Expressions Chapter Questions

Transcription

1 Expressions Chapter Questions 1. Explain how distribution can simplify a problem. 2. What are like terms? 3. How do you combine like terms? NJ Center for Teaching and Learning ~ 1 ~

2 Expressions Chapter Problems Mathematical Expressions Classwork 1) In each expression below, identify the coefficient, constant, and variable. a. 7x + 9 b. 6y 5 c z d. 9w 22 2) Determine if each statement is True or False. If False, determine what needs to be changed in order to make the statement True. a. In 5x 8, 5 is the constant. b. In x 6.5, x is the variable. c. In 9y + 38, 38 is the constant. d. In 2 7z, 7 is the coefficient. e. In 9 3w, 9 is the coefficient. Homework 3) In each expression below, identify the coefficient, constant, and variable. a. 4v + 7 b. 10u 8 c w d x 4) Determine if each statement is True or False. If False, determine what needs to be changed in order to make the statement True. a. In 3b + 9, 9 is the constant. b. In c 2.1, 2.1 is the variable. c. In 2y + 5, 5 is the coefficient. d. In 15 3z, 3 is the coefficient. e. In 11 4w, 11 is the constant. Order of Operations Classwork 5) Simplify each expression using the Order of Operations. a b c. 5 + ( ) d. (5 1) 3 (3 + 2) e f g h i. 21 [110 (6 + 5)] 200 j k. 400 [ ] 2(4 5 6) l m n. 12(10 5) 40 (4 + 1) NJ Center for Teaching and Learning ~ 2 ~

3 o (10+8) (4+5) Homework 6) Simplify each expression using the Order of Operations. a. (11 7) + 3 b c d. 30 (12 2) + 3 e. 2(6 + 4) 4 f. 7 (9 3) 0 g. 2[4 + (9 3)] h. 6( ) 3 1 i. 12 [(12 3) (5 5)] j. k (5+2) l m (1+1) (4+2) n. ( 3 4 5) (4 3) o ) Amy says that the two expressions below are equal. 2 ( ) Is Amy correct when she says that the two expressions have equal values? Explain your answer. Distributive Property Classwork 8) 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 f. ⅝(4x + 12) g. 1.2(3x 7.1) Homework 9) 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 ~ 3 ~

4 e. (x - 2)5 f. ⅔(6x + 12) g. 2.5(3x 4.1) Like Terms Classwork 10) Create a like term for the given term. a. 4x b. 13y c. 15x 2 d. 16xy e. X 11) Simplify the expression if possible. a. 7x + 8x b. 6x + 8y + 2x c. 15x 2 + 5x 2 d. -10y + 4y e. x + 2x f. x 2 + 5x 2 g. 2x + 4x + 3 h. 6y 3y i. 9y + 4y 2y + y 12) Simplify the algebraic expression if possible. a. 7y + 8x + 3y + 2x + 9 b. 6x + 8y - 2x y c. 4x + 7 d. x + 5x + x + 12 e. 8x 3x + 2x + 15 f. 17x + 18x + 3 g. 7y + 8x + 3y + 2x h (x 4)2 4 i. 5x +2(x + 8) j. 9(x + 5) + 7(x 3) k. 8 + (x 4)2 l. 5x +2(x + 8) + 3 m. 9(x - 5) + 7(x + 3) n. 12(x +4) (9x + 3) Homework 13) Create a like term for the given term. a. 6x b. Y c. 10x 2 d. 14xy e. -5x 14) Simplify the expression if possible. a. 15x 2 + 5x 2 + 2x NJ Center for Teaching and Learning ~ 4 ~

5 b. -10y + 4y 5 c. x + 2x + x + 5x d. 6x 2 + 5x 2 e. 12x + 14x + 3y f. 6y 3y + 6xy + 4xy g. 9y + 4y 2y + y h. x + 5x + x x i. 8x 3x + 2x x 15) Simplify the algebraic expression if possible. a. 5x + 4x + 7y + 3y +12 b. 22x + 9y 14 x - 6y c. 25x 15 d. 2x + 42 x + 9x + 13 e. 14x 12x 2x -9 f. 23x + 28x + 11 g. 5x + 7y + 4y + 16x h. 2(x+5) 8 + 5x i. 6x + 5(x + 7) j. 3(4v + 10) + 8(5v + 2) k k+ (7 2k)5 l. 12j + 3(x + 6) + 19 m. 12(x + 0.5) + 14(x + 2) n. 5(2t + 4) (13t 9) Translating Words into Expressions Classwork 16) Translate each phrase into a mathematical expression. a. Twelve more than a number b. A number divided by nine c. Ten decreased by a number d. Double a number e. Five less than six times a number f. The product of four and the sum of a number and seven g. The quotient of a number and ten increased by eleven h. The sum of twenty and a number, divided by two 17) Write each phrase/sentence given below as both a mathematical sentence/phrase and a mathematical expression a. The total amount of money that your mother distributes to you and your 2 siblings, if she gives each person x dollars. b. Your age if you are x years younger than your 15 year old sister. c. How many oranges each person gets if starting with 19 oranges, 4 are eaten, and the rest are divided equally among three friends. d. My speed if I travel m miles in h hours e. The amount of money I make if I earn d dollars per hour and I work for 40 hours. f. The length of my boat if it is 5 feet more than triple the length of my car, which is x feet long. g. Mike earned $12 an hour waiting tables plus $200 in tips. h. Renée s age if she is three years younger than twice her brother, who is b years old NJ Center for Teaching and Learning ~ 5 ~

