Expressions Chapter Questions. 3. Can you name 3 words that indicate each operation (addition, subtraction, multiplication and division)?

Transcription

1 Expressions Chapter Questions 1. How can the order of operations easily be remembered? 2. Why is it important to have an order to the operations? 3. Can you name 3 words that indicate each operation (addition, subtraction, multiplication and division)? 4. How do you evaluate an expression? 5. Explain how distribution can simplify a problem. 6. What are like terms? 7. How do you combine like terms? NJ Center for Teaching and Learning ~ 1 ~

2 Expressions Chapter Problems Mathematical Expressions Classwork 1. Circle the constant and underline the coefficient for each expression below a. 5x 3 b. 2x + 7 c. 2 4x d. x Create an algebraic expression with a coefficient of 7 and a constant of Create an algebraic expression with a coefficient of -1 and a constant of Create an equation that contains a coefficient of Create an equation that contains a coefficient of -13. Homework 6. Circle the constant and underline the coefficient for each expression below a. 3x 5 b. 2x - 1 c. 7 8x d. x Create an algebraic expression with a coefficient of 17 and a constant of Create an algebraic expression with a coefficient of -1 and a constant of Create an equation that contains a coefficient of Create an equation that contains a constant of -12. Order of Operations Classwork x = x = NJ Center for Teaching and Learning ~ 2 ~

3 x 12 = = 15. (7 4) 2 x 3 = x 2 x 2 2 = x 5 = 18. (1 + 4) 5 = (3 1) = 20. (8 + 8) x 3 = 21. (7 4) x 2 (5 3) = 22. [(6 3) x 2] 3 = 23. a. Simplify the expression: 5 x 6 6 = b. Add parentheses to the expression so that it simplifies to a different answer. 24. a. Simplify the expression: = b. Add parentheses to the expression so that it simplifies to a different answer. 25. Your brother buys 3 shirts for $9 each. He also buys a pair of jeans for $25.00 that gets a $4.00 discount. How much does he spend? 26. The repairman charged $36 for parts and $12 per hour for labor to repair a bicycle. If he spent 3 hours repairing the bike, what will the total repair bill be? Homework x 5 = x 2 = x x = x = x 5 = x = x x 3 2 = 34. (9 3) x 6 = 35. (8 + 4) 3 2 = 36. (2 + 8) x (7 3) = ( ) = 38. [20 (10 4)] (8 1) = NJ Center for Teaching and Learning ~ 3 ~

4 39. a. Simplify the expression: = b. Add parentheses to the expression so that it simplifies to a different answer. 40. a. Simplify the expression: 22 6 x 2 = b. Add parentheses to the expression so that it simplifies to a different answer. 41. A landscaping company charges $75 for spring yard clean-up and then $25 each time the grass is cut. If you plan on having the yard cleaned up in the spring, plus the lawn cut 11 times, how much will it cost? 42. At the clothing store you buy 3 pairs of jeans for $22 each and 4 shirts for $8.50 each. You also have a $20 off coupon. How much do you spend? Distributive Property Classwork 43. Use the Distributive Property to rewrite the expressions without parentheses a. (x + 4) b. 8(x 2) c. 6(x + 4) d. 1(x 4) e. (x + 2)8 44. Marla did 65 sit-ups each day for one week. Write an expression using the Distributive Property to find the total number of sit-ups Marla did during the week. Solve the expression. 45. Tickets for the school play cost $9 each. Tessa wrote the expression 9 x 26 to find the cost of 26 tickets to the play. Tessa used the Distributive Property to find the product. Write Tessa s expression after she used addition and the Distributive Property. Homework 46. Use the Distributive Property to rewrite the expressions without parentheses a. 5(x + 4) b. 7(x 12) c. 3(x - 14) d. 1(x 2) NJ Center for Teaching and Learning ~ 4 ~

5 e. (x - 2)5 47. Coach Brown bought 6 basketballs for $16 each and 6 footballs for $24 each. The expression 6 x x 24 gives the total cost in dollars of the basketballs and footballs. Use the Distributive Property to write this expression another way. Then evaluate. 48. Jessica took her mother to a movie. She paid $9 each for 2 tickets, $4 each for 2 nachos, and $3 each for 2 bottles of water. Use the Distributive Property to show two different ways to solve the problem. How much did she spend? Like Terms Classwork 49. Create a like term for the given term. a. 4x b. 13y c. 15x 2 d. 16xy e. x 50. Simplify the expression if possible by combining like terms. a. 7x + 8x b. 6x + 8y + 2x c. 15x 2 + 5x 2 d. 5x +2(x + 8) e. 10y + 4y f. 9(x + 5) + 7(x 3) g. 8 + (x 4)2 h. 7y + 8x + 3y + 2x i. x + 2x j. x 2 + 5x 2 k. 2x + 4x + 3 l. 6y 3y m. 9y + 4y 2y + y n. x + 5x + x + 12 o. 8x 3x + 2x + 15 Homework 51. Create a like term for the given term. a. 6x b. y c. 10x 2 d. 14xy e. 5x NJ Center for Teaching and Learning ~ 5 ~

