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1 - Practice Form G Variables and Expressions Write an algebraic expression for each word phrase.. 0 less than x. 5 more than d x 0 5 d. 7 minus f. the sum of and k 7 f k 5. x multiplied by 6 6. a number t divided by x? 6 t 7. one fourth of a number n 8. the product of.5 and a number t n.5? t 9. the quotient of 5 and y 0. a number q tripled 5 y q?. plus the product of and h. less than the quotient of 0 and x? h 0 x Write a word phrase for each algebraic expression.. n 6. 5 c 5..5 y 6. the sum of n and 6 5 less than c the sum of.5 and y x 7 7. x x 7z 7 less than the 0 more than the the sum of 0x and 7z quotient of x and product of and x Write a rule in words and as an algebraic expression to model the relationship in each table. 9. The local video store charges a monthly membership fee of $5 and $.5 per video. Videos (v) Cost (c) $7.5 $9.50 $.75 $5 plus $.5 times the number of videos; 5.5v Prentice Hall Gold Algebra Teaching Resources

2 - Practice (continued) Form G Variables and Expressions 0. Dorothy gets paid to walk her neighbor s dog. For every week that she walks the dog, she earns $0. Weeks (w) 5 6 Pay (p) $0.00 $50.00 $60.00 $0 times the number of weeks; 0w Write an algebraic expression for each word phrase.. 8 minus the quotient of 5 and y 8 5 y. a number q tripled plus z doubled q z. the product of 8 and z plus the product of 6.5 and y 8z 6.5y. the quotient of 5 plus d and minus w 5 d w 5. Error Analysis A student writes 5y? to model the relationship the sum of 5y and. Explain the error. The word sum indicates that addition should be used and not multiplication. The student has used the multiplication symbol instead of the. 6. Error Analysis A student writes the difference between 5 and the product of 5 and y to describe the expression 5y 5. Explain the error. The number 5 should be first and the expression should be written 5 5y. 7. Jake is trying to mail a package to his grandmother. He already has s stamps on the package. The postal worker tells him that he s going to have to double the number of stamps on the package and then add more. Write an algebraic expression that represents the number of stamps that Jake will have to put on the package. s Prentice Hall Gold Algebra Teaching Resources

3 - Practice Form G Order of Operations and Evaluating Expressions Simplify each expression Q 5 6 R Q 5 R 5. ( ) 6 6. (0.) () 8. Q 6 R (5) 9. (5) () 0. 7(). Q 0 5 R 0() Q 8 R 7. ((5)) Q (6) 7 5 R 8 6 Evaluate each expression for s 5 and t s t s s 7 0. (t) s t. (s) t 5. Q s 5t R s(). Q 5(t) R 9 6 5,65 or Every weekend, Morgan buys interesting clothes at her local thrift store and then resells them on an auction website. If she brings $50.00 and spends s, write an expression for how much change she has. Evaluate your expression for s 5 $7. and s 5 $ s; $.87; $9.86 Prentice Hall Gold Algebra Teaching Resources

4 - Practice(continued) Form G Order of Operations and Evaluating Expressions 6. A bike rider is traveling at a speed of 5 feet per second. Write an expression for the distance the rider has traveled after s seconds. Make a table that records the distance for.0, 5.8,., and.0 seconds. d 5 5.0s Time (s) Distance (ft) Simplify each expression. 7. f( 5) g 8. f( 6) 7g 9..5f Q 6 6 R g f(8 8) 7g. Q ()() 5() R. f (55 5 ) g 9,9, a. If the tax that you pay when you purchase an item is % of the sale price, write an expression that gives the tax on the item with a price p. Write another expression that gives the total price of the item, including tax. 0. p; 0.p p; b. What operations are involved in the expressions you wrote? multiplication and addition c. Determine the total price, including tax, of an item that costs $75. $8 d. Explain how the order of operations helped you solve this problem. First you have to multiply 0. by p to determine the tax, then you have to add the tax to the original sale price.. The cost to rent a hall for school functions is $60 per hour. 60 h Write an expression for the cost of renting the hall for h hours. Make a table to find how much it will cost to rent Hours Rental Charge the hall for, 6, 8, and 0 hours Evaluate each expression for the given values of the variables. 5. (c 5) f ; c 5, f 5 6. f(w 6) xg ; w 5 5, x fh Q j 6 R g; h 5, j 5 8. xfy (55 y 5 ) g; x 56, y ,658 Prentice Hall Gold Algebra Teaching Resources

