1. Distributive Property
Chapter 1
Section 1.4

2. Objective
Students will use the distributive property to simplify expressions

3. 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

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

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

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

7. 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

8. Example
Simplify
75 * * 17

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

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

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

12. Questions

13. Assignment
Worksheet