Ms2019 Gr7 Se 03 - Big Ideas Learning
Expressions3.1 Algebraic Expressions3.2 Adding and SubtractingLinear Expressions3.3 The Distributive Property3.4 Factoring ExpressionsChapter Learning Target:Understand algebraic expressions.Chapter Success Criteria: I can identify parts of an algebraicexpression. I can write algebraic expressions. I can solve problems using algebraicexpressions. I can interpret algebraic expressionsin real-life problems.STEAM Video: “Trophic Status”ms2019 gr7 se 03.indb 881/18/18 3:21 PM
STEAM VideoTrophic StatusIn an ecosystem, energy and nutrients flow between bioticand abiotic components. Biotic components are the livingparts of an ecosystem. Abiotic components are thenon-living parts of an ecosystem. What is an exampleof an ecosystem?Watch the STEAM video “Trophic Status.” Then answerthe following questions.1. Give examples of both biotic and abiotic componentsin an ecosystem. Explain.2. When an organism is eaten, its energy flows into theorganism that consumes it. Explain how to use anexpression to represent the total energy that a persongains from eating each of the items shown.Performance TaskNameCh apt er3ance TaskPerform(continuChlorophyll in PlantsAfter completing this chapter, you will be able to use theconcepts you learned to answer the questions in the STEAMVideo Performance Task. You will be given the numbers ofatoms found in molecules involved in photosynthesis.Dateed)rin the wateof nutrientsuntthe amounts the amoChlorof water uses science class measureof a bodyThe lake isth. Yourhic statushic status.of plant grow determine its trop2. The troptos.the amountto predictngular lakesquare yardx 5600)yll in a recta80(rophofchloareaof(in yards)and has anperimeter80 yards wideesents then that repran expressioNamand simplifyea. Write.of the lakeC h apterthe lake?length ofWhat is thee of x is 90.Chlob. The valuroph of the lake.yll inedgetheatWrtakehat istolaof watepossible Pnentsct 5 samples a lakt. IseditDacolleaparsedtotsyardeto delain. for phteteacher wan be taken at least 20otosync. Yourldlake? Exp terminetheshouofthplePhththe levesis?otosthe lengEach samHoel ofples alongcarbon ynthesisbiolog w can yoall of the samisthdioxu useical pride, an e procthe amoducess by.classdtivityountwhicheach trophic water are?of chplantsrophyll foruslochloedofrophylacquby aamountl inire enplantshows the6 Caerto prrbon Before3. The tableoduc gy from:Dioxe glucthStatusideTrophicose an e sun. SuTrophic 6 Watnlightd dioxersTrophic 1.,ygenYou Clasyll level.ClasswantChlorophto phicfair pr ed in phot e models 6of thojMedDiox0–2.6ect. iumosyntheofygenMesotrophiceach ele Thhe table esis for a moleculesLe20mscHigshent us2.6–ienceowsict x, y,Eutrophcarbon and z re ed for ea the numbepresch mVery high20– 56mod hicatomolecul r, mod ent theel oxHypereutrope.coMolecel hyygenof a ,drog sts, 17.156–155uleatomNum12.3a. WCarb5.7,enatom modelberCarbon Ditaken. areof Atritsamby, ane anplesonoxidomsd simhic class is indicated dls e1reon.a. The chloper billirpresen of the mod an expresOxyg23.1 partssioand,elten0theGluc20.1n toatomlevefol?r ph0findoses yootosyn moleculchlorophyllthe mean2thesis. es used u use toDiox2yllygroph6by aenmean chlotheplthatan1t12levels such0chlorophyllplesam56ofc.0an exampleb. Wtheas Eutrophiritelakeb. Giveand simld classify2to relevel wouplifypresenant theLLCLearning,molec expressio Big Ideasnulesreserved.CopyrightAll rightsprod to find thucede coste7byofGradphthel Lifeotosync. : Modeling Reathesis. model atohat dos MathWIdeams yoBigyou nou use42ent Booktice abAssessmout the expressions inpartd. Yo(a) anu spd partand 0 end 0.5(b)?0Explfind .25 on ea on eachain.mthe toch model odel carbtal