# 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.

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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

The Distributive Property

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

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?

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

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

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

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)

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

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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