THE REAL NUMBERS
Numbers that can be written as a ratio of two integers.
Rational Numbers
The property that allows you to do this:
a+b = b+a
Commutative Property
What kind of intervals use parentheses on both sides
I.e (a , b)
Open Intervals
Simplify the things inside the parentheses
If you are trying to find the overall cost of a product in the market, you will have an answer with this kind of unit...
Dollars (Money)
These numbers can be represented as decimals which either terminate or repeat.
Rational Numbers
This allows you to do this:
(a+b)+c = a+(b+c) and (ab)c= a(bc)
Associative Property
What kind of intervals use brackets on both sides
I.e [ a, b ]
Closed Intervals
The SECOND thing you do when trying to solve an expression
Simplify the things that have exponents
If you are trying to figure out how many shoes your company can make before you it runs out of money, your final answer should have this unit...
Shoes
These numbers have decimal representations that neither terminate nor repeat.
Irrational Numbers
The number 0 in this equation
a+0 = 0+a = a
Additive Identity
What kind of intervals use both a parenthesis and a bracket
(a, b] or [a, b)
The THIRD thing you do when trying to solve an expression
Multiplication and division from
left ---> right.
If you are trying to figure out how many years it will take for your $5 to become $55,000 your answer should have this unit...
Years
These numbers cannot be written as a ration of two integers.
Irrational Numbers
The number 1 in this equation
a * 1 = 1 * a = a
Multiplicative Identity
The distance a number "a" is from 0 on the number line.
Absolute Value
|a|
The FOURTH thing you do when trying to solve an expression.
Addition and subtraction from
left ---> right
These numbers are the regular counting numbers that you learned in Kindergarten
Natural Numbers (1,2,3,...)
This allows you to do this:
a(b+c) = ab+ac
Distributive Law
The difference between an expression and an ________ is that one contains an equal sign.
Equation
Which operation should you do first, multiplication or division?
It depends which one comes first in the expression from
left ---> right