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Multiplying andDividing Integers?6MODULELESSON 6.1ESSENTIAL QUESTIONMultiplying Integers6.3.C, 6.3.DHow can you use multiplicationand division of integers tosolve real-world problems?LESSON 6.2Dividing Integers6.3.C, 6.3.DLESSON 6.3Applying IntegerOperations Houghton Mifflin Harcourt Publishing Company Image Credits: wusuowei/Fotolia6.3.DReal-World Videomy.hrw.commy.hrw.comThe giant panda is an endangered animal. Forsome endangered species, the population hasmade a steady decline. This can be represented bymultiplying integers with different signs.my.hrw.comMath On the SpotAnimated MathPersonal Math TrainerGo digital with yourwrite-in studentedition, accessible onany device.Scan with your smartphone to jump directlyto the online edition,video tutor, and more.Interactively explorekey concepts to seehow math works.Get immediatefeedback and help asyou work throughpractice sets.143
Are YOU Ready?PersonalMath TrainerComplete these exercises to review skills you will needfor this chapter.Multiplication FactsEXAMPLES7 9 7 9 6312 10 12 10 120my.hrw.comOnlineAssessment andInterventionUse patterns. When you multiply 9 by a number 1through 9, the digits of the product add up to 9.6 3 9Products of 10 end in 0.Multiply.1. 9 32. 7 103. 9 84. 15 105. 6 96. 10 237. 9 98. 10 20Division FactsEXAMPLE48 6 48 6 8Think: 6 times what number equals 48?6 8 48So, 48 6 89. 54 910. 42 611. 24 312. 64 813. 90 1014. 56 715. 81 916. 110 11Order of OperationsEXAMPLE32 - 2(10 - 7)32 - 2(3)32 - 626To evaluate, first operate within parentheses.Then multiply and divide from left to right.Finally add and subtract from left to right.Evaluate each expression.144Unit 217. 12 8 218. 15 -(4 3) 219. 18 -(8 - 5)220. 6 7 3 - 521. 9 (22 3)2 222. 6 5 - 4 3 2 Houghton Mifflin Harcourt Publishing CompanyDivide.
Reading Start-UpVisualize VocabularyUse the words to complete the chart. You may put morethan one word in each box. , or put into equal groups , or repeated additionMultiplying and Dividing Integers32, -32VocabularyReview Words divide (dividir) dividend (dividendo) divisor (divisor) integers (enteros) multiply (multiplicar) negative number (númeronegativo)operation (operación) opposites (opuestos) positive number (númeropositivo)product (producto) quotient (cociente)32 4 8Understand VocabularyComplete the sentences using the review words.1. Ais a number that is less than 0. Ais a number that is greater than 0. Houghton Mifflin Harcourt Publishing Company2. Division problems have three parts. The part you want to divide into groups is called3.the. The number that is divided into another number is calledthe. The answer to a division problem is called the.are all whole numbers and their opposites.Active ReadingDouble-Door Fold Create a double-door fold tohelp you understand the concepts in this module.Label one flap “Multiplying Integers” and the otherflap “Dividing Integers.” As you study each lesson,write important ideas under the appropriate flap.Include information that will help you remember theconcepts later when you look back at your notes.Module 6145
MODULE 6Unpacking the TEKSUnderstanding the TEKS and the vocabulary terms in the TEKSwill help you know exactly what you are expected to learn in thismodule.6.3.DAdd, subtract, multiply, anddivide integers fluently.Key Vocabularyinteger (entero)A member of the set of wholenumbers and their opposites.What It Means to YouYou will use your knowledge of multiplication of whole numbersand addition of negative numbers to multiply integers.UNPACKING EXAMPLE 6.3.DMultiply 4 (-5).4 (-5) -5 (-5) (-5) (-5) -20Multiplication isrepeated addition.The product of 4 and -5 is the same as the negative productof 4 and 5.A positive number times a negative number is negative.Add, subtract, multiply, anddivide integers fluently.Key Vocabularyinteger (entero)A member of the set of wholenumbers and their opposites.What It Means to YouYou will use your knowledge of division of whole numbersand multiplication of integers to divide integers.UNPACKING EXAMPLE 6.3.DThe temperature in Fairbanks, Alaska,dropped over four consecutive hoursfrom 0 F to -44 F. If the temperaturedropped the same amount each hour,how much did the temperature changeeach hour?