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MODULE QUIZReadyPersonalMath Trainer10.1 Modeling and Writing ExpressionsOnline Assessmentand InterventionWrite each phrase as an algebraic expression.my.hrw.com1. p divided by 62. 65 less than j3. the sum of 185 and h4. the product of 16 and g5. Let x represent the number of television show episodes that are tapedin a season. Write an expression for the number of episodes taped in4 seasons.10.2 Evaluating ExpressionsEvaluate each expression for the given value of the variable.6. 8p; p 97. 11 r; r 78. 4(d 7); d 2609.m; m 510. To find the area of a triangle, you can use the expression b h 2,where b is the base of the triangle and h is its height. What is the area ofa triangle with a base of 6 and a height of 8?10.3 Generating Equivalent Expressions Houghton Mifflin Harcourt Publishing Company11. Draw lines to match the expressions inList A with their equivalent expressionsin List B.ESSENTIAL QUESTIONList AList B7x 147 7x7( x - 1 )7( 1 x )7x - 77( x 2 )12. How can you solve problems involving equivalent expressions?Module 10283
MODULE 10 MIXED REVIEWPersonalMath TrainerAssessmentReadinessSelected Response1. Which expression represents the productof 83 and x?A 83 xA the product of r and 9B the quotient of r and 99 less than rp6060DpC4. Using the algebraic expression 4n 6,what is the greatest whole-number value ofn that will give you a result less than 100?A 22CB 23D 25245. Evaluate 7w - 14 for w 9.B 18C49D 77A Associative Property of AdditionCCommutative Property ofMultiplicationD Distributive PropertyMini-Task8. You can convert a temperature givenin degrees Celsius to a Fahrenheittemperature by using the expression9x 5 32, where x is the Celsiustemperature.a. Water freezes when the temperature is0 C. At what Fahrenheit temperaturedoes water freeze?b. Water boils at 100 C. At whattemperature does water boil indegrees Fahrenheit?c. The temperature of some water is15 C. What is the Fahrenheittemperature?284Unit 4 Houghton Mifflin Harcourt Publishing Company3. Rhonda was organizing photos in aphoto album. She took 60 photos anddivided them evenly among p pages.Which algebraic expression represents thenumber of photos on each page?A 27. The expression 12(x 4) represents thetotal number of CDs Mei bought in Apriland May at 12 each. Which property isapplied to write the equivalent expression12x 48?B Associative Property of MultiplicationD r more than 9B 60 - p200D 2502. Which phrase describes the algebraicexpression 9r ?A p - 60A 40C83xD 83 - xC6. Katie has read 32% of a book. If she hasread 80 pages, how many more pagesdoes Katie have left to read?B 170B 83 xCmy.hrw.comOnlineAssessment andIntervention
UNIT 4Study GuideMODULEMODULE?9ReviewGenerating EquivalentNumerical ExpressionsKey Vocabularybase (base (ennumeración))exponent (exponente)order of operations (ordende las operaciones)power (potencia)ESSENTIAL QUESTIONHow can you generate equivalent numerical expressions and usethem to solve real-world problems?EXAMPLE 1Find the value of each power.A. 0.924C. ( 41 )B. 1800.92 0.9 0.9 0.811( 41 ) ( 41 ) ( 41 ) ( 41 ) ( 41 ) 256Any number raised to thepower of 0 is 1.4180 1EXAMPLE 2Find the prime factorization of 60.60 2 2 3 5 Houghton Mifflin Harcourt Publishing Company2 602 303 155 5160 22 3 5The prime factorization of 60 is 22 3 5.EXAMPLE 3Simplify each expression.A. 4 (23 5)B. 27 32 6 4 (8 5)23 8 27 9 632 9 4 13Add. 3 6Divide. 52Multiply. 18Multiply.EXERCISESUse an exponent to write each expression. (Lesson 9.1)1. 3.6 3.62. 9 9 9 93. 45 45 45Unit 4285
