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

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

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

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 

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)

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)

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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