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Chapter 3 Lesson 1 pgs. 98-102 What you will learn: Use the Distributive Property to write equivalent numerical and equivalent algebraic expressions

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Vocabulary and Key Concept: Equivalent expression (98): expressions that have the same value Ex.) 3(4+2) and 3 4 + 3 2 both have the same value of 18 Distributive Property (98): To multiply a number by a sum, multiply each number inside the parentheses by the number outside the parentheses. a(b+c) = ab + ac (b+c)a = ba + ca 3(4+2) = 3 4 + 3 2 (5+3)2 = 5 2 + 3 2 What two operations are combined by the Distibutive Property? Multiplication and Addition

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Use the Distributive Property Use the Distributive Property to write each expression As an equivalent expression. Then evaluate the expression. 2(6+4) 2 6 +2 4 12 + 8 Multiply 20 Add (8+3)5 8 5 + 3 5 40 + 15 Multiply 55 Add On your own: 5(7+3) 5 7 + 5 3 35 +15 50 (10-3)(-5) 10 (-5) - 3 (-5) -50 - (-15) -35

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Use the Distributive Property to solve a problem: A one-day pass to an amusement park costs $40. A round-trip bus ticket to the park costs $5. Write two equivalent expressions to find the total cost of a one-day pass and a bus ticket for 15 students. Method 1: Find the cost for 1 person, then multiply by 15. 15($40 + $5) cost for one person Method 2: Find the cost of 15 passes and 15 tickets. 15($40) + 15($5) ---> cost of 15 tickets cost of 15 passes

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Find the total cost. Evaluate either expression to find the total cost. 15($40 + $5)= 15($40) + 15($5) Distributive Property $600 + $75Multiply $675 Add The total cost is $675 You can check your results by evaluating 15($45)

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Simplify Algebraic Expressions Use the Distributive Property to write each expression as an equivalent algebraic expression. 3(x+1) 3 x + 3 1 3x + 3 Simplify (y+4)5 y 5 + 4 5 5y + 20 Simplify On your own: 4(x+3) 4x +12 -6(x+5) -6x + (-30)

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Simplify Expressions with Subtraction 2(x-1) =2[x+(-1)] Rewrite x-1 as x+(-1) =2x + 2(-1) Distributive Property =2x + (-2) Simplify =2x-2 Definition of Subtraction Your turn: -3(n-5) = -3[n+(-5)] Rewrite n-5 as n+(-5) = -3n + (-3)(-5) Distributive Property = -3n + 15 Simplify

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Take a practice sheet by the door!

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