6 52. Simplify the expression if possible by combining like terms. a. 17x + 18x + 3 b. 6x + 8y - 2x y c. 15x 2 + 5x 2 + 2x d. 5x +2(x + 8) + 3 e. 10y + 4y 5 f. 9(x + 5) + 7(x + 3) g (x 4)2 4 h. 7y + 8x + 3y + 2x + 9 i. x + 2x + x + 5x j. 6x 2 + 5x 2 k. 12x + 14x + 3y l. 6y 3y + 6xy + 4xy m. 9y + 4y 2y + y + y 2 n. x + 5x + x x o. 8x 3x + 2x y Translating between Words & Expressions Classwork Translate the words into an algebraic expression times x 54. The sum of x and The product of 9 and y 56. w less than more than x 58. The difference of 6 and x times the product of x and The product of 5 and y, divided by The quotient of 300 and the quantity of x times x less than The quotient of 35 and the quantity of x minus The product of 7 and x, minus the quantity of 4 less than y 65. The quantity of 9 more than x divided by the quantity of 12 less than y 66. Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price, given the child ticket price. NJ Center for Teaching and Learning ~ 6 ~

7 Child Ticket Price Adult Ticket Price $5 $7 $10 $ Write an expression that represents the adult price, if the child price is x 68. For NJASK testing, 25 students are placed in each classroom. Determine the number of classrooms needed, given the number of students testing. Number of Students Testing Number of Classroom Needed Write an expression that represents the number of classrooms needed, if the number of students testing is x 70. Mary has ½ the amount of money that Jim has. Determine the amount of money that Mary has, given Jim s amount of money. Jim s Amount of Money Mary s Amount of Money $50 $100 $175 $ Write an expression that represents the amount of money Mary has, given the amount of Jim s money. 72. Each person running in the race paid $20. Determine the amount of money collected, given the amount of people running in the race. Number of People Running Amount of Money Collected Write an expression that represents the amount of money collected, given the number of people running in the race. NJ Center for Teaching and Learning ~ 7 ~

8 Write an expression for each of the following situations. 74. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob s weight: 75. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany s money: 76. Samantha has 12 more stickers than Mike. Mike has x stickers. Samantha s sticker amount: 77. The recipe calls for twice the amount of sugar than flour. There is f amount of flour in the recipe. Amount of sugar: 78. Mark s quiz grade is one more than twice Ted s quiz grade. Ted s quiz grade is x. Mark s quiz grade: 79. Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth s prom gown price: 80. David ran the 5k in x minutes. Harry ran the same race in five minutes less than double David s time. Harry s time: 81. The beans grew k inches. The tomatoes grew 3 inches more than triple the height of the beans. Tomato height: Create a scenario for the following expressions: 82. x (x 3) Homework Translate the words into an algebraic expression. 84. The product of 14 and x 85. The quotient of x and The sum of 19 and w 87. w less than less than x NJ Center for Teaching and Learning ~ 8 ~

9 89. The difference of 16 and y times the quotient of x and The product of 6 and x, less The quotient of 100 and the sum of x and x less than The product of 5 and the quantity of x less than The product of 27 and y, divided by the quantity of 4 more than y 96. The quantity of 6 less than x divided by the quantity of 2 more than y Homework 97. Child ticket prices are $3 less than adult ticket prices. Determine the child ticket price, given the adult ticket price. Adult Ticket Price Child Ticket Price $10 $15 $20 $ Write an expression that represents the child price, if the adult price is x 99. For busing, 40 students are assigned to each bus. Determine the number of buses needed, given the number of students riding. Number of Students Riding Number of Buses Needed Write an expression that represents the number of buses needed, if the number of students riding is x NJ Center for Teaching and Learning ~ 9 ~