cohyonst ofyour drogen ato atom, 0science fa m. Writ .75 on eae andir projch modevaluect.Copyate an el oxygenright All rigBig Ideexprhts resessio atom,as Leervedn toarning., LLPlantsophyll in3PerformanceTaskGlucose Molecule6 carbon atoms12 hydrogen atoms6 oxygen atomsYou will be asked to determine the total cost for amodel of a molecule given the costs of different typesof atom models. How can you find the total cost ofpurchasing several identical objects?CBigIdeas Math: ModelingRealLiAsse fe Gradssment Boe 7ok418989ms2019 gr7 se 03.indb 891/18/18 3:21 PM
Getting Ready for ChapterChapter ExplorationWork with a partner. Rewrite the algebraic expression so that it has fewer symbolsbut still has the same value when evaluated for any value of ExpressionOriginalExpression1. 2x 4 x2. 3(x 1) 43. x (3 x)4. 5 2x 35. x 3 2x 46. 2x 2 x 37. WRITING GUIDELINES Work with a partner. Use your answers in Exercises 1 6 towrite guidelines for simplifying an expression.Simplifying an Algebraic ExpressionKey Idea Use the following steps tosimplify an algebraic expression.1.2.3.APPLYING A DEFINITION Work with a partner. Two expressions are equivalent ifthey have the same value when evaluated for any value of x. Decide which twoexpressions are equivalent. Explain your reasoning.Expression AExpression BExpression C8. x (2x 1) x 1 x 19. 2x 3 x 4x 7x 110. 3 x 2(x 1) x 1 x 511. 2 2x (x 2) 3x 3x 4VocabularyThe following vocabulary terms are defined in this chapter. Think aboutwhat each term might mean and record your thoughts.like termslinear expressionfactoring an expression9090ms2019 gr7 se 03.indb 901/18/18 3:21 PM
3.1 Algebraic ExpressionsLearning Target:Simplify algebraic expressions.Success Criteria: I can identify terms and like terms of algebraic expressions. I can combine like terms to simplify algebraic expressions. I can write and simplify algebraic expressions to solve real-life problems.EXPLORATION 1Simplifying Algebraic ExpressionsWork with a partner.a. Choose a value of x other than 0 or 1 for the last column in the table.Complete the table by evaluating each algebraic expression for eachvalue of x. What do you notice?Value Whenx 0Expression13x 1x ?73A. — x —B.0.5x 3 1.5x 1C.2x 6D. x 4Math PracticeE. 2x 2AnalyzeConjecturesF.—x x —x 4A student says that xand x3 are equivalentbecause they have thesame value whenx 1, x 0, andx 1. Explain whythe student is oris not correct.1232G. 4.8x 2 x 3.8xH. x 2I. x 2J.3x 2 x 4b. How can you use properties of operations to justify your answers inpart (a)? Explain your reasoning.c. To subtract a number, you can add its opposite. Does a similar rule applyto the terms of an algebraic expression? Explain your reasoning.Section 3.1ms2019 gr7 se 03.indb 91Algebraic Expressions911/18/18 3:21 PM
3.1LessonIn an algebraic expression, like terms are terms that have the same variablesraised to the same exponents. Constant terms are also like terms. To identifyterms and like terms in an expression, first write the expression as a sumof its terms.Key Vocabularylike terms, p. 92simplest form, p. 92EXAMPLE 1Identifying Terms and Like TermsIdentify the terms and like terms in each expression.a. 9x 2 7 xb. z 2 5z 3z 2 zRewrite as a sum of terms.Rewrite as a sum of terms.9x ( 2) 7 ( x)Terms: 9x, 2,7, xLike terms: 9x and x, 2 and 7Try Itz 2 5z ( 3z 2) zTerms: z 2, 5z, 3z 2,zLike terms: z 2 and 3z 2, 5z and zIdentify the terms and like terms in the expression.322. 2r 2 7r r 2 91. y 10 — y3. 7 4p 5 p 2qAn algebraic expression is in simplest form when it has no like terms andno parentheses. To combine like terms that have variables, use theDistributive Property to add or subtract the coefficients.EXAMPLE 2Simplifying Algebraic Expressionsa. Simplify 6n 10n.6n 10n (6 10)nRememberThe DistributiveProperty statesa(b c) ab acanda(b c) ab ac. 4n 8.5w 5.2w w 8.5w 5.2w 1wms2019 gr7 se 03.indb 92ExpressionsMultiplication Property of 1 ( 8.5 5.2 1)wDistributive Property 2.3wAdd.Simplify the expression.4. 10y 15yChapter 3Subtract.b. Simplify 8.5w 5.2w w.Try It92Distributive Property38345. — b — b6. 2.4g 2.4g 9.8gMulti-Language Glossary at BigIdeasMath.com1/18/18 3:21 PM