-444 -11The quotient of -44 and 4 is the sameas the negative quotient of 44 and 4.A negative number divided by a positive number is negative.Visit my.hrw.comto see alltheunpacked.my.hrw.com146Unit 2 Houghton Mifflin Harcourt Publishing Company Image Credits: Carol Falcetta/Flickr/Getty Images6.3.D
LESSON6.1 Multiplying Integers?Number andoperations— 6.3.D Add,subtract, multiply, and divideintegers fluently. Also 6.3.C.ESSENTIAL QUESTIONHow do you multiply integers?6.3.CEXPLORE ACTIVITY 1Multiplying Integers Usinga Number LineYou can use a number line to see what happens when you multiply a positivenumber by a negative number.A Henry made three withdrawals of 2 each from his savings account.What was the change in his balance?Find 3(-2).To graph -2, you would start at 0 and move) (3(-2) means () ().To graph 3(-2), start at 0 and move2 units to the leftThe result is (-2) (-2) (-2)times.-8 -7 -6 -5 -4 -3 -2 -1.The change in Henry’s balance was Houghton Mifflin Harcourt Publishing Companyunits to the left.0.B Lisa plays a video game in which she loses points. She loses3 points 2 times. What is her score?Find 2(-3).2( 3) means () (Show this on the number line.Lisa has a score of.).-8 -7 -6 -5 -4 -3 -2 -10Reflect1.What do you notice about the product of two integers with differentsigns?Lesson 6.1147
EXPLORE ACTIVITY 26.3.CModeling Integer MultiplicationCounters representing positive and negative numberscan help you understand how to find the product oftwo negative integers. 1 -1Find the product of -3 and -4.Write (-3)(-4) as -3(-4), which means the opposite of 3(-4).STEP 1Use negative counters to model 3(-4).3 groups of -4STEP 2Make the same model using positive counters tofind the opposite of 3(-4).The opposite of3 groups of -4STEP 3Translate the model into a mathematical expression:(-3)(-4) .Reflect2.What do you notice about the sign of the product of two negative integers?3.Make a Conjecture What can you conclude about the sign of theproduct of two integers with the same sign?148Unit 2 Houghton Mifflin Harcourt Publishing CompanyThe product of -3 and -4 is
Multiplying IntegersThe product of two integers with opposite signs is negative. The productof two integers with the same sign is positive. The product of 0 and anyother integer is 0.Math On the Spotmy.hrw.comEXAMPL 1EXAMPLE6.3.DA Multiply: (13)(-3).STEP 1Determine the sign of the product.13 is positive and -3 is negative. Since the numbers haveopposite signs, the product will be negative.STEP 2AnimatedMathmy.hrw.comFind the absolute values of the numbers and multiply them. 13 13 -3 313 3 39STEP 3Assign the correct sign to the product.13(-3) -39The product is -39.B Multiply: (-5)(-8).STEP 1Determine the sign of the product.-5 is negative and -8 is negative. Since the numbers havethe same sign, the product will be positive.STEP 2Find the absolute values of the numbers and multiply them. -5 5 -8 8Math Talk Houghton Mifflin Harcourt Publishing Company5 8 40STEP 3Mathematical ProcessesAssign the correct sign to the product.(-5)(-8) 40The product is 40.C Multiply: (-10)(0).(-10)(0) 0Compare the rules forfinding the product ofa number and zero andfinding the sum of anumber and 0.One of the factors is 0, so the product is 0.YOUR TURNFind each 3)9.8(4)PersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comLesson 6.1149