10 101. The farm always has four times the number of chicks as hens. Determine the number of chicks, given the number of hens. Number of Hens Number of Chicks Write an expression that represents the number of chicks, given the number of hens Each person running in the race will eat two hotdogs. Determine the number of hotdogs needed, given the amount of people running in the race. Number of People Running Number of Hotdogs needed Write an expression that represents the number of hotdogs needed, given the number of people running in the race. Write an expression for each of the following situations Bob weighs 17 pounds less than Jack. Jack weighs x pounds. Bob s weight: 106. Tiffany has 50 dollars more than Jessica. Jessica has x dollars. Tiffany s money: 107. Samantha has 12 times as many stickers than Mike. Mike has x stickers. Samantha s sticker amount: 108. The recipe calls for triple the amount of sugar than flour. There is f amount of flour in the recipe. Amount of sugar: 109. Mark s quiz grade is six more than double Ted s quiz grade. Ted s quiz grade is x. Mark s quiz grade: NJ Center for Teaching and Learning ~ 10 ~

11 110. Laura paid x dollars for her prom dress. Beth paid 16 dollars more than Laura. Beth s prom gown price: 111. David ran the 5k in x minutes. Harry ran the same race in half the time that David ran the race. Harry s time: 112. The beans grew k inches. The tomatoes grew triple the height of the beans, less 2 inches. Tomato height: Create a scenario for the following expressions: (x + 3) 114. x - 4 Evaluating Expressions Classwork 115. Evaluate the expression for the given value a. (2n + 1) 2 for n = 3 b. 2(n + 1) 2 for n = 4 c. 2n for n = 3 d. 4x + 3x for x = 5 e. 3(x 3) for x = 7 f. 8(x + 5)(x 2) for x = 4 g. 3x 2 for x = 2 h. 5x + 45 for x = 6 i. 4x for x = 10 5 j. 4y + x for x = 2 and y = 3 k. x + 17 for x = 12 and y = 2 y l. 6x + 8y for x = 9 and y = ¼ m. x + (2x 8) for x = 10 n. 5(3x) + 8y for x = 2 and y = 10 Homework 116. Evaluate the expression for the given value a. (2n + 1) 2 for n = 1 b. 2(n + 1) 2 for n = 3 c. 2n for n = 5 d. 4x + 3x for x = 6 e. 3(x 3) for x = 3 f. 8(x + 5)(x 2) for x = 6 NJ Center for Teaching and Learning ~ 11 ~

12 g. 3x 2 for x = 8 h. 5x + 45 for x = 3 i. 4x for x = 15 5 j. 4y + x for x = 12 and y = 13 k. x + 17 for x = 2 and y = 2 y l. 6x + 8y for x = 8 and y = ¾ m. x + (2x 8) for x = 11 n. 5(3x) + 8y for x = 12 and y = 5 NJ Center for Teaching and Learning ~ 12 ~

13 Expressions Unit Review Determine whether the given terms are like terms. Circle your response. 1. 3x and -2x Are Like Terms Are Unlike Terms 2. 5a and 5b Are Like Terms Are Unlike Terms 3. 4y and 5xy Are Like Terms Are Unlike Terms 4. x 2 y and xy 2 Are Like Terms Are Unlike Terms and 14 Are Like Terms Are Unlike Terms 6. xy and xy Are Like Terms Are Unlike Terms 7. Match the expression 3(-4 + 3) with an equivalent expression. a. 4(3) + 4(3) b. 3(-4) + 3(3) c. 4(3) - 4(3) d. 3(4) + 3(3) 8. Which algebraic expression represents the number of days in w weeks? a. w 7 w b. 7 c. w + 7 d. 7w 9. Which algebraic expression represents the number of hours in m minutes? a. m 60 m b. 60 c. m + 60 d. 60m 10. In the expression 3x + 5, the value of 3 is best described as: a. the constant b. the operation c. the variable d. the coefficient NJ Center for Teaching and Learning ~ 13 ~

14 11. In the expression 2x + 16, the value of 16 is best described as: a. the coefficient b. the variable c. the operation d. the constant 12. Evaluate the expression 2x, when x = 10 a. 20 b. 12 c. 210 d What operation is being performed between the coefficient and variable in the expression 20 x? a. addition b. division c. subtraction d. multiplication 14. A group of 15 parents buys tickets to a fundraiser show and receives a group discount of $2 off the regular ticket price p. Which expression represents the total cost of the tickets, in dollars? a. 15 p + 2 b. 15 (p - 2) c. p d. p (15-2) 15. A music store sells CDs for $15 and tapes for $3. Which expression could be used to find the dollar total of the sales for an hour if the store sold 8 CDs and 5 tapes? a. (8 + 15) (5 + 3) b. (8 15) + (5 3) c. (8 3) + (5 15) d. (15 8) + (5 3) NJ Center for Teaching and Learning ~ 14 ~