EXAMPLE 3Simplifying Algebraic Expressions3412a. Simplify — y 12 — y 6.34( )( )[ ( )]123412— y 12 — y 6 — y 12 — y ( 6)3412Commutative Propertyof Addition12Distributive Property — y — y 12 ( 6)34Rewrite as a sum. — — y 12 ( 6)14 —y 6Combine like terms.b. Simplify 3y 5y 4z 9z. 3y 5y 4z 9z ( 3 5)y (4 9)zDistributive Property 8y 13zTry ItSimplify.Simplify the expression.7. 14 3z 8 z8. 2.5x 4.3x 5Self-Assessment9. 2s 9s 8t tfor Concepts & SkillsSolve each exercise. Then rate your understanding of the success criteriain your journal.10. WRITING Explain how to identify the terms and like termsof 3y 4 5y.SIMPLIFYING ALGEBRAIC EXPRESSIONS Simplify the expression.11. 7p 6p4571012. — n 3 — n13. 2w g 7w 3g14. VOCABULARY Is the expression 3x 2x 4 in simplest form? Explain.15. WHICH ONE DOESN’T BELONG? Which expression does not belong withthe other three? Explain your reasoning. 4 6 3x3x 9 75x 10 2x5x 4 6 2xSection 3.1ms2019 gr7 se 03.indb 93Algebraic Expressions931/18/18 3:21 PM
EXAMPLE 4Modeling Real LifeEach person in a group buys an evening ticket, a medium drink, and alarge popcorn. How much does the group pay when there are 5 peoplein the group?Write an expression that represents the sum of the costs of the itemspurchased. Use a verbal leExpression CostNumber ofper mediumticketdrinks Cost perNumbermedium of largedrinkpopcornsThe same number of each item is purchased. So, x canrepresent the number of tickets, the number of medium drinks,and the number of large popcorns.7.50x 2.75x7.50x 2.75x 4x (7.50 2.75 4)xRememberVariables canbe lowercase oruppercase. Make sureyou consistently usethe same case for avariable when solvinga problem. Cost perlargepopcorn 14.25x 4xDistributive PropertyAdd coefficients.The expression 14.25x indicates that the cost per person is 14.25. To findthe cost for a group of 5 people, evaluate the expression when x 5.14.25(5) 71.25The total cost for a group of 5 people is 71.25.Self-Assessmentfor Problem SolvingSolve each exercise. Then rate your understanding of the success criteriain your journal.16. MODELING REAL LIFE An exercise mat is 3.3 timesas long as it is wide. Write expressions in simplestform that represent the perimeter and the area ofthe exercise mat.17.94Chapter 3ms2019 gr7 se 03.indb 94DIG DEEPERA group of friends visits the movie theater in Example 4.Each person buys a daytime ticket and a small drink. The group shares2 large popcorns. What is the average cost per person when there are4 people in the group?Expressions1/18/18 3:21 PM
3.1PracticeGo to BigIdeasMath.com to getHELP with solving the exercises.Review & RefreshFind the product or quotient. Write fractions in simplest form.2774231. — —91049( )2. — —29( )3. 1— —Order the numbers from least to greatest.7834454. —, 0.85, 87%, —, 78%5. 15%, 14.8, 15—, 1450%6. A bird’s nest is 12 feet above the ground. A mole’s den is 12 inches belowthe ground. What is the difference in height of these two positions?A. 24 in.B. 11 ftC. 13 ftD. 24 ftConcepts, Skills, & Problem SolvingREASONING Determine whether the expressions are equivalent.Explain your reasoning. (See Exploration 1, p. 91.)7.8.Expression 13 5xExpression 24.25 5x 4.25Expression 11.25x 4 0.75x 3Expression 22x 1IDENTIFYING TERMS AND LIKE TERMS Identify the terms and like terms inthe expression.9. t 8 3t10. 