1. 1.1/1.2 Sets and Properties of Real Numbers Mr. Mostafa Mamdouh

2. Quick Review

3. Let’s Get Real Real Numbers denoted by (R) are divided into 2 categories: Irrational numbers denoted by (I): Decimals that neither terminate nor repeat and square roots of non-perfect squares. Examples:

4. Rational Numbers Rational numbers denoted by (Q): terminating or repeating decimals. Can be expressed as where a and b are not decimals and b is not equal to zero Examples:

5. Special Rational Numbers Integers denoted by (Z): -3,-2,-1,0,1,2,3 Whole Numbers denoted by (W): 0,1,2,3 Natural Numbers denoted by (N): 1,2,3

6. Simple Rules Every Natural number is also whole, integer and rational Every Whole number is also integer and rational Every Integer is also rational Number

7. Picture Perfect

8. Classify -23 = = -185 = =

9. Group Activity 3, 4.1

10. Expressing Numbers

11. Number Line Real numbers greater than 2 and less than or equal to -4 in number line, interval and set-builder notation

12. Number Line Real numbers greater than 2 and less than or equal to -4 in number line, interval and set-builder notation https://apps.mathlearningcenter.org/nu mber-line/https://apps.mathlearningcenter.org/nu mber-line/ Interval notation: (2, ∞) or (-∞,4] Set-Builder Notation: {x| x>2 or x≤-4}

13. Challenge Questions

14. End of Part-1

15. Start of Part-2 Review Group Activity

16. Properties of Real Numbers A+B = B+A AxB = BxA (A+B) + C = A + (B+C) (AxB) x C = A x (BxC) A + 0 = A A x 1 = A

17. Properties Cont’d Distributive: a (b+c) = ab + ac Inverse: Additive: A + (-A) = 0 Multiplicative: A x = 1

18. Distributive Property 3(2q+r) + 5(4q-7r) 3(4x-2y) – 2(3x+y)

19. Inverse Property (multiplicative, additive) 1.25

20. Build Your Own Burger ItemPrice (LE) Buns3 Beef8 Lettuce4 Onions2 Tomato3 Sauce2 Total22 What is the cost if you are making burgers for 24 guests?

21. Thank you and have a great day!