Lesson Lesson Tutorials

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1 .4 Lesson Lesson Tutials Key Vocabulary like terms, p. 6 Distributive Property Wds To multiply a sum difference by a number, multiply each number in the sum difference by the number outside the parentheses. Then evaluate. Numbers (7 + ) = 7 + Algebra a(b + c) = ab + ac (7 ) = 7 a(b c) = ab ac Using Mental Math Use the Distributive Property and mental math to find 5. 5 = (50 + ) Write 5 as = (50) + () Distributive Property = Multiply. = 44 Add. Using the Distributive Property Use the Distributive Property to find 4. 4 = ( + 4) = ( ) ( + 4) Rewrite 4 as the sum + 4. Distributive Property = + = Multiply. Add. Exercises 5 6 Use the Distributive Property to find the product (7) Chapter Algebraic Expressions and Properties

2 Study Tip You can use the Distributive Property when there are me than two terms in the sum difference. Simplifying Algebraic Expressions Use the Distributive Property to simplify the expression. a. 4(n + 5) 4(n + 5) = 4(n) + 4(5) Distributive Property = 4n + 0 Multiply. b. (y ) (y ) = (y) () Distributive Property = 4y 6 Multiply. c. 9(6 + x + ) 9(6 + x + ) = 9(6) + 9(x) + 9() Distributive Property = x + Multiply. = 9x Commutative Property of Addition = 9x + 7 Add 54 and. Exercises 7 Use the Distributive Property to simplify the expression. 7. 7(a + ). (d ) 9. 7( + 6 4d) 4 Real-Life Application José is x years old. His brother, Felipe, is years older than José. Their aunt, Maria, is three times as old as Felipe. Write and simplify an expression that represents Maria s age in years. Name Description Expression José He is x years old. x Felipe Maria He is years older than José. So, add to x. She is three times as old as Felipe. So, multiply and (x + ). x + (x + ) (x + ) = (x) + () Distributive Property = x + 6 Multiply. Maria s age in years is represented by the expression x + 6. Section.4 The Distributive Property 5

3 0. Alexis is x years old. Her sister, Glia, is 7 years older than Alexis. Their grandfather is five times as old as Glia. Write and simplify an expression that represents their grandfather s age in years. In an algebraic expression, like terms are terms that have the same variables raised to the same exponents. Constant terms are also like terms. Like terms 5x x + Use the Distributive Property to combine like terms. Like terms 5 Combining Like Terms Simplify each expression. a. x x 5 x x 5 = x + x Commutative Property of Addition = ( + )x Distributive Property = 5x + 4 Simplify. b. y + y + y y + y + y = y + y + y Multiplication Property of One = ( + + )y Distributive Property = y Add coefficients. c. 7z + (z 5y) 7z + (z 5y) = 7z + (z) (5y) Distributive Property = 7z + z 0y Multiply. = (7 + )z 0y Distributive Property = 9z 0y Add coefficients. Exercises 9 5 Simplify the expression.. + z z. (b + 5) + b + 6 Chapter Algebraic Expressions and Properties

4 .4 Exercises Help with Homewk. WRITING One meaning of the wd distribute is to give something to each member of a group. How can this help you remember the Distributive Property?. OPEN-ENDED Write an algebraic expression in which you use the Distributive Property and then the Associative Property of Addition to simplify.. WHICH ONE DOESN T BELONG? Which expression does not belong with the other three? Explain your reasoning. (x + ) 5(x ) 4 + (x 4) (9 x) 4. Identify the like terms in the expression x + + 7x (-6)= +(-)= 4+(-9)= 9+(-)= Use the Distributive Property and mental math to find the product (4). 5() (6). 7() Use the Distributive Property to find the product Use the Distributive Property to simplify the expression. 7. (x + 4). 0(b 6) 9. 6(s 9) 0. 7( + y). ( + a). 9(n + ). (6 k) 4. (5 w) 5. 9( + c + 4) 6. 7( + x + ) 7. (5g + 5 ). 6(0 + z + ) 9. 4(x + y) 0. 5(x y). 7(p + q + 9). (n m). ERROR ANALYSIS Describe and crect the err in rewriting the expression. 6(y + ) = 6y + 4. ART MUSEUM A class of 0 students visits an art museum and a special exhibit while there. a. Use the Distributive Property to write and simplify an expression f the cost. b. Estimate a reasonable value f x. Explain. c. Use your estimate f x to evaluate the iginal expression and the simplified expression in part (a). Are the values the same? PRICES Museum Child (under 5) Free Student $ Regular $ Seni $0 Exhibit Free $x $4 $ Section.4 The Distributive Property 7

5 5. FITNESS Each day, you run on a treadmill f r minutes and lift weights f 5 minutes. Which expressions can you use to find how many minutes of exercise you do in 5 days? Explain your reasoning. 5(r + 5) 5r r + 5 r (5 + 5) 6. SPEED A cheetah can run 0 feet per second. A zebra can run x feet per second. Use the Distributive Property to write and simplify an expression f how much farther the cheetah can run in 0 seconds. UNIFORMS Your baseball team has 6 players. Use the Distributive Property to write and simplify an expression f the total cost of buying the items shown f all the players. 7.. and Pants: $0 and and Belt: $x Jersey: $ Socks: $4 Hat: $x 5 Simplify the expression. 9. 6(x + 4) ( + x) 4. 7( + 4k) + 4. x + + 5x 4. 7y y 44. w + w + 5w 45. 4d + 9 d 46. n + (n ) 47. v + v 5v 4. 5(z + 4) + 5( z) 49..7(w 5.) 50. y + y + y 5. 7(x + y) 7x 5. 4x + 9y + (x + y) 4 ( 5 ) 5. z + + z 54. ERROR ANALYSIS Describe and crect the err in simplifying the expression. 6 x x + 5x = x 7x = ( 7)x =x ALGEBRA Find the value of x that makes the expressions equivalent (x 5); (x + 9); ( x); REASONING Simplify the expressions and compare. What do you notice? Explain. 4(x + 6) Chapter ms_green pe_004.indd (x + 6) + (x + 6) + (x + 6) + (x + 6) Algebraic Expressions and Properties //5 ::45 PM

6 GEOMETRY Write and simplify expressions f the area and perimeter of the rectangle x 7 x x 6. FUNDRAISER An art club sells 4 large candles and 56 small candles. a. Use the Distributive Property to write and simplify an expression f the profit. b. A large candle costs $5, and a small candle costs $. What is the club s profit? Price: $0 Cost: $x Price: $5 Cost: $y Profit Price Cost 6. REASONING Evaluate each expression by () using the Distributive Property and () evaluating inside the parentheses first. Which method do you prefer? Is your preference the same f both expressions? Explain your reasoning. a. (. 0.) b. ( REASONING Write and simplify an expression f the difference between the perimeters of the rectangle and the hexagon. Interpret your answer. ) x x x x x 7 x x x Add one set of parentheses to the expression 7 x + + x + x + 9 so that it is equivalent to (9x + 0). Evaluate the expression. (Section.4, Section.5, and Section.6) MULTIPLE CHOICE What is the GCF of 4, 0, and 96? (Section.5) A B 6 C 4 D 40 Section.4 The Distributive Property 9