5 - Practice Form K Real Numbers and the Number Line Simplify each expression..!.!5 5.!69.!9 7 5.! ! Å Å ! ! Estimate the square root. Round to the nearest integer..!8 6.!65 8.!99 0.!5.5 5.! !6.6 8 Find the approximate side length of each square figure to the nearest whole unit. 7. a tabletop with an area 5 ft 5 ft 8. a wall that is 05 m 0 m Prentice Hall Foundations Algebra Teaching Resources 5

6 - Practice (continued) Form K Real Numbers and the Number Line Name the subset(s) of the real numbers to which each number belongs. 9. rational π rational, integer irrational. 5,68.!. rational, natural, whole, integer irrational Compare the numbers in each exercise using an inequality symbol. 5.!6,!9 6.,!.5 rational!6 R!9 R!.5 7.!00,! ,.8!00 S!69 9 R.8 Order the numbers in each exercise from least to greatest ,!5,!6 0..5,,!.5.!6,.75,!5 80 5, 0.6,!. 5,!9, , 5,!,!.5,.5!9, 80 5, 0 9. Kate, Kevin, and Levi are comparing how fast they can run. Kate was able to run 5 miles in 7.5 minutes. Kevin was able to run 8 miles in 7 minutes. Levi was able to run miles in minutes. Order the friends from the fastest to the slowest. Levi, Kevin, Kate Prentice Hall Foundations Algebra Teaching Resources 6

7 - Practice Form K Properties of Real Numbers Match statements 8 with the property, a h, that the statement illustrates. a Commutative Property of Addition: a b 5 b a b. Commutative Property of Multiplication: a? b 5 b? a c. Additive Identity: a 0 5 a d. Multiplicative Identity: a? 5 a e. Associative Property of Addition: (a b) c 5 a (b c) f. Associative Property of Multiplication: (a? b)? c 5 a? (b? c) g. Zero Property of Multiplication: a? h. Multiplicative Property of :? a 5 a a. 5? g. 5? x 5 x? 5 b. (x? )? 5 x? (? ) f 5. m 0 5 m c 6. 5? 5 5 d 7. (5 9) 5 5 (9 ) e 8.? 6 56 h Simplify each expression. Justify each step that has not been justified (x ) 5 5 ( x) Commutative Property of Addition 5 (5 ) x Associative Property of Addition 5 7 x Combine like terms. 0.? (x? 6) 5? (6? x) Commutative Property of Multiplication 5 (? 6)? x Associative Property of Multiplication 5 8x Multiply. Prentice Hall Foundations Algebra Teaching Resources 5

8 - Practice (continued) Form K Properties of Real Numbers Simplify each expression. Justify each step.. ( 7m) 5. 9? (r? ) 5 (7m ) 5 Commutative Property of Addition 5 7m ( 5) Associative Property of Addition 5 7m 7 Combine like terms. Tell whether the expressions in each pair are equivalent.. x and x?. (5 )? x and x equivalent b and 8 6b 6. 5? ( ) and 0 not equivalent 7. You have prepared 0 ml of vanilla, 0 ml of chocolate, and 50 ml of milk for a milkshake. a. How many milliliters of milkshake will you have if you first pour the vanilla, then the chocolate, and finally the milk into your glass? 0 ml b. How many milliliters of milkshake will you have if you first pour the chocolate, then the vanilla, and finally the milk into your glass? 0 ml c. Explain how you can tell whether the amounts of milkshake described in parts (a) and (b) are equal. Commutative Property of Addition Use deductive reasoning to tell whether each statement is true or false. If it is false, give a counterexample. 8. For all real numbers a and b, a b 5 b a. False 7 u 7 9. For all real numbers p, q, and r, p q r 5 p r q. True 0. For all real numbers x, y, and z, (x y) z 5 z (x y). True. For all real numbers n, n 5 n. False 8 u 8 5 9? (? r) Commutative Property of Multiplication 5 (9? )? r Associative Property of Multiplication 5 89r Multiply. equivalent equivalent. Writing Explain why the commutative and associative properties do not hold true for subtraction and division. Answers will vary. Counterexamples: 5 u 5; (5 ) u 5 ( ); 6 u 6; ( 6) u (6 ) Prentice Hall Foundations Algebra Teaching Resources 6