3z 4 2 4z11. 2n n 4 7n12. x 9x 2 12x 2 713. 1.4y 5 4.2 5y 2 z14. — s 4 — s — s 315.12YOU BE THE TEACHERYour friend identifiesthe terms and like terms in the expression3x 5 2x 9x. Is your friend correct?Explain your reasoning.34183x 5 2x 9xTerms: 3x, 5, 2x , and 9xLike Terms: 3x, 2x , and 9xSIMPLIFYING ALGEBRAIC EXPRESSIONS Simplify the expression.16. 12g 9g17. 11x 9 718. 8s 11s 6s19. 4b 24 1920. 4p 5p 30p21. 4.2v 5 6.5v22. 8 4a 6.2 9a23. — y 4 7 — y2591023Section 3.1ms2019 gr7 se 03.indb 959531024. — c — 14c —Algebraic Expressions951/18/18 3:21 PM
25. MODELING REAL LIFE On a hike, eachhiker carries the items shown. Write andinterpret an expression in simplest formthat represents the weight carried byx hikers. How much total weight iscarried when there are 4 hikers?4.6 lb26.STRUCTURE Evaluate the expression 8x 5 2x 4 5x when x 2before and after simplifying. Whichmethod do you prefer? Explain.3.4 lb2.2 lb27. OPEN-ENDED Write an expression with five different terms that is equivalentto 8x 2 3x2 3y. Justify your answer.28.29.STRUCTURE Which of the following shows a correct way of simplifying6 (3 5x)? Explain the errors made in the other choices.A.6 (3 5x) (6 3 5)x 4xB.6 (3 5x) 6 (3 5)x 6 ( 2)x 6 2xC.6 (3 5x) (6 3) 5x 9 5xD.6 (3 5x) (6 3 5) x 14 xPRECISION Two comets orbit the Sun. Onecomet travels 30,000 miles per hour and the othercomet travels 28,500 miles per hour. What is themost efficient way to calculate the difference ofthe distances traveled by the comets for any givennumber of minutes? Justify your answer.CarTruckWash 8 10Wax 12 1530. MODELING REAL LIFE Find theearnings for washing and waxing12 cars and 8 trucks. Justify your answer.31. CRITICAL THINKING You apply gold foil to a pieceof red poster board to make the design shown.x in.a. Find the area of the gold foil when x 3.Justify your answer.b. The pattern at the right is called“St. George’s Cross.” Find a countrythat uses this pattern as its flag.x in.12 in.20 in.32. GEOMETRY Two rectangles have different dimensions. Each rectanglehas a perimeter of (7x 5) inches. Draw and label diagrams thatrepresent possible dimensions of the rectangles.96Chapter 3ms2019 gr7 se 03.indb 96Expressions1/18/18 3:21 PM
3.2Adding and SubtractingLinear ExpressionsLearning Target:Find sums and differences of linear expressions.Success Criteria: I can explain the difference between linear and nonlinear expressions. I can find opposites of terms that include variables. I can apply properties of operations to add and subtract linear expressions.EXPLORATION 1 1 1 variable variableMath PracticeConsider SimilarProblemsHow is using integercounters to find sumsand differences ofintegers similar tousing algebra tilesto find sums anddifferences of algebraicexpressions?Using Algebra TilesWork with a partner. You can use the algebra tiles shown at the left to findsums and differences of algebraic expressions.a. How can you use algebra tiles to model a sum of terms that equals 0?Explain your reasoning.b. Write each sum or difference modeled below. Then use the algebra tilesto simplify the expression.()()()()() (())()c. Write two algebraic expressions of the form ax b, where a and b arerational numbers. Find the sum and difference of the expressions.EXPLORATION 2Using Properties of OperationsWork with a partner.a. Do algebraic expressions, such as 2x, 3y, and 3z 1 have additiveinverses? How do you know?b. How can you find the sums and differences modeled in Exploration 1without using algebra tiles? Explain your reasoning.Section 3.2ms2019 gr7 se 03.indb 97Adding and Subtracting Linear Expressions971/18/18 3:21 PM
