1-A3 Identity and Equality Properties Alg 1H

Transcription

1 -A Identity and Equality Properties Alg H Identify the IDENTITY OR EQUALITY PROPERTY that is shown in each statement. You may write on this handout. Put the code on the answer line = 8 2. If 5 = + 2, then + 2 = = x = (-)x 5. If = 6 + 5, then = = ( 5) = = 8 9. a + b + 0 = a + b 0. x x. If + a = a + b, then a + b = + a 2. If 0 = 5 5 and 5 5 = 7 7, then 0 = () = 6 4. If = 2 and 2 = 2, then = x y = (5)x + (-)y 6. t + r + 0 = t + r 7. r = r = (x 2y + 6) = x 2y (x + y + z) = 0 8x x 22. If x = 0 and y =, then xy = 0 2. If 7 = 4(x 2) then 4(x 2) = x + 5 = x If 5 x = 0 then 0 = 5 x 26. If x = 2, and x + = y, then 2 + = y 27. If x 2 = y 2, then y 2 = x If x = a + b and a + b = y, then x = y Choose from the following codes: Property Codes A Id Additive Identity M Id Multiplicative Identity MPZ Multiplicative Property of Zero PNO Property of Negative One A Inv Additive Inverse Property M Inv Multiplicative Inverse Prop. Rflx Reflexive Property Sym Symmetric Property Sub. Substitution Property T Transitive Property Explain whether or not each set is closed under the given operation. Use examples. 29. Is the set of odd integers closed under addition? 0. Is the set of positive integers closed under multiplication?. Is the set of even integers closed under multiplication? 2. Is the set of odd integers closed under multiplication?

2 Identify the COMMUTATIVE, ASSOCIATIVE OR DISTRIBUTIVE PROPERTY shown = = ( + 4) + 5 = + (4 + 5) 6. (7 )5 = 7( 5) 7. 2( + 7) = (9 + 4) = 2(4 + 9) 9. a(b + c) = (b + c)a 40. (5 2) = (2 )4 = 4(2 - ) 42. (x + y) + c = c + (x + y) 4. ( + a) + b + c = ( + a + b) + c 44. a + b + c = c + b + a 45. a b c = c a b 46. ( + 4) + 2 = 2 + ( + 4) 47. x + (y + z) = (x + y) + z 48. (x 2) + 4(x 5) = 4(x 5) + (x 2) 49. (a + b) 2(a + b) = a + b 2a 2b 50. (a + b) = (a + b) 5. a + b + 5x + 5y = (a + b) + 5(x + y) 52. a(b + ) + (c + ) = (c + ) + a(b + ) 5. a(b + c)(c + ) = a(c + )(b + c) 54. (a + )( b) + = ( b)(a + ) (a + b) + = + 0(a + b) = 2(8 2) 57. (a + )(b + 2)x = x(a + )(b + 2) 58. ( + c+ d) = + c + d 59. a 2 ( b + 5)(c) = a( b + 5)(ac) 60. (x + y) + (r + s) = x + (y + r) + s Choose from the following codes: Property Codes CA Commutative Property of Add. AA Associative Property of Add. CM Commutative Property of Mult. AM Associative Property of Mult. D Distributive Property Explain whether or not each set is closed under the given operation. Use examples. 6. Is the set of even natural numbers closed under addition? 62. Is the set of odd integers closed under division? 6. Is the set of positive integers closed under subtraction? 64. Is the set of negative integers closed under addition?

3 -A4 Distributive Property and Combining Like Terms DIRECTIONS: Simplify each expression by using the distributive property and then combining like terms. Follow the format given in the example below. Example Problem: 5-2(x - ) x 4x 5 2x 6 4x 6x or 6x step write out the problem as shown optional step 2 change all subtraction to addition of a negative step perform distributive property step 4 combine the "like" terms step 5 circle or box your simplified expression 5 2 x 4x 5 2 x 4 5 2x 6 4x 6x or 6x x Do in Spiral or on Binder Paper.) 7 + (y + 4) + 6y 9.) 2x - 5(x - ) + 8x + 2.) 2-4(x - ) + 5x 0.) 2y(y - 4) + 5(y + ) + y.) x(x - 2) + 5(x + 4).) u(x - 2y) + u(x - z) + 5uy 4.) (x - 2y) - (x - 5y) 2.) 7-2x(5 + z) + 7x - + 8xz 5.) u - 2(u - 4) - 5u.) y - 4(x - 2y) + (2x - 6) ) 8-5(2z - ) + 6z 4.) z(z - 4) - 2(z - 5) z 2 7.) 2 + x(z - 5) + 5xz 5.) u(u - 4) - 4(u - 8) - 6u ) -2 (y - ) - 5(y + ) 6.) 4x(y + ) - 2(x - y) + 6x - 8xy

