1. Math 081 January 27th, 2014

2. Real Numbers Rational Numbers Irrational Numbers Integers
Types of Numbers
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers

3. Real Numbers (R)
All numbers used in everyday life, the set of all rational and irrational numbers.
Ex: ½ , -3, 4.667,

4. All Integers except negative numbers and zero. Ex: {1, 2, 3, 4, 5, ….}
Natural Numbers (N)
All Integers except negative numbers and zero.
Ex: {1, 2, 3, 4, 5, ….}

5. All Integers except for all the negative numbers.
Whole Numbers (W)
All Integers except for all the negative numbers.
Ex: {0, 1, 2, 3, 4, 5, ….}

6. Integers (Z)
All non-decimal or fractional numbers including all positive numbers, negative numbers and zero.
Ex: {...-2, -1, 0, 1, 2, 3, …}

7. Rational Numbers (Q)
Any number , where m and n are integers and n is a non-zero. The decimal form is either a terminating or repeating decimal.
Ex: ½ , 2.555,

8. Irrational Numbers (I)
Any number which can not be written as a fraction. The decimal form neither repeats or terminates.
Ex: …

9. Examples -4
….. 8

10. Just how far from zero are you?
Absolute Value
Just how far from zero are you?

11. What are opposites on a number line?
Graph the integer set from –5 to + 5
Two numbers that are the same distance from zero are said to be opposites

12. But what is Absolute Value?
Absolute Value is the distance a number is from zero. Remember distance itself is ALWAYS positive

13. How do we denote absolute value?
SO let’s try a few:
What general statement can you make about absolute value?

14. Be careful!
In math a negative sign in front of the absolute value sign should be read “take the opposite of”. This means treat the absolute value sign like a grouping symbol. Do the work inside first THEN take the opposite of

15. Let’s try a few

16. What if the variable is in the absolute value sign?
This simply means what are ALL the solutions that make this a true statement? -7 7

17. Velocity and Speed
Velocity is how fast is something going AND in what direction is it headed? Example: If I am plummeting to earth in a hot air balloon my velocity would be –15 feet per second!
BUT my speed would be the absolute value which is 15 feet per second!

18. Final Thought for Today
In math it is not enough to just know the answer you have to PROVE you know it. If you say something is FALSE you must provide a counter example.
Give a counter example to this statement:
All of the students in Mrs. Rose’s algebra classes are boys.
Now determine if these are true or false. If false, provide a counter example:
The expression – x is never positive
The absolute value of a number will always be greater than or equal to that number