# 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
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.
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.
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

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