4 -A5 Review Lessons 6 Chapter Alg. H Do on binder paper. Show Support work! Begin each problem by copying it down. Simplify:.) (5 27) ( 4) 2 2.) 2 + (-) (-).) - 4 [-5 (-7)] 2 4) 2 5 5) -2[ 4(-6) +(-2)] - (-6 + ) 6) -[ 4(-6-2) (-6 + 7)] 7) (-2) + 4[2(-4) + (5 + (-))2] 8) {[5(-2) + 2(-)] 2(-4) + 7} 9) 2 [6(-2) + (- + )9] + 2[7(-4) 4] Evaluate each expression for a = -5, b =, and c = -2. Show support work with parentheses for all substitution. 0.) a b c.) c - a b 2.) b - a - c.) c - b - a Translate each word phrase into an expression, then simplify it. 4.) The difference of 7 and, decreased by 5. 5.) Five times the sum of a and b, decreased by three times b. 6.) Twelve less than four times the sum of x and two. If the problem is a word problem, you do not have to copy down the problem onto your own paper. 7.) Six more than the sum of negative eleven and 5y, increased by one half the difference of 4y and two. Supply the answer for each blank. Write your answers on your binder paper. You do not have to copy down the problems. 8.) The multiplicative property of zero states that any number times zero equals. 9.) The product of negative one and a number will give you the of the number. 20.) The product of a positive number and a negative number is. 2.) The product of two negative numbers is. 22.) The product of a number and it's multiplicative inverse is always. 2.) In the expression x, the coefficient of x is. 24.) Number 2 above is an example of what property?. 25.) The product of a real number and its reciprocal is.

5 26.) The quotient of two negative numbers is. 27.) The reciprocal of a real number is sometimes called its inverse. 28.) The opposite of x + 7 is. 29.) a b is the same as. Choose your answer from these choices: b a, b, a a b 0.) Explain the 4 rules of order of operations.. Simplify:.) x 6 5x + 2.) (a + 2b) 4(a 5b).) ) (5a 2b) 5.) ( 7a 4b) 7 6.) 4 4x 6) 7.) t + 5 2t 7 8.) -(2x ) 5( 4x) 9.) 4(x 5) 5(x + ) 40.) (-a)(-2a)(5b) 4.) (-5)(-x + ) ) -(-5 y) 2(-y + ) 4.) n (n + ) + n 44.) x + 5 2(x ) Write the reciprocal of each number is simplest form. 45.) 46.) 47.) 0.4 Evaluate each expression if a = -2, b = 4, and c = -5. Show support work with parentheses for all substitution. 48.) b( a c) a 49.) ( a 2c) 50.) ( a b c) b

6 -A6 Review Handout #2 for Lessons 6 Chapter Alg. H Do on binder paper. Show support work. Simplify:.) ) 2 5.) ) ) ) ) Evaluate each expression if a = -, b = 4, and c = ) 0.) x 2 a b c 9.) ab bc a What value for x would result in an impossible division? How is that answer written? Name the property shown:.) h + (i + j) = h + (j + i) 2.) a + (0)(b + 4) = a.) xy + 5z yx = 5z 4.) 5 (x + ) = 5 + ( )(x + ) Write an algebraic expression for the following problems: 5.) Twice the sum of b and 8, decreased by 9. 6.) The product of j and k decreased by twice the difference of x and y. 7.) The quotient of and y, minus four times their sum. 8.) 0 less than the product of 2 and w. 9.) The sum of a number and 5, divided by 2. Simplify each expression. Show all steps. 20.) y 2x 2 (-y) 2.) -x 2(- + x) 22.) -a (2a + b) 2.) -x (- + y) 24.) -(-y) 2 25.) -5b 6b 26.) 5 0 5x 27.) -(-x 9) 28.) 0 [2(w ) 2w] 29.) 9[7x + 5(4 + x)] 6x 8 0.) 2 y + 2[6y + (5y + 2)].) 2[ (m + 4n) n] m 2.) 0(2q + p) + 7[2q + 4(q + 9p + 5)].) 4( d + 2e) (d 5e) 4.) 2(t + s) + 7(t s) 5.) [9(v + 4w + ) 4(v + 7)] 5(8v + w) 6.) [ 26p 9q]F H G I K J 7.) (2y 27) 8.) 8 7 ( 2c + 4d) 9.) (6a 24b) F H G I K J 40.) (45u + 8v) 9