15 16. There were three times as many adults as students attending a school play. If the attendance was 480, how many adults and how many students attended the play? a. 360 students 120 adults b. 240 students 240 adults c. 120 students 360 adults d. 160 students 320 adults 17. Use the distributive property to rewrite the expression without parentheses: 7(x 8) a. 7x 8 b. x 56 c. 7x + 56 d. 7x What is the value of the expression x + y when x = 15 and y = 21? a. 6 b. 30 c. 36 d Collect the like terms: 5x 2 + 2x + x 2 + 9x 3 a. 13x b. 13x 2 c. 17x 3 d. 6x x Claire has had her driver s license for three years. Bill has had his license for b fewer years than Claire. Which expression can be used to show the number of years Bill has had his driver s license? a. 3 + b b. b + 3 c. 3 - b d. b < 3 NJ Center for Teaching and Learning ~ 15 ~

16 21. Which situation is best modeled by the expression 25 x? a. George places x more video games on a shelf with 25 games b. Sarah has driven x miles of a 25 mile trip c. Amelia paid $25 of an x dollar lunch she shared with Ariel d. George has 25 boxes full of x baseball cards each (11 9 ) a. > b. < c. = 23. Nine decreased by the quantity eight times a number x. a. 8x - 9 b. 9 8x c. 9x - 8 d. 8 9x 24. Four more than the quotient of 25 and y. a. b. c. d. 25 y + 4 y y y What is the coefficient of x in the expression 4y x? a. 5 b. 1 c. -1 d A rectangle is 6 inches longer than it is wide. Write and simplify an expression for the perimeter of the rectangle in terms of the width w. NJ Center for Teaching and Learning ~ 16 ~

17 27. You and a friend worked in the school store last week. You worked 4 hours less than your friend. Let h be the number of hours your friend worked. Write an expression in simplest form that represents the total number of hours you both worked. 28. A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is three times the amount of M&Ms; and the amount of raisins is two times the amount of M&Ms. Let m represent the amount of M&Ms. Write and simplify an expression for the total number of pieces of food in the trail mix. 29. Simplify: 5 + 2(3x + 4) + x 30. Evaluate the expression 5 9 (F 32) when F = 41 NJ Center for Teaching and Learning ~ 17 ~

18 31. At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she plays. a) Write an expression for the number of tokens Jenny has left after playing g games. b) Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games. 32. Bob wants to go to the movies with his friends. The movie theater charges $8 per ticket. Bob s friends reserve $48.00 worth of tickets in advance. How many people in total can attend the movie? a) Identify the variable b) Identify the constant c) Write an equation which includes the number of people attending the movie, the price of each ticket, and the total cost of the movie. 33. Write an expression that has four terms and simplifies to 16x+ 5. a) Identify the like terms b) Identify the coefficients c) Identify the constant terms NJ Center for Teaching and Learning ~ 18 ~

19 34. Simplify the expression: a) x 2 6 (Show all steps) b) Add parentheses to the expression so that it simplifies to a different answer. (Show all steps) c) Explain why parts a and b have a different answer. NJ Center for Teaching and Learning ~ 19 ~

20 Answer Key 1) 30) 21 a. constant: -3, coefficient: 5 31) 54 b. constant: 7, coefficient: 2 32) 30 c. constant: 2, coefficient: -4 33) 14 d. constant: 3, coefficient: 1 2) 7x ) 36 3) x ) 2 4) Multiple answers; ex: 6x + 1 = 5 36) 40 5) Multiple answers; ex: -13x + 1 = 7 37) 9 6) 38) 2 a. constant: -5, coefficient: 3 39) b. constant: -1, coefficient: 2 a. 7 c. constant: 7, coefficient: -8 d. constant: 2, coefficient: 1 b. (3 + 12) 3 = 5 7) 17x ) 8) x - 1 a. 10 9) Multiple answers; ex: 4x + 2 = 10 b. (22 6) x 2 = 32 10) Multiple answers; ex: -12x + 2 = 15 41) (25) = $350 11) 27 42) 3(22) + 4(8.5) - 20 = $80 12) 42 43) 13) 37 a. x ) 79 b. 8x ) 27 c. 6x ) 65 d. x ) 56 e. 8x ) 7(60 + 5) = 7(60) + 7(5) = = 18) ) 3 45) 9(20 + 6) = 9(20) + 9(6) = = 20) ) 3 46) 22) 2 a. 5x ) b. 7x - 84 a. 24 c. 3x - 42 d. x - 2 b. 5 x (6-6) = 0 e. 5x ) 47) 6(16+24) = 6(40) = 240 a ) 2(9) + 2(4) + 2(3) = 2( ) = b. 9 (1 + 9) = (16) = 32 25) 3(9) + (25-4) = $48 49) 26) (12) = $72 a. Multiple Answers, ex: 6x b. Multiple Answers, ex: 26y 27) 32 c. Multiple Answers, ex: 3x 2 28) 19 d. Multiple Answers, ex: 4xy 29) 110 e. Multiple Answers, ex: 5x NJ Center for Teaching and Learning ~ 20 ~

