1. P1 Real Numbers

2. Warm-up
How many people: -Are in the class? -Have a brother? -Have a sister? -Have no siblings? Lets make a Venn Diagram of that information.

5. Complex Numbers
We will worry about them down the road. Pretty much they help us define numbers when we have to take the square root of a negative.

6. Real Numbers Numbers that describe quantities in everyday life.
They consist of rational numbers and irrational numbers.
Ex: 2, π, 2/5, .7, …., 2

7. Rational vs. Irrational Numbers
A real number that can be written as the ratio p/q of two integers where q≠0
Fractions/Decimals
-Terminating: ½ , ¼…
-Repeating: 1/3 = …
Irrational
Numbers that cannot be written as a ratio of two integers
Fractions/Decimals
-Non-Terminating
-Non-Repeating
Ex) , etc.

8. Other Subsets… Natural Numbers {1, 2, 3, 4, 5…}
(Counting Numbers)
Whole Numbers {0, 1, 2, 3, 4, 5…}
(Natural Numbers including Zero)
Integers {…-3, -2, -1, 0, 1, 2, 3…}
(Whole Numbers and their Opposites)

9. Peardeck
Give the most specific set for each type of number.

10. Interval Notation
[ ] – Including boundary ( ) – Excluding boundary Write each inequality in interval notation & draw on a number line Ex. 1) Ex. 2)

11. Writing Inequalities
Example 1) x is at least -1 Example 2) y is at most 4 Example 3) z is at least -6 and at most 0

12. Given any two numbers…
There are 3 possibilities… They are equal One is larger than the other Or the other is larger than the first

13. Absolute Value
Measures the distance between the number and the origin (magnitude) If a is a real number, then

14. Examples
1. Evaluate when: a) x >0 b) x <0

15. Examples
2. Evaluate when: a) x > -5 b) x < -5

16. Distance between Two Points
Properties
Distance between Two Points

17. Set up the expression for…
The distance between x and 5 is 10.
b is at most 5 units from a
c is at least d units from 7

18. Algebraic Expressions
Variables (letters) and constants (numbers) with +, -, x, ÷, and exponents Example: Evaluating: Substitute the given value for each of the variables in the expression ~ Evaluate the above expression for x = -5

19. Basic Rules of Algebra
Let a, b, and c be real numbers, variables, or algebraic expressions Property

20. Properties of Negation
Let a and b be real numbers, variables, or algebraic expressions
Property

21. Properties of Equality
Let a, b, and c be real numbers, variables, or algebraic expressions

22. Let a and b be real numbers, variables, or algebraic expressions.
Properties of Zero
Let a and b be real numbers, variables, or algebraic expressions.

23. Properties and Operations of Fractions
Let a, b, c, and d be real numbers, variables, or algebraic expressions such that and

24. Fundamental Theorem of Arithmetic
Prime Numbers
Integer with exactly 2 factors; one and itself
Fundamental Theorem of Arithmetic
Every positive integer greater than 1 can be written as the product of prime numbers
Example)