7 -A7 Writing Equations for Word Problems Review Handout Alg H Write let statements for each. The second unknown must use the same variable as the first.. Reina is 8cm taller than Patricia. a. Let r = Reina s height in centimeters. Then let = Patricia s height. or b. Let p = Patricia s height in centimeters. Then let = Reina s height. 2. Devin ran times as many laps as Claire did. a. Let d = the numb. of laps Devin ran. Then let = the numb. of laps Claire ran. or b. Let c = the numb. of laps Claire ran. Then let = the numb. of laps Devin ran.. Emily skied a slalom course.67 seconds slower than Lauren. a. Let e seconds = Emily s time. Then let seconds = Lauren s time. or b. Let L seconds = Lauren s time. Then let seconds = Emily s time. Write the missing let statement. 4. Let c = Catherine s age. Rachael is 5 years older than Catherine. 5. Let g = the amount that Greg earned last week. Greg earned $45 more this week than last week. 6. Let p be the number of points the Panthers scored. The Lions scored double the number of points the Panthers scored. 7. Let a be the total amount Amanda spent for blouses. Each of the 5 blouses cost the same. 8. Let b be the amount of money Bryan had before he went shopping. Bryan spent $4.50 while shopping. over ---> -A7 cont. For each of the following, write let statements and equations. Do not solve.

8 9. When 0 is subtracted from the quotient of a number and 4, the difference is 2. What is the number? 0. A carpenter cut a board that was 0 feet long into two pieces. The longer piece was three times the length of the shorter piece. What is the length of each piece?. Joseph is times as old as Lisa. Their combined age is 52. How old is each person? 2. When 5 is added to a certain number and the sum is divided by 4, the quotient is 5. What is the number?. On a street that is 75 m long, a fire hydrant is placed so that it is m farther from one end of the street than from the other end. How far is the hydrant from each end of the street? 4. A hockey team played 86 games and finished only 2 games in a tie. It lost one-sixth as many games as it won. How many games did it win? 5. One of the longer sides of Ann Wong s rectangular lot borders on a straight river. She needs 500 m of fence to fence the three sides not on the river. If the length of the lot is 65 m more than the width, what are the dimensions (length and width) of the lot? 6. The sum of three numbers is 20. The second of the numbers is eight less than the first, and the third number is four more than the first. Find the third number.

9 -A Handout Write an algebraic expression for each verbal expression.. Ten less than the product of 4 and a number cubed. 2. Three-fourths the difference of a number and 2. Evaluate each expression. c h c h 4. 6 a f L NM 2 7 Evaluate each expression if x = 2, y = 8, and z = xy z z 7. F HG I x z ykj 2 2 x y Evaluate each expression for the given values ab for a = 2, b = 9. 2 ab 4 b 2 ab a O QP a2 5f f a f = b for a = 2, 4 = x. x 2 + x x for 4 = b, = a 0. ab for 2. Name the property shown in the example at right. Simplify.. 2x (5x + 7) 20 0c) (6a + c) 2(a (b 5) 8(2b + ) a f Give the definition for a solution to an equation. (hint: See your notes, not your book.) 7. Prove or disprove the following statement (show all work steps): 5 2 is a solution to the equation 27 ax 2f 4 8

10 - A 2 P r a c t i c e S i m p l i f y i n g E q u a t i o n s D O O N B I N D E R P A P E R! S H O W A L L S T E P S! ) 6a c 2 a 0c 2 ) 6 q t 5 q t ) 2 k g k 6g 4 ) r 2 r r 5 ) 6x 4y x 5y 6 ) 2 2 a b 2 b a ) 48r 6 64r 4 8 ) 6 4 8w 7w ) 5z 0w 8w 2z 0 ) d e 6d 9e 8 8 ) p p 2 ) 5h 8 40 h Handout Key:. 20a 2c 2. 2q + t. 2k 4. 7r x + 7y 6. a b 7. 24r 8. w 9. 2w 0. d 2e. 8p T e x t b o o k E v e n A n s w e r s : 6. 4; Additive Identity 8. 0; Multiplicative Prop. of Zero Substitution 0 Mult. Prop. Of Zero 0 Mult. Identity Substitution 46. Simplified 48. 9w 2 + w 50. $ Sample answers: It's not raining; you were not outside; you wore a poncho; you borrowed a friend's umbrella. 54. Rational Numbers ,, 5., and Belinda; her bedroom has an area of more than 7 feet. 62. Hours of study is the independent variable as it is unaffected by the score on the math test, and the score on the math test is the dependent variable as it's affected by hours of study.