21 50) a. 15x b. 8x + 8y c. 20x 2 d. 7x + 16 e. 14y f. 16x + 24 g. 2x h. 10y + 10x i. 3x j. 6x 2 k. 6x + 3 l. 3y m. 12y n. 7x + 12 o. 7x ) a. Multiple Answers, ex: 7x b. Multiple Answers, ex: 3y c. Multiple Answers, ex: 8x 2 d. Multiple Answers, ex: 9xy e. Multiple Answers, ex: 3x 52) a. 35x + 3 b. 4x + 7y c. 20x 2 + 2x d. 7x ) x ) e. 14y - 5 f. 16x + 66 g. 2x + 6 h. 10y + 10x + 9 i. 9x j. 11x 2 k. 26x + 3y l. 3y + 10xy m. 12y + y 2 n. 12 o. 7x y 53) 4x 54) x ) 9y 56) 8 - w 57) 5 + x 58) 6 - x 59) 9(4x) 60) 5y 3 61) 300 2x 62) 32 - x 63) 35 x 7 64) 7x - (y - 4) 65) x+9 y 12 Child Ticket Price Adult Ticket Price $5 $8 $7 $10 $10 $13 $12 $15 Number of Students Testing Number of Classroom Needed ) x 25 69) Jim s Amount of Money Mary s Amount of Money $50 $25 NJ Center for Teaching and Learning ~ 21 ~

22 $100 $50 $175 $87.50 $220 $110 70) x 2 71) Number of People Running Amount of Money Collected 150 $3, $4, $8, $10,400 72) 20x 73) x ) x ) x ) 2f 77) 2x ) x ) 2x ) 3k ) Multiple Answers 82) Multiple Answers 83) 14x x 84) 96) 5 85) 19 + w 86) 8 - w 87) x ) 16 - y 89) 9( x 20 ) 90) 6x ) 100/(x + 2) 92) 2 - x 93) 5(7 - x) 94) 27y y+4 95) x 6 y+2 Adult Ticket Price Child Ticket Price $10 $7 $15 $12 $20 $17 $25 $22 97) x ) Number of Students Riding Number of Buses Needed ) x ) NJ Center for Teaching and Learning ~ 22 ~

23 Number of Hens Number of Chicks ) 4x 102) Number of People Running Number of Hotdogs needed ) 2x 104) x ) x ) 12x 107) 3f 108) 2x ) x + 16 x 110) 2 111) 3k ) Multiple Answers 113) Multiple Answers 114) a. 49 b. 50 c. 10 d. 35 e. 12 f. 144 g. 12 h. 75 i. 8 j. 14 k. 23 l. 56 m. 22 n ) a. 9 b. 32 c. 14 d. 42 e. 0 f. 352 g. 192 h. 60 i. 12 j. 64 k. 18 l. 54 m. 25 n. 220 Expressions Unit Review Answer Key 1. Are Like Terms 2. Are Unlike Terms 3. Are Unlike Terms NJ Center for Teaching and Learning ~ 23 ~

24 4. Are Like Terms 5. Are Like Terms 6. Are Like Terms 7. b 8. d 9. b 10. d 11. d 12. a 13. b 14. b 15. b 16. c 17. d 18. c 19. d 20. c 21. b 22. b 23. b 24. a 25. c 31. a. 25-2g b. 25-2(1) = 23 tokens left after 1 game 25-2(4) = 17 tokens left after 4 games 25-2(6) = 13 tokens left after 6 games 25-2(10) = 5 tokens left after 10 games 25-2(12) = 1 token left after 12 games 26. w+w+(w + 6)+(w+6) 4w h + (h - 4) 2h m + 2m + m 6m x x 7x a. Variable: p = number of people b. Constant: 8 (dollars per ticket) c. 8p = a. Answers will vary; for example 4(4x + 3) -7 b. Like Terms: All terms that contain x are like terms; all numerical terms are like terms c. Coefficients: The numbers with x in the x terms d. Constants: The numbers in the numerical terms. a x 2 6 = 15 b. (15 + 3) x 2 6 = 30 c. The parentheses cause you to do the addition prior to the multiplication. NJ Center for Teaching and Learning ~ 24 ~