5 x 3 Distributive Property The factor 5 represents the number of books

# 5 x 3 distributive property the factor 5 represents

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= 5( x 3) Distributive Property The factor 5 represents the number of books purchased. The factor ( x 3) represents the price of each book. This factor is a difference of two terms, showing that the price x of each book is decreased by \$3. So, the factored expression shows a \$3 discount for every book you buy. The original expression shows a total savings of \$15. EXAMPLE Factoring an Algebraic Expression 3 Factor the expression using the GCF. 1. 7 + 14 2. 44 11 3. 18 12 4. 70 + 95 5. 60 36 6. 100 80 7. 84 + 28 8. 48 + 80 9. 2 x + 10 10. 15 x + 6 11. 26 x 13 12. 50 x 60 13. 36 x + 9 14. 14 x 98 15. 10 x 25 y 16. 24 y + 88 x 17. REASONING The whole numbers a and b are divisible by c . Is a + b divisible by c ? Is b a divisible by c ? Explain your reasoning. 18. OPEN-ENDED Write five expressions that are equivalent to 8 x + 16. 19. GEOMETRY The area of the parallelogram is 4 ft (4 x + 16) square feet. Write an expression for the base. 20. STRUCTURE You buy 37 concert tickets for \$8 each, and then sell all 37 tickets for \$11 each. The work below shows two ways you can determine your profit. Describe each solution method. Which do you prefer? Explain your reasoning. profit = 37(11) (37)8 = 407 296 = \$111 profit = 37(11) (37)8 = 37(11 8) = 37(3) = \$111 Quiz 3.3–3.4 142 Chapter 3 Algebraic Expressions and Properties Tell which property the statement illustrates. (Section 3.3) 1. 3.5 z = z 3.5 2. 14 + (35 + w ) = (14 + 35) + w Simplify the expression. Explain each step. (Section 3.3) 3. 3.2 + ( b + 5.7) 4. 6 (10 k ) Use the Distributive Property and mental math to find the product. (Section 3.4) 5. 6 × 49 6. 7 × 86 Use the Distributive Property to simplify the expression. (Section 3.4) 7. 5( x 8) 8. 7( y + 3) Simplify the expression. (Section 3.4) 9. 6 q + 2 + 3 q + 5 10. 4 r + 3( r 2) Factor the expression using the GCF. (Section 3.4) 11. 12 + 21 12. 16 x 36 13. GEOMETRY The expression 18 + 7 + (18 + 2 x ) + 7 represents the perimeter of the trapezoid. Simplify the expression. (Section 3.3) 14. MOVIES You and four of your friends go to a movie and each buy popcorn. (Section 3.4) a. Use the Distributive Property to write an expression for the total cost to buy movie tickets and popcorn. Simplify the expression. b. Choose a reasonable value for x. Evaluate the expression. 15. GEOMETRY The length of a rectangle is 16 inches, and its area is (32 x + 48) square inches. Factor the expression for the area. Write an expression for the width. (Section 3.4) Progress Check 18 à 2 x 18 7 7 Movie Tickets Snacks Student \$8 Adult \$10 Candy \$3 Popcorn \$ x Chapter Review 143 3.2 Writing Expressions (pp. 118–123) Write the phrase as an expression. a. a number z decreased by 18 z 18 The phrase decreased by means subtraction . b. the sum of 7 and the product of a number x and 12 7 + 12 x The phrase sum of means addition . The phrase product of means multiplication . 3 Chapter Review Review Key Vocabulary Review Examples and Exercises algebraic expression, p. 112 terms, p. 112 variable, p. 112 coefficient, p. 112 constant, p. 112 equivalent expressions, p. 128 like terms, p. 136 factoring an expression, p. 140 Vocabulary Help a. Evaluate a ÷ b when a = 48 and b = 8.  #### You've reached the end of your free preview.

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• Addition, Algebraic Expressions, Algebraic Expressions and Properties
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