Algebra Period 3 (Monday)

CHAPTER 2-1: ABSOLUTE VALUE
Note:
It is difficult to show the symbol for absolute value here so l n l should be read as “the absolute value of n”

l n l = 5 has 2 possible answers: {-5, 5}
l n l= -5 is impossible! It's the null set and that symbol is either { } or a 0 with a slanted line through it

FORMAL DEFINITION OF ABSOLUTE VALUE:
absolute value of n is n if n was a positive number or zero
absolute value is the opposite of n if n was a negative number
(since absolute value is always positive)

The absolute value is a distance concept- the absolute value is the distance a number is from zero on a number line.

2 words often misunderstood:
withdrawing money is actually considered negative, while depositing is considered positive
The focus is not the money in your wallet, but the money in your bank account!

CHAPTER 2-2: RATIONAL NUMBERS:
Counting Numbers = natural numbers = 1, 2, 3, 4 …..
Whole Numbers = the natural numbers + 0… so 0, 1, 2, 3, 4, ….
Integers = the whole numbers and their opposites… so …-4, -3, -2, -1, 0, 1, 2, 3, 4….
Rational number = any number that can be expressed as the ratio (fraction) of two integers
a/b, where a and b are both integers and b cannot be zero
b cannot be zero because you cannot divide by zero.....IT'S UNDEFINED!
Proof of this was done in class

There are positive and negative rational numbers.
One way to put them in order from least to greatest is to simply place them on the REAL number line. Numbers will be least to greatest if read from the left to the right.
If you have both fractions and decimals, it's often easier to change the fractions into decimals by simply dividing the numerator by the denominator.
REMEMBER: When numbers are NEGATIVE, the closer they are to zero, the bigger they are.
Example: -1/2 is greater than -3/4
-2.3 is greater than -2.5

You can also find the absolute value of rational numbers -
They are ALWAYS POSITIVE unless you're talking about zero (which is neutral)