1. The Distributive Property Section 1-7 Part 1

2. Goals Goal To use the Distributive Property to simplify expressions. Rubric Level 1 – Know the goals. Level 2 – Fully understand the goals. Level 3 – Use the goals to solve simple problems. Level 4 – Use the goals to solve more advanced problems. Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary Distributive Property

4. To solve problems in mathematics, it is often useful to rewrite expressions in simpler form. The Distributive Property, illustrated by the area model on the next slide, is another property of real numbers that helps you to simplify expressions.

5. You can use algebra tiles to model algebraic expressions. 1 1 1 -tile This 1-by-1 square tile has an area of 1 square unit. x -tile x 1 This 1-by- x square tile has an area of x square units. 3 x + 2 Area = 3(x + 2) 3 2 3 x Area = 3(x ) + 3(2) Model the Distributive Property using Algebra Tiles M ODELING THE D ISTRIBUTIVE P ROPERTY x + 2 +

6. The Distributive Property is used with Addition to Simplify Expressions. The Distributive Property also works with subtraction because subtraction is the same as adding the opposite. Distributive Property

7. T HE D ISTRIBUTIVE P ROPERTY a(b + c) = ab + ac (b + c)a = ba + ca 2(x + 5)2(x) + 2(5)2x + 10 (x + 5)2(x)2 + (5)22x + 10 (1 + 5x)2(1)2 + (5x)22 + 10x y(1 – y)y(1) – y(y)y – y 2 USING THE DISTRIBUTIVE PROPERTY = = = = = = = = The product of a and (b + c):

8. Distributive Property For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + bc; a(b - c) = ab - ac and (b - c)a = ba - bc; The mailman property Find the sum (add) or difference (subtract) of the distributed products. The Distributive Property

9. (y – 5)(–2)= (y)(–2) + (–5)(–2) = –2y + 10 –(7 – 3x)= (–1)(7) + (–1)(–3x) = –7 + 3x = –3 – 3x (–3)(1 + x) = (–3)(1) + (–3)(x) Simplify. Distribute the –3. Simplify. Distribute the –2. Simplify. –a = –1 a U SING THE D ISTRIBUTIVE P ROPERTY Remember that a factor must multiply each term of an expression. Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

10. 1) 2) 3) 4) 5) 6) Your Turn: Simplify

11. Your turn: 1.2(x + 5) =5. (x - 4)x = 2.(15+6x) x =6. y(2 - 6y) = 3.-3(x + 4) =7. (y + 5)(-4) = 4.-(6 - 3x) =8.

12. Rewriting Fractions Expression Write division as multiplication Use the distributive Property Simplify

13. Your Turn

14. Joke Time What’s green and has wheels? Grass… I lied about the wheels. Why did the squirrel fall out of the tree? Because it was dead. What do you call a fly with no wings? A walk.

15. Assignment 1.7 Pt 1 Exercises Pg. 54 – 55: #3 – 35