Objective - To use the distributive property to simplify numerical and variable expressions. Distributive Property or Order of Operations Distributive Property It works! Why use the distributive property?

Simplify using the distributive property. 1) 2) 3) 4) 5) 6)

Use the distributive property to write an equivalent expression. Then simplify both to show they have the same value. 1) 2) 3) same same same

Simplify using the distributive property. 1) 2) 3) 4) 5) 6)

Geometric Model for Distributive Property Two ways to find the area of the rectangle. As a whole As two parts 4 5 2

Geometric Model for Distributive Property Two ways to find the area of the rectangle. As a whole As two parts 4 5 2 same

Find the area of the rectangle in terms of x, y and z in two different ways. x y z As a whole As two parts

Find the area of the rectangle in terms of x, y and z in two different ways. x y z As a whole As two parts same

Use the distributive property to write an equivalent variable expression. Then simplify. 1) 2) 3) 4) 5) 6)

Use the distributive property to help simplify the following without a calculator. 1) 2)

Use the distributive property to help simplify the following without a calculator. 3) 4)

Now try distributing with negative numbers. 1) –3(-4x + 12) – 3(-4x) + -3(12) 12x + -36 2) 8(2x + y - 8) 8(2x) + 8(y) + 8(-8) 16x + 8y + -64 -1(-14x)+-1(12)+-1(u) 3) –1(-14x + 12 + u) 14x + -12 + -1u 14x + -12 + -u Remember how to add and multiply negative numbers! Pre-Algebra Stops Here.

The Property of –1 (Negative One) -1 · a = - a Negative one times a is the additive inverse of a . Rename each additive inverse without parentheses. In other words: distribute the negative/opposite sign. -(3 + x) = -(3x + 2y +4) = -(x + 2) = -(a – 7) = -(5x + 2y +8) = -(3c – 4d + 1) =

The Inverse of a Sum Property -(a +b) = -a + (-b) The additive inverse of a sum is the sum of the additive inverses. Distributing a negative/opposite sign to other negative numbers gives a positive number. -(5 – y) = -(2a –7b – 6) = -(6 – t) = -(-4a + 3t – 10) = -(18 – m –2n + 4t) =

Simplifying Expressions Involving Parentheses. Remember Order of Operations!!! Grouping symbols start at the innermost and work outward. Simplify: 5x – 2y – (2y – 3x – 4)= 5y – (3y + 4) = 3y – 2 – (2y – 4)= 5x – (3x + 9)= 3x – (4x + 2) = 3x + ( - (4x +2)) 3x + ( - 4x + ( - 2)) 3x – 4x – 2 -x - 2

Grouping Symbols ( ), [ ], and { } . Innermost to Outermost, keeping Order of Operation in mind. Simplify. [3 – (7 + 3)] = {8 – [9 – (12 +5)]} = 4(2 +3) – {7 – [4 – (8 +5)]} = [5(x + 2) – 3x] – [3(y + 2) – 7(y-3)] = 3(4+2) – {7-[4-(6+5)]} =

Assignment #12: Pages 96-97: 1-39 odd.