3.2LessonA linear expression is an algebraic expression in which the exponent of eachvariable is 1.Key Vocabularylinearliketerms,expression,p. 92p. 98 form, p. 92simplest16Linear Expressions 4x3x 5y5 —xNonlinear Expressions—x1 22 7x 3 xx5 1You can use either a vertical or a horizontal method to add linear expressions.EXAMPLE 1Adding Linear ExpressionsFind each sum.a. (x 2) (3x 8)Vertical method: Align like terms vertically and add.x 2 3x 84x 6ions areLinear express h then witusually writtefirst.variable termThe sum is 4x 6.b. ( 4y 3) (11y 5)Horizontal method: Use properties of operations to group liketerms and simplify.( 4y 3) (11y 5) 4y 3 11y 5Rewrite the sum. 4y 11y 3 5Commutative Propertyof Addition ( 4y 11y) (3 5)Group like terms. 7y 2Combine like terms.The sum is 7y 2.Try It98Chapter 3ms2019 gr7 se 03.indb 98Find the sum.1. (x 3) (2x 1)2. ( 8z 4) (8z 7)3. (4.5 n) ( 10n 6.5)4.Expressions1214( w 3) ( w 3)——Multi-Language Glossary at BigIdeasMath.com1/18/18 3:21 PM
To subtract one linear expression from another, add the opposite of each termin the expression. You can use a vertical or a horizontal method.EXAMPLE 2Subtracting Linear ExpressionsFind each difference.a. (5x 6) ( x 6)Vertical method: Align like terms vertically and subtract.(5x 6) ( x 6)Common ErrorWhen subtractingan expression,make sure you add theopposite of each termin the expression, notjust the first term.Add the opposite.5x 6 x 66xThe difference is 6x.b. (7y 5) (8y 6)Horizontal method: Use properties of operations to group like termsand simplify.(7y 5) (8y 6) (7y 5) ( 8y 6)Add the opposite. 7y ( 8y) 5 6Commutative Propertyof Addition [7y ( 8y)] (5 6)Group like terms. y 11Combine like terms.The difference is y 11.Try ItFind the difference.5. (m 3) ( m 12)6. ( 2c 5) (6.3c 20)Self-Assessmentfor Concepts & SkillsSolve each exercise. Then rate your understanding of the success criteriain your journal.7. WRITING Describe how to distinguish a linear expression from anonlinear expression. Give an example of each.8. DIFFERENT WORDS, SAME QUESTION Which is different?Find “both” answers.What is x more than 3x 1?Find 3x 1 decreased by x.What is the difference of 3x 1 and x?Section 3.2ms2019 gr7 se 03.indb 99Subtract (x 1) from 3x.Adding and Subtracting Linear Expressions991/18/18 3:21 PM
EXAMPLE 3Modeling Real LifeSkateboard kits cost d dollars and you have a coupon for 2 off each oneyou buy. After assembly, you sell each skateboard for (2d 4) dollars.Find and interpret your profit on each skateboard sold.Understandthe problem.You are given information about purchasing skateboard kits and selling theassembled skateboards. You are asked to find and interpret the profit madeon each skateboard sold.Make a plan.Find the difference of the expressions representing the selling price and thepurchase price. Then simplify and interpret the expression.Solve andcheck.You receive 2 off of d dollars, so you pay (d 2) dollars for each kit.ProfitSelling pricePurchase price (dollars)(dollars)(dollars) (2d 4) (d 2)Write the difference. (2d 4) ( d 2)Add the opposite. 2d d 4 2Group like terms. d 2Combine like terms.Your profit on each skateboard sold is (d 2) dollars. You pay (d 2)dollars for each kit, so you are doubling your money.Look Back Assume each kit is 40. Verify that you double your money.When d 40:You pay d 2 40 2 38.You sell it for 2d 4 2(40) 4 80 4 76. Because 38 2 76, you double your money.Self-Assessment for Problem SolvingSolve each exercise. Then rate your understanding of the success criteriain your journal.9.DIG DEEPER In a basketball game, the home team scores(2m 39) points and the away team scores (3m 40) points, wherem is the number of minutes since halftime. Who wins the game? Whatis the difference in the scores m minutes after halftime? Explain.10. Electric guitar kits originally cost d dollars online. You buy the kits onsale for 50% of the original price, plus a shipping fee of 4.50 per kit.After painting and assembly, you sell each guitar online for(1.5d 4.5) dollars. Find and interpret your profit on each guitar sold.100Chapter 3ms2019 gr7 se 03.indb 100Expressions1/18/18 3:21 PM
