katrina opened a bank account. Find her account balance after the four transactions, listed below. Deposits: \$200 and \$20 Deposits: \$200 and \$20 Withdrawals: \$166 and \$38 Withdrawals: \$166 and \$38 200 + 20 -166 – 38 = \$16 200 + 20 -166 – 38 = \$16

Section 2.2: Subtracting Integers

Example 1: Subtracting Integers -5 – 5 -5 – 5 2 – (-4) 2 – (-4) -11 – (-8) -11 – (-8) Try these on your own… Try these on your own… -7 – 4 -11 8 – (-5) 13 -6 – (-3) -3

Example 2: Evaluating Expressions with Integers 4 – t for t = -3 4 – t for t = -3 4 – (-3) 4 – (-3) 4 + 3 4 + 3 7 -5 – s for s = -7 -5 – s for s = -7 -5 – (-7) -5 – (-7) -5 + 7 -5 + 7 2 -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 = -6 14 -9 – y for y = -4 -5 n – 6 for n = -2 -8

Example 3: Architecture Application The roller coaster Desperado has a maximum height of 209 feet and maximum drop of 225 feet. How far underground does the roller coaster go? The roller coaster Desperado has a maximum height of 209 feet and maximum drop of 225 feet. How far underground does the roller coaster go?

Try this one on your own… The top of Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? The top of Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? 1454 – (-43) 1454 – (-43) 1497 feet 1497 feet

Section 2.3: Multiplying and Dividing Integers

Example 1: Multiplying and Dividing Integers Multiply or Divide. Multiply or Divide. 6(-7) 6(-7) -42 -42 -45 / 9 -45 / 9 -5 -5 -12 (-4) -12 (-4) 48 48 18 / -6 18 / -6 -3 -3 Try these on your own… Try these on your own… -6(4) -24 -8(-5) 40 -18/2 -9 -25/-5 5

Example 2: Using the Order of Operations 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… Simplify… Simplify… 3(-6 - 12) 3(-6 - 12) -54 -54 -5(-5 + 2) -5(-5 + 2) 15 15 -2(14 – 5) -2(14 – 5) -18 -18

Example 3: Plotting Integer Solutions of Equations. x-2x – 1y(x,y) -2-2(-2) – 13(-2,3) -2(-1) – 11(-1,1) 0-2(0) – 1(0,-1) 1-2(1) – 1-3(1, -3) 2-2(2) - 1-5(2, -5) Complete a table of solutions for y = -2x – 1 for x = -2, -1, 0, 1, 2. Plot the points on a coordinate plane. Complete a table of solutions for y = -2x – 1 for x = -2, -1, 0, 1, 2. Plot the points on a coordinate plane.

Try this one on your own… Complete a table of solutions for y =3x – 1 for x = -2, -1, 0, 1, and 2. Plot the points on a coordinate grid. Complete a table of solutions for y =3x – 1 for x = -2, -1, 0, 1, and 2. Plot the points on a coordinate grid. x3x-1y(x,y) -23(-2) – 1-7(-2,-7) 3(-1) – 1-4(-1,-4) 03(0) – 1(0,-1) 13(1) – 12(1,2) 23(2) - 15(2,5)

Section 2.4: Solving Equations Containing Integers Example 1: Adding and Subtracting to Solve Equations Example 1: Adding and Subtracting to Solve Equations Solve… Solve… y + 8 = 6 y + 8 = 6 -5 + t = -25 -5 + t = -25 x = -7 + 13 x = -7 + 13

Try these on your own… x – 3 = -6 x – 3 = -6 x = -3 x = -3 -5 + r = 9 -5 + r = 9 r = 14 r = 14 -6 + 8 = n -6 + 8 = n n = 2 n = 2 Z + 6 = -3 Z + 6 = -3 z = -9 z = -9

Example 2: Multiplying and Dividing to Solve Equations Try these on your own… Try these on your own… -5x = 35 -5x = 35 x = -7 x = -7 z / -4 = 5 z / -4 = 5 z = -20 z = -20 Solve… Solve… k / -7 = -1 -51 = 17b

Example 3: Problem Solving Application Net force is the sum of all forces acting on an object. Expressed in newtons (N), it tells you in which direction and how quickly the object will move. If two dogs are playing tug-of-war, and the dog on the right pulls with a force of 12 N, what force is the dog on the left exerting on the rope if the new force is 2N? Net force is the sum of all forces acting on an object. Expressed in newtons (N), it tells you in which direction and how quickly the object will move. If two dogs are playing tug-of-war, and the dog on the right pulls with a force of 12 N, what force is the dog on the left exerting on the rope if the new force is 2N?