9 -5 Practice Form G Adding and Subtracting Real Numbers Use a number line to find each sum () 5. 6 () (0) (7) 8. 9 (9) Find each sum. 0. () 8. 6 () (0) 5. 8 (8) (6.7) (7.) Q 5 9 R 0. Q 8 R Writing Explain how you would use a number line to find 6 (8). Answers may vary. Sample: Start at 0. Move 6 spaces to the right and then 8 spaces to the left. The answer is.. Open-Ended Write an addition equation with a positive addend and a negative addend and a resulting sum of 8. Answers may vary. Sample: The Bears football team lost 7 yards and then gained yards. What is the result of the two plays? a gain of 5 yd Prentice Hall Gold Algebra Teaching Resources

10 -5 Practice (continued) Form G Adding and Subtracting Real Numbers Find each difference (6) 8. () (5) 0..7 (.8) (.) Q 8 R Q R Evaluate each expression for m 5, n 5 5, and p m p m n p n m p At :00 a.m., the temperature was 98F. At noon, the temperature was 88F. What was the change in temperature? 7 degrees. A teacher had $57.7 in his checking account. He made a deposit of $09.5. Then he wrote a check for $7.00 and another check for $7.50. What is the new balance in his checking account? $ A scuba diver went down 0 feet below the surface of the water. Then she dove down more feet. Later, she rose 7 feet. What integer describes her depth? 6. Reasoning Without doing the calculations, determine whether 7 () or 7 () is greater. Explain your reasoning. 7 () is greater; 7 () is the same as 7 which is greater than 7 (). Prentice Hall Gold Algebra Teaching Resources

11 -6 Practice Form G Multiplying and Dividing Real Numbers Find each product. Simplify, if necessary.. 5(7). 8(). 9? (9) (9) (.) 8. (0.6) 9. 8(.) ? 9. 5 Q 5 8 R. Q R 6 9. After hiking to the top of a mountain, Raul starts to descend at the rate of 50 feet per hour. What real number represents his vertical change after hours? 55 ft. A dolphin starts at the surface of the water. It dives down at a rate of feet per second. If the water level is zero, what real number describes the dolphin s location after seconds? 0 ft Simplify each expression. 5.!600 6.!65 7.!0, w00 8.!0.8 9.!. 0.! w. 0.. % 9 w. % % 00 0 Prentice Hall Gold Algebra Teaching Resources 5

12 -6 Practice (continued) Form G Multiplying and Dividing Real Numbers. Writing Explain the differences among!5,!5, and!5. There are square roots of 5, 5 and 5.!5 represents the positive square root and!5 represents the negative square root, and w!5 represents both square roots. 5. Reasoning Can you name a real number that is represented by!6? Explain. no; There is no number that can be multiplied by itself and have a negative product. Find each quotient. Simplify, if necessary (5) () 0. 9 () ().8..7 (0) Q 9 0 R Evaluate each expression for a 5, b 5, and c ab 9. b c 0. a c 8 8. Writing Explain how you know that 5 and 5 are multiplicative inverses. Because 5 5 5, the two numbers are multiplicative inverses.. At 6:00 p.m., the temperature was 55 F. At :00 p.m. that same evening, the temperature was 0 F. What real number represents the average change in temperature per hour? 8 F/h Prentice Hall Gold Algebra Teaching Resources 5

13 -7 Practice Form G The Distributive Property Use the Distributive Property to simplify each expression.. (h 5). 7(5 m). (6 9v)6. (5n ) h 5 7m 5 5v 6 60n (8 a) 6. 5(y 5) 7. (x ) 8. (7 6w)6 9. ( 9p). 0. (b 0).. (z ). Q t 5R 9.9p 5. 6.b z t 0. (5x )(5.). Q r 5 7 R 5. 0(6.85j 7.65) 6. Q m R 5.5x 7. r 5 7 Write each fraction as a sum or difference. 7. 0a 60 n 5 7 n y 75 6x 9 9 6x 9 x j d 5 6 d 5 6 6w 9 m p 6 p. 8 8z 6 z. 5n 5n 56 8w w. 8f 6 9 9f 7 Simplify each expression. 5. ( x) 6. (8 6t) 7. (6 d) 8. (r ) x 8 6t 6 d r 9. (m 6n) 0. (5.8a.b). (x y ). (f g 7) m 6n 5.8a.b x y f g 7 Use mental math to find each product You buy 75 candy bars at a cost of $0.9 each. What is the total cost of 75 candy bars? Use mental math. $6.75. The distance around a track is 00 m. If you take laps around the track, what is the total distance you walk? Use mental math m. There are classmates that are going to the fair. Each ticket costs $9. What is the total amount the classmates spend for tickets? Use mental math. $608 Prentice Hall Gold Algebra Teaching Resources 6