Guided PracticeFind each product. (Explore Activity 2 and Example 1)1. -1(9)2. 14(-2)3. (-9)(-6)4. (-2)(50)5. (-4)(15)6. -18(0)7. (-7)(-7)8. -15(9)9. (8)(-12)10. -3(-100)11. 0(-153)12. -6(32)13. Flora made 7 withdrawals of 75 each from her bank account. What wasthe overall change in her account? (Example 1)14. A football team lost 5 yards on each of 3 plays. Explain how you could usea number line to find the team’s change in field position after the 3 plays.(Explore Activity 1)15. The temperature dropped 2 F every hour for 6 hours. What was thetotal number of degrees the temperature changed in the 6 hours?(Explore Activity 1)17. A mountain climber climbed down a cliff 50 feet at a time. He did this 5 timesin one day. What was the overall change in his elevation? (Explore Activity 1)?ESSENTIAL QUESTION CHECK-IN18. Explain the process for finding the product of two integers.150Unit 2 Houghton Mifflin Harcourt Publishing Company16. The price of one share of Acme Company declined 5 per day for 4 daysin a row. How much did the price of one share change in total after the4 days? (Explore Activity 1)
NameClassDate6.1 Independent Practice6.3.DPersonalMath Trainermy.hrw.com19. Critique Reasoning Lisa used a numberline to model –2(3). Does her number linemake sense? Explain why or why not. (-3) (-3)-8 -7 -6 -5 -4 -3 -2 -1OnlineAssessment andIntervention22. Adam is scuba diving. He descends 5 feetbelow sea level. He descends the samedistance 4 more times. What is Adam’s finalelevation?023. The price of jeans was reduced 6 per weekfor 7 weeks. By how much did the price ofthe jeans change over the 7 weeks?20. Represent Real-World Problems Mikegot on an elevator and went down 3 floors.He meant to go to a lower level, so hestayed on the elevator and went down3 more floors. How many floors did Mikego down altogether? Houghton Mifflin Harcourt Publishing CompanySolve. Show your work.24. Casey uses some of his savings on battingpractice. The cost of renting a batting cagefor 1 hour is 6. He rents a cage for 9 hoursin each of two months. What is the changein Casey’s savings after two months?21. When Brooke buys lunch at the cafeteria,money is withdrawn from a lunch account.The table shows amounts withdrawn inone week. By how much did the amount inBrooke’s lunch account change by the endof that week?Lunch AccountWeek 1LunchCostBalance 28MondayPizza 4TuesdayFish Tacos 4WednesdaySpaghetti 4ThursdaySandwich 4Chicken 4Friday25. Volunteers at Sam’s school use some ofthe student council’s savings for a specialproject. They buy 7 backpacks for 8 eachand fill each backpack with paper and pensthat cost 5. By how much did the studentcouncil’s savings change because of thisproject?Lesson 6.1151
26. Communicate Mathematical Ideas Describe a real-world situationthat can be represented by the product 8(–20). Then find the product andexplain what the product means in terms of the real-world situation.27. What If? The rules for multiplying two integers can be extended to aproduct of 3 or more integers. Find the following products by using theAssociative Property to multiply 2 numbers at a time.a. 3(3)(–3)b. 3(–3)(–3)c. –3(–3)(–3)d. 3(3)(3)(–3)e. 3(3)(–3)(–3)f.3(–3)(–3)(–3)g. Make a Conjecture Based on your results, complete the followingstatements:When a product of integers has an odd number of negative factors,then the sign of the product is.When a product of integers has an even number of negative factors,then the sign of the product is.FOCUS ON HIGHER ORDER THINKINGWork Area29. Analyze Relationships When is the product of two nonzero integers lessthan or equal to both of the two factors?30. Justify Reasoning The sign of the product of two integers with the samesign is positive. What is the sign of the product of three integers with thesame sign? Explain your thinking.152Unit 2 Houghton Mifflin Harcourt Publishing Company28. Multiple Representations The product of three integers is –3.Determine all of the possible values for the three factors.