3.2PracticeGo to BigIdeasMath.com to getHELP with solving the exercises.Review & RefreshSimplify the expression.1. 4f 11f2. b 4b 9b453. 4z 6 7z 313Evaluate the expression when x — and y —.4. x y5. 2x 6y6. x 4y7. What is the surface area of a cube that has a side length of 5 feet?A. 25 ft2B.75 ft2125 ft2C.150 ft2D.Concepts, Skills, & Problem SolvingUSING ALGEBRA TILES Write the sum or difference modeled by the algebra tiles.Then use the algebra tiles to simplify the expression. (See Exploration 1, p. 97.)8.9.(()()) ()ADDING LINEAR EXPRESSIONS Find the sum.10. (n 8) (n 12)11. (7 b) (3b 2)12. (2w 9) ( 4w 5)13. (2x 6) (4x 12)14. ( 3.4k 7) (3k 21)15. — z 4 — z 1516. (6 2.7h) ( 1.3j 4)17. — x 5 (2y 3.5) — x 5() (72(74)15)(14)18. MODELING REAL LIFE While catching fireflies, you anda friend decide to have a competition. After m minutes,you have (3m 13) fireflies and your friend has(4m 6) fireflies.a. How many total fireflies do you and your friendcatch? Explain your reasoning.b. The competition lasts 3 minutes. Who has morefireflies? Justify your answer.Section 3.2ms2019 gr7 se 03.indb 101Adding and Subtracting Linear Expressions1011/18/18 3:21 PM
SUBTRACTING LINEAR EXPRESSIONS Find the difference.19. ( 2g 7) (g 11)20. (6d 5) (2 3d)21. (4 5y) (2y 16)22. (2n 9) ( 2.4n 4)1838( c 16 ) ( 3c )25. ( 6m ) ( n 8 )—23.—1314—27.—24.9454( x 6 ) ( x 24 )——26. (1 5q) (2.5s 8) (0.5q 6)YOU BE THE TEACHERYour friend finds the difference (4m 9) (2m 5).Is your friend correct? Explain your reasoning.(4m 9) (2m 5) 4m 9 2m 5 4m 2m 9 5 2m 428. GEOMETRY The expression 17n 11 represents theperimeter of the triangle. What is the length of the third side?Explain your reasoning.29.265calories burned31.5n 64n 5LOGIC Your friend says the sum of two linear expressionsis always a linear expression. Is your friend correct? Explain.30. MODELING REAL LIFE You burn 265 calories running andthen 7 calories per minute swimming. Your friend burns273 calories running and then 11 calories per minuteswimming. You each swim for the same number ofminutes. Find and interpret the difference in theamounts of calories burned by you and your friend.DIG DEEPERYou start a new job. After w weeks, you have (10w 120) dollarsin your savings account and (45w 25) dollars in your checking account.a. What is the total amount of money in the accounts? Explain.b. How much money did you have before you started yournew job? How much money do you save each week?y4c. You want to buy a new phone for 150, and still have 500left in your accounts afterwards. Explain how to determinewhen you can buy the phone.321 5 4 3 2 132.102REASONING Write an expression in simplest form thatrepresents the vertical distance between the two lines shown.What is the distance when x 3? when x 3?Chapter 3ms2019 gr7 se 03.indb 102134 xy x 1 3 4y 2x 4Expressions1/18/18 3:21 PM
