1. Warm Up Problem 1. The area of a circle 6 meters in diameter exceeds the combined areas of a circle 4 meters in diameter and a circle 2 meters in diameter by how many square meters? a)0 b)3 pi c)4 pi d)5 pi

2. Homework Page 11 (26-29,36-39,63-66) Page 17 (51-56, 58)

3. Numbers September 7, 2010

4. Vocabulary Set: Collection of items. Element: Items of a set. Subset: A set whose elements belong to another set. Empty Set: Set containing no elements. Finite Set: A definite or finite number of elements. Infinite Set: Unlimited or infinite number of elements.

5. Types of Numbers Rational Numbers (Q) Integers (Z) Whole Numbers (W) Natural Numbers (N) Irrational Numbers

6. Set Notations Roster Notation: Elements are listed inside {}. {1,2,3,4,5,6} Interval Notation: Elements indicating the endpoints of the set as follows. – Parenthesis’s: Represents the endpoints are not included in the answer. (4,12) – Brackets: Represents the endpoints are included in the answer. [1,21]

7. WordsRoster Notation Interval Notation Inequality Notation All real numbers Except 1 Cannot be written in roster notation. x 1 Positive Odd Numbers {1,3,5,7,…}Cannot be notated. Numbers within 3 units of 2. Cannot be written. [-1,5]

8. Practice Write in interval notation. -10<x<10 Order the given numbers from least to greatest and classify each number by the subsets of the real numbers. -15 -10 -5 0

9. Properties of Numbers WordsNumbersAlgebra Additive Identity Property: The sum of a number and 0 is the original number. 3 + 0 = 3N + 0 = 0 + N = N Multiplicative Identity: The product of a number and 1 is the original number. N * 1 = 1 * N = N Additive Inverse: The sum of a number and its opposite, or additive inverse, is 0. 5 + (-5) = 0N + (-N) = 0 Multiplicative Inverse: The product of a nonzero number and its reciprocal, or multiplicative inverse is 1.

10. WordsNumbersAlgebra Closure Property: The sum or product of any two real numbers is a real number. 2 + 3 = 5 2(3) = 6 Commutative Property: Add or multiply real numbers in any order without changing the result. 7 + 11 = 11 + 7 7(11) = 11(7) a + b = b + a ab = ba Associative Property: Sum or product of three or more real numbers is the same regardless of the way the numbers are grouped. (5 + 3) + 7 = 5 + (3 + 7) (5 * 3) * 7 = 5 * (3 * 7) (a + b) + c = a + (b + c) (ab)c = a(bc) Distributive Property: When you multiply a sum by a number, the result is the same whether you add and then multiply or vise versa. 5(2 + 8) = 5(2) + 5(8) (2 + 8)5 = (2)5 + (8)5 a(b + c) = a(b) + a(c) (b + c)a = (b)a + (c)a

11. Examples Find the additive and multiplicative inverse. -9 Identify the property.

12. The base price for an airplane ticket from Austin to Houston is $185. The final price includes an additional $16 for airport fees and $12 fuel surcharge. Jose’ purchased a ticket online for 40% off the base price. Explain how to use mental math to find Jose’s final price to the nearest dollar.

13. Practice Problems Identify the property. An art supply company is having a sale on certain items. Colored Pencils ($8.89), Sketch books ($9.96), Acrylic Paints ($11.99), and Paint Brushes ($14.99). Write an expression and simplify. – Cost of 3 sketch books at a 10% discount and 5 acrylic paints at a 25% discount.

14. Exit Slip A store is offering a 25% discount on every item purchased. To find the total discount on a purchase, Gary found the sum of the prices and then multiplied the sum by a quarter. Maria found the total discount by multiplying each price by quarter and then adding the discounts. Do both methods give the same results? Use properties of real numbers to explain why or why not. Place exit slip in the bin on my desk when finished.