The document provides information about absolute values and the real number system. It includes: - Definitions of rational numbers, integers, whole numbers, natural numbers, and irrational numbers. - Examples of absolute value and how it measures the distance from zero, including that operations inside the absolute value signs must be done first before taking the absolute value. - Class work assignments on opposites and absolute values problems from pages 17-18 including a mixed review.

1. TGIF: September 21, 2012
Today:
Warm-Up
The Real Number System
Absolute Value
Class Work:
Absolute Value
Note: Links to Textbooks & Workbooks should be fixed.

2. Warm-Up Questions
For the following, identify the
Terms Like Terms Coefficients Constants
1. 2 + 6a + 4a 2. 4/7a + 3/7b + 1/5a 3. (-2x + y)5 - 15x
then simplify where possible
Simplify the following:
1. -12c + 3 - 9(11 - c) 2. -.3x - 4.2 + 6.1x - .9

3. The Real Numbers
Rational Numbers:
Numbers expressed in the form
a/b, where a and b are integers Includes all fractions,
Mixed numbers, Ratios,
and b ≠ 0 Proportions, & decimals.
Integers: {…, -2, -1, 0, 1, 2, …}
Whole Numbers: {0, 1, 2, 3,
…}
Natural Numbers: {1, 2, 3, …}
Irrational Numbers:
These numbers don't end and
they don't repeat. Ex. √2, Pi,

4. Real Numbers
Practice: For each of the numbers, write Natural, Whole,
Integer, Rational, or Real according to its type. Most will
have more than one classification.
1. 0.25 2. 8.25252525 3. -1/2 4. 5 5. 0 6. -5
7. √5 8. 200 ft. below sea level

5. Absolute Value: |x|
• An important concept in Algebra; one that you should try
to master.
Absolute Value measures the distance a number is from
zero.
The following are illustrations of what absolute value means
using the numbers 3 and -3:
Since Absolute Value is a measure of distance, the
result can never be negative. (There can be no negative
distances)

6. Absolute Value: |x|
• If a number is positive (or zero), the absolute value function
does nothing to it: |4| = 4
• If a number is negative, the absolute value function makes it
positive: |-4| = 4
Find the value of the following: |5 + (-2)|
Did you get 7? Unfortunately, that's wrong.
If there is arithmetic to do inside the absolute value
sign, you must do it before taking the absolute value
sign. The correct answer is: |5 + (-2)| = |3| = 3

7. Absolute Value: |x|
• Simplify | 0 – 6 |
• Simplify | 4+ (– 6)|
• Simplify | 2 – 5 |
• Simplify | 0(–4) |
• Simplify | 2 + 3(–4) |
• Simplify –| –4 |
• Simplify –| (–2)2 |
• Simplify –| –2 |2

8. Class Work:
• Opposites & Absolute Values 1-9
• Pages 17-18, everything, including Mixed Review
• You must show all your work in order to receive
credit, even if you turn in your assignment.