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

Section 2.5: Solving Inequalities Containing Integers Solve and Graph… Solve and Graph… w + 3 < -1 w + 3 < -1 n – 6 > -5 n – 6 > -5 Try these on your own… Try these on your own… k + 3 > -2 k > -5 r – 9 > 12 r > 21 u – 5 < 3 u < 8 c + 6 < 2 c < -4

Example 2: Multiplying and Dividing to Solve Inequalities Solve and Graph… Solve and Graph… Try these on your own… Try these on your own… Solve and Graph.

Section 2.6: Exponents Power Power Exponential Form Exponential Form Base Base Exponent Exponent

Example 1: Writing Exponents Write in exponential form. Write in exponential form. 3x3x3x3x3x3 3x3x3x3x3x3 (-2)(-2)(-2)(-2) (-2)(-2)(-2)(-2) NxNxNxNxN NxNxNxNxN 12 12 Try these on your own… Try these on your own… 4x4x4x4 DxDxDxDxD (-6)(-6)(-6) 5x5

Example 2: Evaluating Powers Evaluate… Evaluate… Try these on your own… Try these on your own…

Example 3: Simplifying Expressions Containing Exponents Try this one on your own… Try this one on your own… Simplify… Simplify…

Example 4: Geometry Application The number of diagonals of an n-sided figure is. Use the formula to find the number of diagonals for a 5-sided figure. The number of diagonals of an n-sided figure is. Use the formula to find the number of diagonals for a 5-sided figure.

Try this one on your own… Use the formula to find the number of diagonals in a 7-sided figure. Use the formula to find the number of diagonals in a 7-sided figure.

Section 2.7: Properties of Exponents

Example 1: Multiplying Powers with the Same Base Multiply. Write the product as one power. Multiply. Write the product as one power. Try these on your own… Try these on your own…

Example 2: Dividing Powers with the Same Base Divide. Write the quotient as one power. Divide. Write the quotient as one power. Try these on your own… Try these on your own…

Example 3: Physical Science Application There are aboutmolecules in a cubic meter of air at sea level, but onlymolecules at a high altitude (33km). How many times more molecules are there at sea level than at 33 km? There are aboutmolecules in a cubic meter of air at sea level, but onlymolecules at a high altitude (33km). How many times more molecules are there at sea level than at 33 km?

Try this one on your own… A light-year, or the distance light travels in one year, is almostcentimeters. To convert this number to kilometers, you must divide by. How many kilometers is a light year? A light-year, or the distance light travels in one year, is almostcentimeters. To convert this number to kilometers, you must divide by. How many kilometers is a light year?

Section 2.8: Look for a Pattern in Integer Exponents Example 1: Using a Pattern to Evaluate Negative Exponents Example 1: Using a Pattern to Evaluate Negative Exponents Evaluate the powers of 10. Evaluate the powers of 10.

Try these on your own… Evaluate the powers of 10. Evaluate the powers of 10.

Example 2: Evaluating Negative Numbers Evaluate… Evaluate… Try this one on your own… Try this one on your own…

Example 3: Evaluating Products and Quotients of Negative Exponents Try these on your own… Try these on your own… Evaluate… Evaluate…

Section 2.9: Scientific Notation Scientific Notation is a method of writing very large or very small numbers by using powers of 10. Scientific Notation is a method of writing very large or very small numbers by using powers of 10.

Example 1: Translating Scientific Notation to Standard Notation Write each number in standard notation. Write each number in standard notation. Try these on your own… Try these on your own…

Example 2: Translating Standard Notation to Scientific Notation Write 0.000002 in scientific notation. Write 0.000002 in scientific notation. Try this one on your own… Try this one on your own… Write 0.00709 in scientific notation.

Example 3: Money Application Suppose you have a million dollars in pennies. A penny is 1.55 mm thick. How tall would a stack of all your pennies by? Write your answer in scientific notation? Suppose you have a million dollars in pennies. A penny is 1.55 mm thick. How tall would a stack of all your pennies by? Write your answer in scientific notation?

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

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