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Numbers with the same sign The product of 2 positive numbers or 2 negative numbers is positive. Numbers with different signs The product of a positive number and a negative number is negative. Section 1-7 Distributive Property SPI 11e: apply order of operations when computing with integers Objectives: Use the Distributive Property

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The Distributive Property

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Suppose you were a teacher and wished to purchase 34 graphing calculators. You go to Walmart to make a purchase and discover the calculators cost $102 each. You only have $3500. Use the distributive property to mentally calculate the total cost. Use Mental Math & Distro Property to Simplify (Shopping) Use Distributive Property to simplify a Numerical Expression Simplify 34(102). 34(102) = 34(100 + 2) Rewrite the term in parentheses. = 34(100) + 34(2) Mentally use the Distro Prop = 3400 + 68 Mentally simplify each term = 3468 Mentally add

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Using Mental Math and the Distributive Property, find the total cost of 4 CDs that cost $12.99 each. 4(12.99) = 4(13 – 0.01)Rewrite 12.99 as 13 – 0.01. = 4(13) – 4(0.01)Use the Distributive Property. = 52 – 0.04Simplify. = 51.96 The total cost of 4 CDs is $51.96. How could you rewrite 12.99 that would allow you to easily calculate the total cost?

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An algebraic expression in simplest form has no grouping symbols. Use the Distributive Property to Simplify an Expression Simplify 2(5x + 3).2(5x + 3) =2(5x)+ 2(3) Distribute terms = 10x + 6 Simplified Simplify 1/3(3b – 2).(1/3)(3b-2) =(1/3)(3b)+ (1/3)(-2) = b - 2/3 Simplified Simplify 6(m + 5). 6(m + 5) = 6(m) + 6(5) = 6m + 30

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Simplify -(6x + 4). Use the Multiplication Property of –1 -(6x + 4) = (-)(6x) + (-)(4) -(6x + 4) = (-1)(6x) + (-1)(4) = -6x + (- 4) or = -6x - 4 Simplify -(2x + 1) -(2x + 1) = (-)(2x) + (-)(1) = -2x - 1

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Term: a number, variable, or product of a number and variable. Example: (6, a, 6a) Constant: term that has no variable (-6, 12) Coefficient: numerical factor of a term. In the expression 3a, 3 is the coefficient. Like Terms: have exactly the same variable factors. Like TermsNot Like Terms 3x and -2x8x and 7y -5x 2 and 9x 2 5y and 5y 2 xy and –xy4y and 5xy -7x 2 y 3 and 15x 2 y 3 x 2 y and xy 2 Vocabulary of Monomials

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Combine Like Terms Simplify –2w 2 + w 2. –2w 2 + w 2 = (–2 + 1)w 2 Use the Distributive Property. = –w 2 Simplify. Relate: –6 times the quantity 7 minus m Write: –6 (7 – m) Write an expression for the product of –6 and the quantity 7 minus m. –6(7 – m)

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Model the Distributive Property using Algebra Tiles Use tiles to model x + 5. You model x – 3 with tiles. Use tiles to model 2(x + 5) First group of x + 5 Second group of x + 5 Add together 2x + 10

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Practice modeling the Distributive Property using Algebra Tiles 1. Write an equation for the model shown. 3. Use Algebra tiles to model the following: a. 3(x + 1) b. 2(x + 4) 2. Write an equation for the model shown. (x-4) +(x-4) = 2x - 8 (2x+3) +(2x+3) = 4x + 6

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Simplifying Algebraic Expressions

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