LESSON6.2 Dividing Integers?Number andoperations—6.3.D Add,subtract, multiply, and divideintegers fluently. Also 6.3.C.ESSENTIAL QUESTIONHow do you divide integers?6.3.CEXPLORE ACTIVITYA diver needs to descend to a depth of 100 feet. She wants to do it in5 equal descents. How far should she travel in each descent?A Use the number line at the right to find how far the diver should travelin each of the 5 descents.0-10-20-100 ?B To solve this problem, you can set up a division problem:-30-40-50-60C Rewrite the division problem as a multiplication problem.Think: Some number multiplied by 5 equals -100.-70-80 ? -100D Remember the rules for integer multiplication. If the product isnegative, one of the factors must be negative. Sincepositive, the unknown factor must be Houghton Mifflin Harcourt Publishing CompanyE You know that 5 -100-110positive / negative. 100. So, using the rules for integermultiplication you can say that 5 The diver should descendis-90 -100.feet in each descent.F Use the process you just learned to find each of the quotients below.14 -7-36 -9-55 11-45 -5Reflect1.Make a Conjecture Make a conjecture about the quotient of twointegers with different signs. Make a conjecture about the quotient oftwo integers with the same sign.Lesson 6.2153
Dividing IntegersMath On the Spotmy.hrw.comYou used the relationship between multiplication and division to makeconjectures about the signs of quotients of integers. You can use multiplicationto understand why division by zero is not possible.Think about the division problem below and its related multiplication problem.5 0 ?0 ? 5The multiplication sentence says that there is some number times 0 that equals5. You already know that 0 times any number equals 0. This means division by 0is not possible, so we say that division by 0 is undefined.EXAMPLE 1My Notes6.3.DA Divide: 24 (-3)STEP 1Determine the sign of the quotient.24 is positive and -3 is negative. Since the numbershave opposite signs, the quotient will be negative.STEP 2Divide.24 (-3) -8B Divide: -6 (-2)STEP 1Determine the sign of the quotient.-6 is negative and -2 is negative. Since the numbershave the same sign, the quotient will be positive.STEP 2Divide: -6 (-2) 3STEP 1Determine the sign of the quotient.The dividend is 0 and the divisor is not 0. So, thequotient is 0.STEP 2Divide: 0 (-9) 0YOUR TURNPersonalMath TrainerOnline Assessmentand Interventionmy.hrw.com154Unit 2Find each quotient.2.0 (-6)3.38 (-19)4.-13 (-1) Houghton Mifflin Harcourt Publishing CompanyC Divide: 0 (-9)
Using Integer Division toSolve ProblemsYou can use integer division to solve real-world problems. For some problems,you may need to perform more than one step. Be sure to check that the sign ofthe quotient makes sense for the situation.EXAMPL 2EXAMPLEMath On the Spotmy.hrw.com6.3.DJake answers questions in two different online Olympic trivia quizzes. Ineach quiz, he loses points when he gives an incorrect answer. The tableshows the points lost for each wrong answer in each quiz and Jake’s totalpoints lost in each quiz. In which quiz did he have more wrong answers?Olympic Trivia QuizSTEP 1Points lost foreach wrong answerTotal points lostWinter Quiz-3 points-33 pointsSummer Quiz-7 points-56 pointsFind the number of incorrect answers in the winter quiz.-33 (-3) 11STEP 2Find the number of incorrect answers Jake gave in thesummer quiz.-56 (-7) 8 Houghton Mifflin Harcourt Publishing CompanySTEP 3Divide the total points lost by the numberof points lost per wrong answer.Divide the total points lost by the numberof points lost per wrong answer.Math TalkMathematical ProcessesWhat is the sign of eachquotient in Steps 1 and 2?Why does this make sensefor the situation?Compare the numbers of wrong answers.11 8, so Jake had more wrong answers in the winter quiz.YOUR TURN5.A penalty in Meteor-Mania is -5 seconds. A penalty in Cosmic Calamityis -7 seconds. Yolanda had penalties totaling -25 seconds in a gameof Meteor-Mania and -35 seconds in a game of Cosmic Calamity. Inwhich game did Yolanda receive more penalties? Justify your answer.PersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comLesson 6.2155
Guided PracticeFind each quotient. (Example 1)-141.22. 21 (-3)263.-134. 0 (-4)-455.-56. -30 (10)-117.-18. -31 (-31)09.-7-12110.-1111. 84 (-7)50012.-2513. -6 (0)-6314.-21Write a division expression for each problem. Then find the value of theexpression. (Example 2)15. Clark made four of his truck payments late and was fined four late fees.The total change to his savings from late fees was - 40. How much wasone late fee?16. Jan received -22 points on her exam. She got 11 questions wrong out of50 questions. How much was Jan penalized for each wrong answer?18. Louisa’s savings change by - 9 each time she goes bowling. In all, itchanged by - 99 during the summer. How many times did she gobowling in the summer?ESSENTIAL QUESTION CHECK-IN19. How is the process of dividing integers similar to the process ofmultiplying integers?156Unit 2 Houghton Mifflin Harcourt Publishing Company17. Allen’s score in a video game was changed by -75 points because hemissed some targets. He got -15 points for each missed target. Howmany targets did he miss?