3.3 The Distributive PropertyLearning Target:Apply the Distributive Property to generate equivalent expressions.Success Criteria: I can explain how to apply the Distributive Property. I can use the Distributive Property to simplify algebraic expressions.EXPLORATION 1Using Models to Write ExpressionsWork with a partner.a. Write an expression that represents the area of the shaded regionin each figure.16 z5z4x 134x2x1.5yy3.5yMath PracticeUse ExpressionsHow can youdetermine whetherexpressions thatappear to be differentare equivalent?yy2y 1b. Compare your expressions in part (a) with other groups in your class.Did other groups write expressions that look different than yours?If so, determine whether the expressions are equivalent.Section 3.3ms2019 gr7 se 03.indb 103The Distributive Property1031/18/18 3:21 PM
3.3LessonYou can use the Distributive Property to simplify expressions involving variableterms and rational numbers.EXAMPLE 1Using the Distributive PropertySimplify each expression.13a. —(3n 6)Remember131313( ) —(3n 6) —(3n) — (6)The DistributiveProperty statesa(b c) ab acanda(b c) ab ac.Distributive Property n ( 2)Multiply. n 2Add the opposite.b. 5( x 3y)5( x 3y) 5( x) 5(3y)Distributive Property 5x 15yTry ItSimplify the expression.232. —( 3z 6)1. 1(x 9)EXAMPLE 2Multiply.3. 1.5(8m n)Simplifying ExpressionsSimplify 3( 1 2x 7).Common ErrorMultiply eachterm in the sumby 3, not 3. 3( 1 2x 7)Method 1: Use the Distributive Property before combining like terms. 3( 1 2x 7) 3( 1) ( 3)(2x) ( 3)(7) 3 ( 6x) ( 21)Multiply. 6x 18Combine like terms.Method 2: Combine like terms in parentheses before using theDistributive Property. 3( 1 2x 7) 3(2x 6)Try ItChapter 3ms2019 gr7 se 03.indb 104Combine like terms. ( 3)(2x) ( 3)(6)Distributive Property 6x 18Multiply.Simplify the expression.4. 2( 3s 1 5)104Distributive Property325. —(a 4 2a)Expressions1/18/18 3:21 PM
EXAMPLE 3Simplifying ExpressionsSimplify each expression.12a. —(6n 4) 2n12( )1212 —(6n 4) 2n —(6n) — (4) 2nDistributive Property 3n ( 2) 2nMultiply. n 2Combine like terms.34( )(6d 5) 8( d 1 ) (6d 5) [ 8( d ) 8(1) ]b. (6d 5) 8 —d 13434—iply anYou can mult 1 to ybexpressionte ofsiopfind the opn.iossrethe expTry It—Distributive Property (6d 5) (6d 8)Multiply. (6d 5) ( 6d 8)Add the opposite. [6d ( 6d)] ( 5 8)Group like terms. 3Combine like terms.Simplify the expression.457. — (10w 5) 2(w 9)6. 3.5m 1.5(m 10)Self-Assessmentfor Concepts & SkillsSolve each exercise. Then rate your understanding of the success criteriain your journal.8. WRITING Explain how to use the Distributive Property when simplifyingan expression.USING THE DISTRIBUTIVE PROPERTY Simplify the expression.5610. 6(3s 2.5 5s)31012. 2.25 2(7.5 4h)9. — ( 2y 3)11. —(4m 8) 9m83x324x—13.STRUCTURE Use the terms at the left to complete the expressionbelow so that it is equivalent to 9x 12. Justify your answer.( ) Section 3.3ms2019 gr7 se 03.indb 105The Distributive Property1051/18/18 3:21 PM
EXAMPLE 4Modeling Real LifeA square pool has a side length of s feet. How many 1-foot square tilesdoes it take to tile the border of the pool?Understandthe problem.Make a plan.You are given information about a square pool and square tiles. You areasked to find the number of tiles it takes to tile the border of the pool.Draw a diagram that represents the situation. Use the diagram to write anexpression for the number of tiles needed.s 2Solve andcheck.1 ftss fts1 fts ft1 fts 21 ftThe diagram shows that the tiled border can be divided into two sectionsthat each require s 2 tiles and two sections that each require s tiles. So, thenumber of tiles can be represented by 2(s 2) 2s. Simplify the expression.2(s 2) 2s 2(s) 2(2) 2s 4s 4Distributive PropertySimplify.The expression 4s 4 represents the number of tiles that are needed.Another MethodDraw a different diagram.s 14(s 1) 4(s) 4(1) 4s 4 s 1s 1s 1Self-Assessmentfor Problem SolvingSolve each exercise. Then rate your understanding of the success criteriain your journal.14. A rectangular room is 10 feet longer than it is wide. How many1-foot square tiles does it take to tile along the inside walls of the room?15. How many 2-foot square tiles does it take to tile the border of the poolin Example 4? Explain.106Chapter 3ms2019 gr7 se 03.indb 106Expressions1/18/18 3:21 PM