6 Homework 18) Translate each phrase into a mathematical expression. a. Six less than a number b. A number multiplied by ten c. Eight increased by a number d. Triple a number e. Fifteen more than eleven times a number f. The quotient of five and the difference of a number and three g. The product of a number and twenty decreased by eleven h. The difference of thirty and a number, multiplied by two 19) Write each phrase/sentence given below as both a mathematical sentence/phrase and a mathematical expression a. The total amount of money that your mother distributes to you and your 4 siblings, if she gives each person x dollars. b. Your age if you are x years older than your 8 year old brother. c. How many bananas each person gets if starting with 11 bananas, 1 is eaten, and the rest are divided equally among five friends. d. The length of a rectangle is six inches longer than its width. The width is w inches. e. A dog weighs four pounds more than triple the weight of a cat, whose weight is c pounds. f. The length of my boat if it is 7 feet less than quadruple the length of my car, which is x feet long. g. Samantha earned $13 an hour waiting tables plus $250 in tips. h. Nicole ate 3 more brownies than Haley. Sam ate twice as many brownies as Nicole. If x represents the number of brownies that Haley ate, what is the expression that represents the number of brownies that Sam ate? Evaluating Expressions Classwork 20) Evaluate each expression if a = -3, b = 7 and c = 5 35 a. + 3 c b. 8a b c. (ab 4) 5 d. b 2 c 5 e. (c 2 a 3 ) 2 7 3a f. Homework c 1 g c c 2 b a+c h. ac 21) Evaluate each expression if a = 4, b = -6 and c = 8 48 a. + 7 b b. 12a + 3b c. 2(11 ab) a d. a 2 + b + c e. c 2 3b + 4a f. c 2 4 4a 1 g. b 2 a 3 4c a+b+c h. a+c NJ Center for Teaching and Learning ~ 6 ~

7 Chapter Review Determine whether the given terms are like terms. Circle your response. 22) 3x and -2x Are Like Terms Are Unlike Terms 23) 5a and 5b Are Like Terms Are Unlike Terms 24) 4y and 5xy Are Like Terms Are Unlike Terms 25) x 2 y and xy 2 Are Like Terms Are Unlike Terms 26) 22 and 14 Are Like Terms Are Unlike Terms 27) xy and xy Are Like Terms Are Unlike Terms 28) 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) 29) Simplify the expressions: a. 2x + 3x 7 b. 17b + 9 2b + 16 c. 2x 2 + 4x + 13x 2 + x 2 d. 4(g 5) + 9g e. 12h (6h -5) ) Determine the constant, coefficient, and variable in the expressions below: a. 94w b. 18x 3 c. -5y 7 d z 31) Write an expression to match each phrase given below: a. The sum of a number and ten b. Thirteen less than the quotient of nine and a number c. Nine times the quantity of a number plus four d. Four more than the product of eleven and a number 32) Simplify each expression using the order of operations a (6) 42 6 b (2 + 5) 2 c. (5+7) NJ Center for Teaching and Learning ~ 7 ~

8 33) Evaluate each expression if p = 7, q = -9, and r = 2 a. 63 q r2 b. [(p + r) 2 + pr] 5 c. (q r) 2 4pq r + 5 d. pq 1 + r r 34) Translate each sentence/phrase into a mathematical phrase and then a mathematical expression. a. When Anna babysits, she gets paid $12 per hour. b. In order to get internet access in her home, Audra had to purchase a wireless modem for $50 and pays the cable company $40 per month. c. The width of a rectangle is 8 feet more than a quarter of the length. d. How many tomatoes each person gets if starting with 30, 6 are eaten, and the rest are divided equally among eight friends 35) Write an expression containing three terms that is in simplest form. One of the terms should be a constant. 36) Simplify: 5 2(3x 4) + x 37) 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. NJ Center for Teaching and Learning ~ 8 ~

9 38) Write an expression that has four terms and simplifies to 16x. a) Identify the like terms b) Identify the coefficients c) Identify the constant terms 39) A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: Plan B: $ 40 fee plus $0.45 per minute $70 fee plus $0.35 per minute a) Write an expression to represent the cost of Plan A b) Write an expression to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes? NJ Center for Teaching and Learning ~ 9 ~

