Properties of Real Numbers Students will identify and use associative, commutative, and distributive properties.

Associative Property …of addition … of multiplication a + ( b + c ) … is exactly the same as… … is exactly the same as… ( a + b ) + c a ● ( b ● c ) The associative property does NOT work for subtraction or division.

Commutative Property …of addition … of multiplication a + b a ● b … is exactly the same as… … is exactly the same as… b + a b ● a The commutative property does NOT work for subtraction or division.

Distributive Property If a letter or number is next to a parenthesis, it means multiply. a ( b + c ) ? ab + ac Example: 4 ( x – 3 ) 4x – 12

Distributive Property or Order of Operations Distributive Property It works!

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

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

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

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

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

Algebra Examples EXAMPLE 1: EXAMPLE 2:

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

Guided Practice (cont.) 7) 10) 8) 11) 9) 12)

Summary Distributive Property means multiply the number or term outside the parentheses times each term inside the parentheses. a ( b + c ) a ( b – c ) ab – ac ab + ac STOP