Distributive Property Chapter 1 Section 1.4

Objective Students will use the distributive property to simplify expressions

Concept Distributive Property: For all real numbers a, b, and c: a(b + c) = ab + ac and (b + c)a = ba + ca a(b – c) = ab – ac and (b – c)a = ba – ca

Concept The following two examples show how the distributive property can make mental math easier

Example 5 * 83 = 5(80 + 3) = (5 * 80) + (5 * 3) = 400 + 15 = 415 6(9.5) = 6(9 + 0.5) = (6 * 9) + (6 * 0.5) = 54 + 3 = 57

Example Simplify 5(x + 2) (6y + 7)4

Concept The distributive property of multiplication can also be written in the following form: ab + ac = a(b + c) ba + ca = (b + c)a ab – ac = a(b – c) ba – ca = (b – c)a

Example Simplify 75 * 17 + 25 * 17

Concept Remember when solving expressions, you may multiply variables together but you may only combine like terms together when using addition or subtraction.

Example Simplify 6(y + 7) 2(6x + 9y)

Example Simplify 9k – 7 – 2k 4a + 6b – a + 3b

Questions

Assignment Worksheet