The Distributive Property Section 1 7 Part 1

The Distributive Property Section 1 -7 Part 1

Goals Goal Rubric • To use the Distributive Property to simplify expressions. 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.

Vocabulary • Distributive Property

Distributive Property • 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.

MODELING THE DISTRIBUTIVE PROPERTY You can use algebra tiles to model algebraic expressions. 1 1 1 -tile 1 x-tile x This 1 -by-1 square tile has an area of 1 square unit. This 1 -by-x square tile has an area of x square units. Model the Distributive Property using Algebra Tiles x+2 Area = 3(x + 2) 3 + 3 x 3 2 Area = 3(x ) + 3(2)

Distributive Property 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.

USING THE DISTRIBUTIVE PROPERTY The product of a and (b + c): a(b + c) = ab + ac 2(x + 5) = 2(x) + 2(5) = 2 x + 10 (b + c)a = ba + ca (x + 5)2 = (x)2 + (5)2 = 2 x + 10 y(1 – y) = y(1) – y(y) = y – y 2 (1 + 5 x)2 = (1)2 + (5 x)2 = 2 + 10 x

The 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; The mailman property Find the sum (add) or difference (subtract) of the distributed products.

USING THE DISTRIBUTIVE PROPERTY Remember that a factor must multiply each term of an expression. (– 3)(1 + x) (y – 5)(– 2) –(7 – 3 x) = (– 3)(1) + (– 3)(x) Distribute the – 3. = – 3 x Simplify. = (y)(– 2) + (– 5)(– 2) Distribute the – 2. = – 2 y + 10 Simplify. = (– 1)(7) + (– 1)(– 3 x) –a = – 1 • a = – 7 + 3 x Simplify. Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

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

Your turn: 1. 2(x + 5) = 5. (x - 4)x = 2. (15+6 x) x = 6. 3. -3(x + 4) = 7. (y + 5)(-4) = 4. -(6 - 3 x) = 8. y(2 - 6 y) =

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

Your Turn • •

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.

Assignment • 1. 7 Pt 1 Exercises Pg. 54 – 55: #3 – 35