NameClassDate6.2 Independent Practice6.3.DPersonalMath Trainermy.hrw.comOnlineAssessment andIntervention20. Walter buys a bus pass for 30. Every time he rides the bus,money is deducted from the value of the pass. He rode12 times and 24 was deducted from the value of the pass.How much does each bus ride cost?21. Analyze Relationships Elisa withdrew 20 at a time from her bankaccount and withdrew a total of 140. Francis withdrew 45 at a time fromhis bank account and withdrew a total of 270. Who made the greaternumber of withdrawals? Justify your answer.22. Multistep At 7 p.m. last night, the temperature was 10 F. At 7 a.m. thenext morning, the temperature was -2 F.a. By how much did the temperature change from 7 p.m. to 7 a.m.? Houghton Mifflin Harcourt Publishing Companyb. The temperature changed by a steady amount overnight. By howmuch did it change each hour?23. Analyze Relationships Nola hiked down a trail at a steady rate for10 minutes. Her change in elevation was -200 feet. Then she continuedto hike down for another 20 minutes at a different rate. Her change inelevation for this part of the hike was -300 feet. During which portion ofthe hike did she walk down at a faster rate? Explain your reasoning.24. Write a real world description to fit the expression -50 5.Lesson 6.2157
25. Communicate Mathematical Ideas Two integers, a and b, have differentsigns. The absolute value of integer a is divisible by the absolute valueof integer b. Find two integers that fit this description. Then decide if theproduct of the integers is greater than or less than the quotient of theintegers. Show your work.Determine if each statement is true or false. Justify your answer.26. For any two nonzero integers, the product and quotient have thesame sign.27. Any nonzero integer divided by 0 equals 0.FOCUS ON HIGHER ORDER THINKINGWork Area28. Multi-step A perfect score on a test with 25 questions is 100. Eachquestion is worth the same number of points.b. Fred got a score of 84 on the test. Write a divisionsentence using negative numbers where the quotientrepresents the number of questions Fred answeredincorrectly.29. Persevere in Problem Solving Colleen divided integera by -3 and got 8. Then she divided 8 by integer b andgot -4. Find the quotient of integer a and integer b.30. Justify Reasoning The quotient of two negative integers results in aninteger. How does the value of the quotient compare to the value of theoriginal two integers? Explain.158Unit 2 Houghton Mifflin Harcourt Publishing Companya. How many points is each question on the test worth?
LESSON6.3?Applying IntegerOperationsNumber andoperations—6.3.D Add,subtract, multiply, and divideintegers fluently.ESSENTIAL QUESTIONHow can you use integer operations to solve real-world problems?Using the Order of Operationswith IntegersThe order of operations applies to integer operations as well as positivenumber operations. Perform multiplication and division first, and then additionand subtraction. Work from left to right in the expression.EXAMPL 1EXAMPLEProblemSolvingMath On the Spotmy.hrw.com6.3.DHannah made four withdrawals of 20 from her checking account. Shealso wrote a check for 215. By how much did the amount in her checkingaccount change?Analyze InformationYou need to find the total change in Hannah’s account. Since withdrawalsand writing a check represent a decrease in her account, use negativenumbers to represent these amounts.Formulate a PlanWrite a product to represent the four withdrawals. Houghton Mifflin Harcourt Publishing Company-20 (-20) (-20) (-20) 4(-20)Add -215 to represent the check that Hannah wrote.4(-20) (-215)Justify and EvaluateSolveEvaluate the expression to find by how much the amount in theaccount changed.4(-20) - 215 -80 - 215 -295Multiply first.Then subtract.The amount in the account decreased by 295.Justify and EvaluateThe value -295 represents a decrease of 295 dollars. This makessense, since withdrawals and writing checks remove money fromthe checking account.Lesson 6.3159
YOUR TURNPersonalMath TrainerOnline Assessmentand Intervention1. Reggie lost 3 spaceships in level 3 of a video game. He lost 30 points foreach spaceship. When he completed level 3, he earned a bonus of 200points. By how much did his score change?my.hrw.com2. Simplify: -6(13) - 21Using Negative Integers to RepresentQuantitiesMath On the Spotmy.hrw.comYou can use positive and negative integers to solve problems involvingamounts that increase or decrease. Sometimes you may need to use morethan one operation.EXAMPLE 26.3.CThree brothers each have their own savings. They borrow 72 from theirparents for concert tickets. Each brother must pay back an equal shareof this amount. Also, the youngest brother owes his parents 15. By howmuch will the youngest brother’s savings change after he pays his parents?STEP 1Determine the signs of the values and the operations you will use.Write an expression.Math TalkMathematical ProcessesSuppose the youngestbrother has 60 in savings.How much will he have leftafter he pays his parentswhat he owes?STEP 2Since an equal share of the 72 will be paid back, use division todetermine 3 equal parts of -72. Then add -15 to one of theseequal parts.Change to youngest brother’s savings (-72) 3 (-15)Evaluate the expression.(-72) 3 (-15) -24 (-15) -39DivideAdd.The youngest brother’s savings will decrease by 39.Reflect3.160Unit 2What If? Suppose there were four brothers in Example 2. How muchwould the youngest brother need to pay? Houghton Mifflin Harcourt Publishing CompanySince the money is being paid back, it will decrease the amount ineach brother’s savings. Use -72 and -15.