10 a. 7 = coefficient, 9 = constant, x = variable b. 6 = coefficient, -5 = constant, y = variable c = coefficient, 4.5 = constant, z = variable d. -9 = coefficient, -22 = constant, w = variable a. False; 5 is the coefficient OR -8 is the constant b. True c. True d. False; -7 is the coefficient e. False; -9 is the constant OR -3 is the coefficient a. 4 = coefficient, 7 = constant, v = variable b. 10 = coefficient, -8 = constant, u = variable c = coefficient, -3.6 = constant, w = variable d = coefficient, -6.1 = constant, x = variable a. True b. False; c is the variable OR -2.1 is the constant c. False; 5 is the constant OR 2 is the coefficient d. False; -3 is the coefficient e. True a. 31 b. 3 c. 24 d. 57 e. 57 f. 32 g. 4 h. 79 i. 11 j. 35 k. 328 l. 4 m. 3 2 = 1.5 n. 52 o. 8 a. 7 b. 32 c d. 6 e. 5 f. 7 Answer Key g. 14 h. -11 i. 3 j. 1 1 k. 4 1 l. 7 m. 2 n. 1 2 o No, Amy is not correct. When you simplify the expression using the Order of Operations, the first expression simplifies to: 2(8 + 25) 3 2(33) and These answers are not equal. 8. a. x+4 b. 8x-16 c. 6x+24 d. x+4 e. 8x x f. 2 2 g. 3.6x a. 5x + 20 b. 7x 84 c. 3x 42 d. x + 2 e. 5x 10 f. 4x +8 g. 7.5x a. Multiple Answers b. Multiple Answers c. Multiple Answers d. Multiple Answers e. Multiple Answers 11. a. 15x b. 8x + 8y c. 20x 2 d. -6y e. 3x f. 6x 2 g. 6x + 3 NJ Center for Teaching and Learning ~ 10 ~

11 h. 3y i. 12y a. 10x + 10y +9 b. 4x + 7y c. 4x + 7 d. 7x + 12 e. 7x + 15 f. 35x + 3 g. 10x + 10y h. 2x + 6 i. 7x + 16 j. 16x + 24 k. 2x l. 7x + 19 m. 16x 24 n. 3x a. Multiple Answers b. Multiple Answers c. Multiple Answers d. Multiple Answers e. Multiple Answers 14. a. 20x 2 + 2x b. -6y -5 c. 9x d. 11x 2 e. 26x + 3y f. 3y + 10xy g. 12y h. 12 i a. 9x + 10y + 12 b. 8x + 3y c. 25x -15 d. 53x + 13 e. -9 f. 51x + 11 g. 21x + 11y h. 7x + 2 i. 11x + 35 j. 52v + 46 k. -8k + 44 l. 12j + 3x + 37 m. 26x + 34 n. -3t a. n + 12 b. n 9 c. 10 n d. 2n e. 6n 5 f. 4(n + 7) g. n h. 20+n Note: phrases may vary a. 3 times x; 3x b. x less than 15 OR 15 minus x; 15 x c. the quantity of 19 minus 4 divided by 3; d. m divided by n; m n e. d times 40; 40d f. 3 times x plus 5; 3x + 5 g. 12 times h plus 200; 12h h. 3 less than twice b; 2b a. n 6 b. n 10 c. 8 + n d. 3n e. 11n f. n 3 g. n h. (30 n) a. 5 times x; 5x b. 8 plus x; 8 + x c. the quantity of 11 minus 1 divided by 5; d. w plus 6; w + 6 e. 3 times c plus 4; 3c + 4 f. 4 times x minus 7; 4x 7 g. 13 times h plus 250; 13h h. the quantity of h plus 3, multiplied by 2; 2(h + 3) 20. a. 10 b. 31 c. 5 d. 48 e. 26 f. 4 g. 0 h a. 1 b. 30 c = 17.5 d. 18 e. 98 f. 4 g. 76 h. 1 2 = 0.5 NJ Center for Teaching and Learning ~ 11 ~

12 Unit Review 22. Like terms 23. Unlike terms 24. Unlike terms 25. Unlike terms 26. Like terms 27. Like terms 28. B 29. a. 5x 7 b. 15b + 25 c. 16x 2 + 4x d. 13g 20 e. 6h a. 103 = constant, 94 = coefficient, w = variable b. -3 = constant, 18 = coefficient, x = variable c. -7 = constant, -5 = coefficient, y = variable d. 16 = constant, -24 = coefficient, z = variable 31. a. n + 10 b. 9 n 13 c. 9(n + 4) d. 11n a. 32 b. 21 c a. 11 b. 19 c. 252 d a. 12 times h 12h b. 40 times m plus 50 40m + 50 c. ¼ times l plus l + 8 d. the quantity of 30 minus 6, divided by Answers will vary x a. 25 2g b Answers will vary 39. a m b m c. Plan A NJ Center for Teaching and Learning ~ 12 ~