Introduction to Basic Algebra

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					Introduction to
 Basic Algebra


             Prepared by:

             Sir Angelo
             February 26, 2009
                 Mental Computation

Find the mode of the given set of numbers:

  11, 16, 12, 11, 13, 15, 11,
           18, 11, 16
                           Let’s try!!!

The highest elevation in North America is
Mt. McKinley, which is 20,320 feet above
sea level. The lowest elevation is Death
Valley, which is 282 feet below sea level.
What is the distance from the top of Mt.
McKinley to the bottom of Death Valley?
The problem question uses the notion of
opposites. Above sea level is the opposite
of below sea level. Can you give other
examples of opposites?


           top-bottom
           increase-decrease
           forward-backward
           positive-negative
The problem question may be solved
using the concept of integers, but what are
integers?




            Integers are the set of whole
            numbers and their opposites.
A number line can be used to represent
the set of integers.

                unsigned or
                  neutral
negative integers integer positive integers



-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

                 opposites
       Facts about Integers in a
             Number Line
• The number line extends infinitely in both
  directions. This is indicated by arrows.
  Therefore, there are no smallest and
  biggest numbers or integers.
• Whole numbers greater than zero are
  called positive integers. These numbers
  are to the right of zero on the number line.
       Facts about Integers in a
             Number Line
• Whole numbers less than zero are called
  negative integers. These numbers are to
  the left of zero on the number line.
• The integer zero is neutral. It is neither
  positive nor negative.
• On a number line, any number is bigger
  than all the numbers to its left. The
  number gets smaller as you move to the
  left on the number line.
      Facts about Integers in a
            Number Line
• Two integers are opposite if they are each
  the same distance away from zero, but on
  opposite sides of the number line. One will
  have a positive sign, the other a negative
  sign.
     Let’s go back to our problem
            question earlier.
 Let us now                Elevation           Integer
 solve the
                      20,320 feet above        20,320
 problem using
                           sea level
 the concept of
 integers. We              sea level               0
 can represent        282 feet below sea         -282
 each elevation              level
 as an integer.
The distance from the top of Mt. McKinley to the sea
level is 20,320. The distance from the bottom of Death
Valley to the sea level is 282. Therefore, the answer is
20,602 feet.
               Comparing Integers
• Write >, <, or =.
  a.)     3 ___ -8
  b.)     -15 ___ -1
  c.)     -2 ___ 0
  d.)     -8 ___ -6
  e.)     4 ___ -9
  f.)     -1 ___ 1
  g.)     -26 ___ -25
    Give an integer to represent each
                situation.
•   10 degrees above zero
•   A loss of 16 pesos
•   A gain of 5 points
•   8 steps backward
Name the opposite of each
        integer.
       •   -12
       •   21
       •   -17
       •   9
       •   25
       •   -346
       •   -9
                         Seatwork
• Answer Test Yourself A, B, C on pages
  247-248.
• Answer Test Yourself A and B on pages
  252-253.
• Answer Challenge Yourself on pages 253-
  254.
Schedule of Quiz 5 and Long Test 2
• Quiz 5 – March 4 (Wednesday)
  Integers, Comparing Integers, and
  Operations on Integers

• Long Test 2 – March 6 (Friday)
  Statistics, Probability, and Integers