YOUR TURNSimplify each expression.4. (-12) 6 26. 40 (-5) 30PersonalMath Trainer5. -87 (-3) -9Online Assessmentand Intervention7. -39 3 -15my.hrw.comComparing Values of ExpressionsOften, problem situations require making comparisons between two values.Use integer operations to calculate values. Then compare the values.Math On the SpotEXAMPL 3EXAMPLE6.3.CJill and Tony play a board game in which they move counters along aboard. Jill moves her counter back 3 spaces four times, and then movesher counter forward 6 spaces. Tony moves his counter back 2 spaces threetimes, and then moves his player forward 3 spaces one time. Find eachplayer’s overall change in position. Who moved farther?STEP 1STEP 2Find each player’s overall change in position.Jill: 4(-3) 6 -12 6 - 6Jill moves back 6 spaces.Tony: 3(-2) 3 - 6 3 -3Tony moves back 3 spaces.my.hrw.comMath TalkMathematical ProcessesWhy do you compareabsolute values inStep 2?Compare the numbers of spaces moved by the players. -6 -3 Compare absolute values. Houghton Mifflin Harcourt Publishing CompanyJill moves farther back than Tony.YOUR TURN8. Amber and Will are in line together to buy tickets. Amber moves backby 3 places three times to talk to friends. She then is invited to move5 places up in line. Will moved back by 4 places twice, and then movedup in line by 3 places. Overall, who moved farther back in line?Evaluate each expression. Circle the expression with the greater value.9. (-10) 2 - 2 10. 42 (-3) 9 (-28) 4 1 (-36) 9 - 2 PersonalMath TrainerOnline Assessmentand Interventionmy.hrw.comLesson 6.3161
Guided PracticeEvaluate each expression. (Example 1)1. -6(-5) 122. 3(-6) - 33. -2(8) 74. 4(-13) 205. (-4)(0) - 46. -3(-5) - 16Write an expression to represent the situation. Evaluate theexpression and answer the question. (Example 2)7. Bella pays 7 payments of 5 each to a game store. She returns onegame and receives 20 back. What is the change to the amount of moneyshe has?8. Ron lost 10 points seven times playing a video game. He then lost anadditional 100 points for going over the time limit. What was the totalchange in his score?9. Ned took a test with 25 questions. He lost 4 points for each of the6 questions he got wrong and earned an additional 10 points foranswering a bonus question correctly. How many points did Nedreceive or lose overall?Compare the values of the two expressions using , , or . (Example 3)11. -3(-2) 313. -7(5) - 9?3(- 4) 9-3(20) 1012. -8(-2) - 2014. -16(0) - 3ESSENTIAL QUESTION CHECK-IN15. When you solve a problem involving money, what can a negative answerrepresent?162Unit 23(-2) 2- 8(-2) - 3 Houghton Mifflin Harcourt Publishing Company10. Mr. Harris has some money in his wallet. He pays the babysitter 12 anhour for 4 hours of babysitting. His wife gives him 10, and he puts themoney in his wallet. By how much does the amount in his wallet change?
