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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.
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
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,
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
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)
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
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
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.

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Sept. 21, 2012

  • 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.