Find the value of each power. (Lesson 9.1)4. 1205. 1327. 0.428.6.( 49 )1( 27 )39. 0.73Find the prime factorization of each number. (Lesson 9.2)10. 7511. 2912. 16813. Eduardo is building a sandbox that has an area of 84 square feet.What are the possible whole number measurements for the lengthand width of the sandbox? (Lesson 9.2)Simplify each expression. (Lesson 9.3)22 - (3 4)15.12 4214. 2 52 – (4 1)?10Generating EquivalentAlgebraic ExpressionsESSENTIAL QUESTIONHow can you generate equivalent algebraic expressions and usethem to solve real-world problems?EXAMPLE 1Evaluate each expression for the given values of the variables.A. 2(x2 - 9); x 5algebraic expression(expresión algebraica)coefficients (coeficiente)constant (contante)equivalent expressions(expresión equivalente)evaluating (evaluar)term (término (en unaexpresión))B. w y 2 3w; w 2, y 62(52 - 9)52 252 62 3(2)62 36 2(16)Subtract. 2 36 6Multiply. 32Multiply. 44Add.When x 5, 2(x2 – 9) 32.When w 2 and y 6, w y 2 3w 44.EXAMPLE 2Determine whether the algebraic expressions are equivalent:5(x 2) and 10 5x.5(x 2) 5x 10 10 5xDistributive PropertyCommutative Property5(x 2) is equal to 10 5x. They are equivalent expressions.286Key VocabularyUnit 4 Houghton Mifflin Harcourt Publishing CompanyMODULEMODULE
EXERCISESWrite each phrase as an algebraic expression. (Lesson 10.1)1. x subtracted from 152. 12 divided by t3. 4 groups of y4. the sum of z and 7Write a phrase for each algebraic expression. (Lesson 10.1)5. 8p6. s 7Evaluate each expression for the given values of the variables.(Lesson 10.2)7. 8z 3; z 89. s - 5t s2; s 4, t -18. 3(7 x2); x 210.x - y3; x -7, y 311. The expression 21(h)(b1 b2) gives the area of a trapezoid, withb1 and b2 representing the two base lengths of a trapezoid andh representing the height. Find the area of a trapezoid with baselengths 4 in. and 6 in. and a height of 8 in. (Lesson 10.2)Determine if the expressions are equivalent. (Lesson 10.3)12. 7 7x; 7(x 17 )13. 2.5(3 x); 2.5x 7.5Combine like terms. (Lesson 10.3) Houghton Mifflin Harcourt Publishing Company14. 3m - 6 m2 - 5m 115. 7x 4(2x - 6)16. b2 3 2b2 4 - 717. 3(p 5) - 8 11pUnit 4287
Unit 4 Performance Tasks1.Freelance Computer ProgrammerAntonio is a freelance computer programmer. In his work, he often usesthe power of 2n to find the number of ways bits (or units of information)can be arranged. The n often stands for the number of bits.CAREERS IN MATHa. Antonio is working on programming a new video game calledMillie’s Quest. In the game, the main character, Millie, collects goldenkeys to help her in her quest. Antonio wants to write a formula toshow that Millie can collect one less key than the highest number ofbits that can be arranged in the system. What formula can he use?b. If Antonio is working with a 16-bit system, how many golden keyscan Millie collect?c. Antonio is also working on a new spreadsheet program. Theprogram takes up 14 bytes of memory. If each byte is equal to 8 bits,how many bits is Antonio’s program? Show your work.2. Hannah just bought a new camera. In January she took 14 pictures. Thenumber of pictures she took doubled each month for three months.a. How many pictures did Hannah take in March? Write and solve anexpression with an exponent to show how many pictures she took. Houghton Mifflin Harcourt Publishing Companyb. In April, Hanna took half the number of pictures she took in March.Her brother Jack thinks she took the same number of pictures inApril that she did in February. Hanna knew he was incorrect. Writeand solve an expression to show why Hannah is right.288Unit 4
