1. College Algebra P.1 What types of numbers? What's special about them?

2. Real Numbers This course is all about REAL numbers. The REAL numbers are continuous and infinite, with no holes, like all the positions on a REAL NUMBER LINE.

3. The Story of Number Types The set of ALL real numbers is way cool. It has simple one-digit numbers, and even super famous numbers like pi. But let's go back to the beginning. Once upon a time...

4. Naturals, Wholes, Integers,...

5. ... then Rationals, ... What do rationals look like?

6. ... and then Irrationals too. What do irrationals look like?

7. Real Numbers So how do all those number types fit into the set of REAL NUMBERS?

8. What's special about REALS? Think about the real number line.... It is continuous. It is infinite. It is ORDERED. Because it is ordered, we can have symbols like < , >, and = which make sense.

9. How to note Real Numbers? Suppose we want to distinguish some of the real numbers. There are a few notations we can use to characterize a set of real numbers. inequality notation a number line graph interval notation in words

10. Using these notations In words: Inequality: Number Line: Interval Notation:

11. Using these notations In words: Inequality: Number Line: Interval Notation:

12. Using these notations In words: Inequality: Number Line: Interval Notation:

13. Think of the Number Line What would the notation look like for "The Absolute Value of Negative Five"? "abs. val. of" means "its distance from zero on the real number line.“ So, in other words, you always what?

14. Speaking of Abs. Value, In algebra, what would -a mean? a = -5..... then -a would be what? So instead of seeing this as "negative a," think of this notation as "the opposite of a."

15. What's special about Reals? Associative Property Commutative Property Distributive Property

16. No Dividing by Zero!!!! Thou shalt not!!! Remember the bean story... Video about the consequences.

17. Some Reals are Fractions. Some of the real numbers (the ones that are rational) are fractions. Do you remember how to multiply them? divide them? add them? subtract them?

18. Multiplying Fractions Straight Across

19. Dividing Fractions Keep it, Change it, Flip it.

20. Add/Subtract Fractions Find common denominators first.