NameClassDate6.3 Independent PracticePersonalMath Trainer6.3.Dmy.hrw.comOnlineAssessment andInterventionEvaluate each expression.16. -12(-3) 717. -42 (-6) 5 - 818. 10(- 60) - 1819. (-11)(-7) 5 - 8220. 35 (-7) 621. -13(-2) - 16 - 822. Multistep Lily and Rose are playing a game. In the game, each playerstarts with 0 points and the player with the most points at the end wins.Lily gains 5 points two times, loses 12 points, and then gains 3 points.Rose loses 3 points two times, loses 1 point, gains 6 points, and then gains7 points.a. Write and evaluate an expression to find Lily’s score.b. Write and evaluate an expression to find Rose’s score.c. Who won the game?Write an expression from the description. Then evaluate the expression. Houghton Mifflin Harcourt Publishing Company23. 8 less than the product of 5 and -424. 9 more than the quotient of -36 and -4.25. Multistep Arleen has a gift card for a local lawn and garden store. Sheuses the gift card to rent a tiller for 4 days. It costs 35 per day to rent thetiller. She also buys a rake for 9.a. Find the change to the value on her gift card.b. The original amount on the gift card was 200. Does Arleen haveenough left on the card to buy a wheelbarrow for 50? Explain.Lesson 6.3163
26. Carlos made up a game where, in a deck of cards, the red cards (heartsand diamonds) are negative and the black cards (spades and clubs) arepositive. All face cards are worth 10 points, and number cards are worththeir value.a. Samantha has a king of hearts, a jack of diamonds, and a 3 of spades.Write an expression to find the value of her cards.b. Warren has a 7 of clubs, a 2 of spades, and a 7 of hearts. Write anexpression to find the value of his cards.c. If the greater score wins, who won?d. If a player always gets three cards, describe two different ways toreceive a score of 7.FOCUS ON HIGHER ORDER THINKINGWork Area28. Critique Reasoning Jim found the quotient of two integers and gota positive integer. He added another integer to the quotient and got apositive integer. His sister Kim says that all the integers Jim used to getthis result must be positive. Do you agree? Explain.29. Persevere in Problem Solving Lisa is standing on a dock beside a lake.She drops a rock from her hand into the lake. After the rock hits the surfaceof the lake, the rock’s distance from the lake’s surface changes at a rate of -5inches per second. If Lisa holds her hand 5 feet above the lake’s surface, howfar from Lisa’s hand is the rock 4 seconds after it hits the surface?164Unit 2 Houghton Mifflin Harcourt Publishing Company27. Represent Real-World Problems Write a problem that the expression3(-7) - 10 25 -6 could represent.
MODULE QUIZReadyPersonalMath Trainer6.1 Multiplying IntegersOnline Assessmentand InterventionFind each product.my.hrw.com1. ( -2 )( 3 )2. ( -5 )( -7 )3. ( 8 )( -11 )4. ( -3 )( 2 )( -2 )5. The temperature dropped 3 C every hour for 5 hours.Write an integer that represents the change in temperature.6.2 Dividing IntegersFind each quotient.-636.7-157.-308.-15969.-1210. An elephant at the zoo lost 24 pounds over 6 months.The elephant lost the same amount of weight each month.Write an integer that represents the change in the elephant’sweight each month.6.3 Applying Integer Operations Houghton Mifflin Harcourt Publishing CompanyEvaluate each expression.11. ( -4 )( 5 ) 812. ( -3 )( -6 ) - 7-27- 1113.9-24 (- -2 )14.-3ESSENTIAL QUESTION15. Write and solve a real-world problem that can be represented by theexpression ( –3 )( 5 ) 10.Module 6165
PersonalMath TrainerModule 6 MIXed REVIEWTexas Test PrepSelected Response1. A diver is at an elevation of -18 feet relativeto sea level. The diver descends to anundersea cave that is 4 times as far from thesurface. What is the elevation of the cave?A -72 feetB -22 feetC-18 feetD -14 feet2. The football team lost 4 yards on 2 plays in arow. Which of the following could representthe change in field position?A -12 yardsB -8 yardsC-6 yardsD -2 yards3. Clayton climbed down 50 meters. Heclimbed down in 10-meter intervals. In howmany intervals did Clayton make his climb?A 5my.hrw.comOnlineAssessment andIntervention5. Clara played a video game before she leftthe house to go on a walk. She started with0 points, lost 6 points 3
Math Trainer Online Assessment and Intervention Personal my.hrw.com Math On the Spot my.hrw.com Multiplying Integers The product of two integers with opposite signs is negative. The product of two integers with the same sign is positive. The product of 0 and any other integer is
