SECTION 4.1 – INTRODUCTION
Quick facts:
Numbers that we dealt with before were all greater or equal to zero , called
positive
numbers. Now, we will explore numbers that are less than zero, called negative
numbers .
Negative numbers are distinguished from the positive by placing a negative sign
– in front
of the number. To better understand what negative numbers might re present , think
temperature 15 degrees be low zero , or 100 feet below sea level.
Integers are numbers:
. . . - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, . . .
Numbers above are sorted in increasing order from left to
right, meaning that - 3 < - 1,
-1 < 2, or - 3 < 0.
Notice: Negative 6 is less than negative 2: - 6 < -2
However positive six is greater than positive two
Opposites are numbers that have the same distance
from zero.
Negative sign can be understood as “the opposite of”.
Ex. The opposite of number 12 is –12
The opposite of number - 7 is 7
- (5) = - 5 (the opposite of positive 5 is negative 5)
- ( - 2) = 2 (the opposite of negative 2 is positive 2)
Absolute value of a number is the distance of the
number from zero. Absolute value of a
positive number is the number itself. Absolute value of a negative number is the
opposite
of the number. Absolute value of a number is always positive. Symbol of absolute
value is
Ex. The absolute value of number 5 is 5.
The absolute value of number -3 is 3. 
Note: Only numbers inside the absolute value will become
positive, if you evaluate 
,
the absolute value would leave the positive 10 that is inside positive, but the
negative sign
in front will change it into negative number. 
If you evaluate 
, the
absolute value would turn the negative 4 that is inside into
positive 4, but the negative sign in front will change it back to negative
number.
Rational number is a number that can be written as a/b, in
which the a and the b are
integers, and b ≠ 0 (b does not equal to zero)
Ex. 
are rational
numbers
All integers (that means all whole numbers as well) are
rational numbers, because
integers can be rewritten this way:
All mixed numbers are rational numbers. Remember writing
of a mixed number as an
improper fraction. 
which is a rational
number.
As to the decimals, all terminating (a decimal with finite
number of digits, like 2.45, or
1.12456) and repeating decimals (those that have infinite – never ending -
number of
digits after the decimal point and these decimals show repeating pattern) are
also rational
numbers, because they can be written as fractions.
Ex. 0.875 is a terminating decimal
0.111111… is a repeating decimal, it can be written as the fraction 1/9
to symbolize repeating decimals, we use a bar over the digits that repeat
themselves
Test yourself:
Find the opposite number:
Opposite of –5 is 5
Opposite of 154 is -154
Evaluate the absolute value:
Place a correct symbol between the numbers:
Sort the numbers from smallest to largest:
Challenge Yourself:
Chapter 10.1 of the textbook introduces a concept of number line to simplify the
understanding of the negative and positive numbers. Study the principals of
placing
numbers on the number line and its application on comparing of integers ,
evaluating
opposites, and absolute values.
Assignment:
Textbook Chapter 10.1 (p.408): Exercises 15 – 113 every fourth problem &
Problems
114, 117