3.3PracticeGo to BigIdeasMath.com to getHELP with solving the exercises.Review & RefreshFind the sum or difference.1. (5b 9) (b 8)2. (3m 5) (6 5m)3. (1 9z) 3(z 2)4. (7g 6) ( 3n 4)Evaluate the expression. 5. 62 6. 92 3Copy and complete the statement using , , or . 11 8. 119. 7. ( 7) ( 2) ( 4) 3.5 5.8 10. 3.5 175—Concepts, Skills, & Problem SolvingUSING MODELS Write two different expressions that represent the area of theshaded region. Show that the expressions are equivalent. (See Exploration 1, p. 103.)11.12.3x 42mm 26.51.5mx 2mUSING THE DISTRIBUTIVE PROPERTY Simplify the expression.13. 3(a 7)14. 6(2 x)15. 5(3m 4)16. 9( 5 4c)17. 4.5(3s 6)18. 1.4( 5 7g)254319. —(6 5p)20. —(3q 10)21. 2(3 4y 5)22. 9(8 6n 4)23. 6( 4d 8.3 3d)24. 2.3h(6 k)26. 2( 2w 1.2 7x)27. — — a 9b — a3825. —( 4y z)5 43 3(23)YOU BE THE TEACHERYour friend simplifies the expression. Is your friend correct?Explain your reasoning.29.28. 2(h 8k) 2(h) 2(8k) 3(4 5b 7) 3(11 5b) 3(11) ( 3)(5b) 2h 16k 33 15bSection 3.3ms2019 gr7 se 03.indb 107The Distributive Property1071/18/18 3:22 PM
SIMPLIFYING EXPRESSIONS Simplify the expression.30. 3(5g 1) 8g31. 6a 7( 2a 4)32. 9 3(5 4x)33. —(5p 12) 2 8 — p34. c(4 3c) 0.75(c 3)35. 1 — — —n34(2 63 7(3714))336. MODELING REAL LIFE The cost (in dollars) of a custom-madesweatshirt is represented by 3.5n 29.99, where n is thenumber of different colors in the design. Write and interpret asimplified expression that represents the cost of 15 sweatshirts.337.MODELING REAL LIFE A ski resort makes snow using a snowfan that costs 1200. The fan has an average daily operationcost of 9.50. Write and interpret a simplified expression thatrepresents the cost to purchase and operate 6 snow fans.38.NUMBER SENSE Predict whether the instructions below will produceequivalent expressions. Then show whether your prediction is correct. Subtract 3 from n, add 3 to the result, and then triple that expression. Subtract 3 from n, triple the result, and then add 3 to that expression.USING A MODEL Draw a diagram that shows how the expression can represent thearea of a figure. Then simplify the expression.39. 5(2 x 3)41.40. (4 1)(x 2x)DIG DEEPERA square fire pit with a side length ofs feet is bordered by 1-foot square stones as shown.a. How many stones does it take to border thefire pit with two rows of stones? Use a diagramto justify your answer.Row 1Row 2s ftb. You border the fire pit with n rows of stones.How
3.3 The Distributive Property 3.4 Factoring Expressions Expressions STEAM Video: “Trophic Status” Chapter Learning Target: Understand algebraic expressions. Chapter Success Criteria: I can identify parts of an algebraic expression. I can write algebraic expressions. I can sol
14 15 GR7 GR7s ASSEMBLY STEP 2-1 (for GR7) A A. Release the 4 x BOLTS (L26) from the BOTTLE HOLDER. B Attach HANDLEBAR to the BOTTLE HOLDER using FASTEN PLATE (G03) and 4 x BOLTS (L26) then fasten by ALLEN WRENCH. GR7 SHOWN L26 Z01 Z01 Z02 A Attach FRONT STABILIZER to the MAIN FRAME using BOLTS (2 x Z01 and 2 x Z02) and fasten by ALLEN WRENCH. B Attach REAR STABILIZER to the MAIN FRAME
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Reasoning (Big Ideas) Direct Fractions Multiplication 3-D shapes 10 CONTENT PROFICIENCIES . As teachers we need to have Big Ideas in mind in selecting tasks and when teaching. What is a Big Idea? Big Ideas are Mathematically big Conceptually big Pedagogically big 13 .
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