UNIT 4 MIXED REVIEWPersonalMath TrainerAssessmentReadinessSelected Response1. Which expression is equivalent to2.3 2.3 2.3 2.3 2.3?A 2.3 5B 235C 2 35D 2.3552. Which operation should you perform firstwhen you simplify 63 – (2 54 6) 5?A additionB divisionC multiplicationD subtraction3. Sheena was organizing items in ascrapbook. She took 25 photos and dividedthem evenly between p pages. Whichalgebraic expression represents the numberof photos on each page?A p – 25 Houghton Mifflin Harcourt Publishing CompanyB 25 – ppC 2525Dp4. Which is another way to write7 7 7 7?A 74my.hrw.com5. Angela earns x dollars an hour. On Friday,she worked 6 hours. On Saturday, sheworked 8 hours. Which expression showshow much she earned both days?A 6x 8B 8x 6xC (6 8)x6 8Dx6. Marcus is doing a science experimentin which he measures the rate at whichbacteria multiply. Every 15 seconds, thebacteria double in number. If there are10 bacteria now, how many will there be in2 minutes?A 160 bacteriaB 256 bacteriaC 1,280 bacteriaD 2,560 bacteria7. The prime factorization of which number is25 5?A 50B 125C 160D 5008. Which expression has a value of 36 whenx 4 and y 7?B 7(4)A 2xyC 28B 2x 4yD 47OnlineAssessment andInterventionC 6y - xD 12x - 2yUnit 4289
Hot !TipWhen possible, use logic toeliminate at least two answerchoices.9. What should you do first to simplify theexpression (43 9) 76 5?A Add 4 and 9.B Add 76 and 5.Mini-Tasks13. For every bag of trail mix the local ScoutGuide troop sells, they earn 0.45.a. Write an expression to represent thissituation.b. Sarah sold 52 bags of trail mix. Howmuch did she earn for her troop?C Multiply 4 4 4.D Divide (43 9) by 76.10. Which ratio is equivalent to 4:10?2A58B1012C1616D1011. Travis and Paula went to lunch. Travisordered a sandwich for 7.50, and Paulaordered a burger for 5.25. After lunch, theyleft a 15% tip for their waiter. How muchmoney did they spend altogether?c. Let x represent the total number ofbags of trail mix sold by Sarah’s troop.Write an expression to show whatpercentage of bags Sarah sold.14. Robert is replacing sod in two squareshaped areas of his backyard. One side ofthe first area is 7.5 feet. One side of theother area is 5.7 feet. The sod costs y dollarsper square foot.a. Write an expression to show how muchRobert will spend on sod.A 12.75C 15.95D 16.0012. Which shows the following numbers inorder from greatest to least?1.5, 24, 42, 1.0542A , 1.5, 1.05,4224B 1.05, 1.5, ,4 24 2C , , 1.5, 1.052 44 2D 1.05, , , 1.52 415. Jose wants to find how many gallons ofwater he needs to fill his cube-shapedaquarium. One side of his aquarium is 4 feetlong.a. Write and solve an expression to findthe volume of Jose’s aquarium.b. One cubic foot is equal to 7.48 gallonsof water. How many gallons of waterdoes Jose need to fill his aquarium?Round to the nearest gallon.290Unit 4 Houghton Mifflin Harcourt Publishing Companyb. If the sod costs 3.25 per square foot,about how much will Robert spendto put sod down in both areas of hisbackyard? Round to the nearest dollar.B 14.66
Math Trainer Online Assessment and Intervention Personal my.hrw.com MODULE QUIZ 10.1 Modeling and Writing Expressions Write each phrase as an algebraic expression. 1. p divided by 6 2. 65 less than j 3. the sum of 185 and h 4. the product of 16 and g 5. Let x represent the numbe