14 -7 Practice (continued) Form G The Distributive Property Simplify each expression by combining like terms.. t 6t 0t 5. 7y 5y y 6. b b 7b 7. y 5y 7y 8. n 7n 7n 9. 8x 0x x 50. f 7g 6 8g 5. 8x 5x k 6k k 0 f 5g 6 Write a word phrase for each expression. Then simplify each expression. 5. (n ) 5. 5(x 7) 55. (m 8) two times the sum of a number and one; n x 6 negative five times the difference of a number and seven; 5x 5 6k 7k 0 one-half the difference of four times a number and eight; m 56. The tax a plumber must charge for a service call is given by the expression 0.06(5 5h) where h is the number of hours the job takes. Rewrite this expression using the Distributive Property. What is the tax for a 5 hour job and a 0 hour job? Use mental math...5h; $9.60; $.0 Geometry Write an expression in simplified form for the area of each rectangle x 58. n x 5 0x 8 8n 08 5x 75 Simplify each expression. 60. jk 7jk jk 9jk 6. 7mn mn mn 0mn mn 6. 8xy 7xy xy xy 7xy 6. (5ab 6) 0ab 6. z z 5 z 5 Simplify each expression m n m n m n 5m n 5mn 66. Reasoning Demonstrate why x 6 m n m n 5m n 5mn 6 x 6. Show your work. x (x 6) 5 6 (x) 6 (6) 5 x ; x u x (h ) (h 7) 68. 5(n 8) 6(7 n) 69. 7( x) (x ) 0h (y 5) (y ) 7. (a b 7) 7. (5 s 6t) 5s t 6y z 5 7n a b 7 x 7 Prentice Hall Gold Algebra Teaching Resources 6 s t 0

15 -8 Practice Form G An Introduction to Equations Tell whether each equation is true, false, or open. Explain.. 5 x open; it contains a variable true. (6) ( 8) (0) 5 6 false; (6) 5 5 true 5. n k 8k 55 open; it contains a variable open; it contains a variable 7. 0 (5) () false; 0 (5) 5 50 true Tell whether the given number is a solution of each equation. 9. b 8 5 ; 7 no 0. x 7 5 5; yes. 5 f ; no. 6 5 n; no. 7c (5) 5 6; yes. 5 0z 5 5; no 5. 8a 5; no t 5; 0 yes 7. m 5 7 ; yes Write an equation for each sentence. 8. The difference of a number and 7 is 8. n times the sum of a number and 5 is 6. 6(n 5) A computer programmer works 0 hours per week. What is an equation that relates the number of weeks w that the programmer works and the number of hours h that the programmer spends working? h 5 0w. Josie is years older than Macy. What is an equation that relates the age of Josie J and the age of Macy M? J 5 M Use mental math to find the solution of each equation.. t h 7. p g x 5 7. v x b Prentice Hall Gold Algebra Teaching Resources 7

16 -8 Practice (continued) Form G An Introduction to Equations Use a table to find the solution of each equation. 0. m 5 5. d a 8. 5h y 5. 8n z p Use a table to find two consecutive integers between which the solution lies. 8. 7t n 0. 7d between 7 and 8 between and between 8 and 9. The population of a particular village can be modeled by the equation y 5 0x 56, where x is the number of years since 990. In what year were there 706 people living in the village? 005. Open-Ended Write four equations that all have a solution of 0. The equations should consist of one multiplication, one division, one addition, and one subtraction equation. Answers may vary. Sample: x 5 0; x 55; x 5; x 57. There are 68 members of the marching band. The vans the band uses to travel to games each carry 5 passengers. How many vans does the band need to reserve for each away game? 5 vans Find the solution of each equation using mental math or a table. If the solution lies between two consecutive integers, identify those integers.. d p k.5 7. c 8 5 between 7 and 8 between and 8. 6y (a) h x between and 5. Writing Explain the difference between an expression and an equation. An equation has two different quantities that are equal to each other and an expression does not. An expression can only be simplified whereas an equation can be solved. Prentice Hall Gold Algebra Teaching Resources 7