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=-:;=~------------ -- NAME _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DATE _ _ _ _ PERIOD Study Guide and Intervention The Distributive Property Evaluate Expressions The Distributive Property can be used to help evaluate expressrons. . p For any numbers a, b, and c, a(b + c) = ab + ac and (b Dlstri utrve roperty I a (b - c) = a b - ac an d (b - c) a = b a - ca. '~'b + c)a = ba + ca and Rewrite 6(8 + 10) using the Distributive Property. Then evaluate. 6(8 + 10) = 6 . 8 + 6 . 10 = 48 = 108 Distributive Property + 60 Multiply. Add. .~ ........ .~ + 1) using the Distributive Property. . ""'Itive Property .~. ( 13.2(3x + 2y - <:J 1( 16. "4 16x - 12y + 4z). © Glencoe/McGraw-Hili 17. (2 - 3x + x~) .... 25 Glen.__ l NAME _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DATE _ _ _ _ _ PERIOD Study Guide and Intervention (continued) The Distributive Property Simplify Expressions A term is a number, a variable, or a product or quotient of numbers and variables. Like terms are terms that contain the same variables, with corresponding variables having the same powers. The Distributive Property and properties of equalities can be used to simplify expressions. An expression is in simplest form if it is replaced by an equivalent expression with no like terms or parentheses. Simplify 4(a 2 + 3ab) - abo 4(a 2 -- 3ab) - ab = 4(a 2 + 3ab) - lab = 4a 2 + 12ab - lab = 4a 2 + (12 - l)ab = 4a 2 + 11ab - Multiplicative Identity Distributive Property Distributive Property Substitution ) '± © Glencoe/McGraw-Hili 26 Glencoe Algebra 1 NAME DATE _ _ _ _ _ PERIOD Practice The Distributive Property Rewrite each expression using the Distributive Property. Then simplify. 1. 9(7 + 8) 2. 7(6 - 4) 3. 6(b + 4) 4. (9 - p)3 5. (5y - 3)7 6. 15 (f + 7. 16(3b - 0.25) 8. men + 4) 9. (c - 4)d 1\ 3J Use the Distributive Property to find each product. 10.9 . 499 11.7' 110 13.12 . 2.5 14. 12. 21 . 1004 15. 16(4 ~) 27(2~) Simplify each expression. If not possible, write simplified. 16. w + 14w - 6w 17.3(5 + 6h) 20. 25t 3 22. 3a 2 + 6a + 2b 2 - l. 18. 14(2r - 3) 17t 3 23.4(6p + 2q - 2p) 24. x + 2 x 3x + 3 DINING OUT For Exercises 25 and 26, use the following information. The Ross family recently dined at an Italian restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75. 25. Write an expression that could be used to calculate the cost of the Ross' dinner before adding tax and a tip. 26. What was the cost of dining out for the Ross family? ORIENTATION For Exercises 27 and 28, use the following information. Madison College conducted a three-day orientation for incoming freshmen. Each day, an average of 110 students attended the morning session and an average of 160 students attended the afternoon session. 27. Write an expression that could be used to determine the total number of incoming freshmen who attended the orientation. 28. What was the attendance for all three days of orientation? © Glencoe/McGraw-Hili 28 Glencoe Algebra 1