Chapter 1
 

Section 1.1  Variables and expressions- You should be able to change verbal expressions into mathematical expressions and reverse the process.

Vocabulary for section 1.1

Variables - symbols - generally letters that are used to represent unknown numbers or values.
Algebraic expressions consist of numbers and letters combined with symbols to represent mathematical operations
Factors are variables or numbers that are being multiplied
Product is the result of a multiplication
Exponents are small numbers written as superscripts in the upper right above a number or variable.  The number place here tell you how many times you are to use the given quantity as a factor. 
Base - number or letter is being used as a factor in an exponential expression
Power - refers to the base raised to an exponent
Evaluate - perform the mathematical operations on the given number to find its value

Words used to translate into mathematical operations

+ or addition:  increased by, total, sum of, more than

- or subtraction:  difference, decreased by, less than

multiplication:   product, times, of  (x is not used in algebra often as a multiplication sign as it is confused with the variable)

division:  divided by, into, quotient, ratio

1.2  Order of Operations- You should be able to evaluate numerical and algebraic expressions using order of operations.

Most of  you have learned the order of operations
    Grouping symbols
    Exponents   
    Multiplications and Divisions from left to right
    Additions and Subtractions from left to right

Some of you have learned this as PEMDAS  (Parentheses, exponents, mult and div - left to right whichever comes first- then additions and subtractions -left to right whichever comes first).

Others have learned this as Please Excuse My Dear Aunt Sally (same letters at the start as PEMDAS) and Boca students SEX+  (Symbols,Exponents, X for mult and div, and + for additions and subtractions.  Whatever helps you to keep the order correct, use it!

1.3  Open Sentences- mathematical statement with one or more variables

Vocabulary

solution- finding the value of a variable that will make the open sentence true
equation- a mathematical sentence containing an = symbol.  This means the amount on both sides is of equal value.
replacement set- set of numbers given which can be substituted in for the variable and the sentence evaluated as to whether it is true or false
set- a collection of objects or numbers usually put in brackets {  }
element-  one member of a set
solution set - set of numbers from the replacement set that makes the open sentence true

Inequalities are sentences where one side of an equation is greater than the other.
Symbols for inequalities < is the less than symbol.  2 < 3 is  a true inequality
                                     > greater than     5 > 3 is a true inequality
                                      if an equals bar is under the inequality one side can be of equal or lesser value or  of equal or greater value

1.4  Identity and Equality Properties- recognize and use the identity and equality properties

Multiplicative Identity- The number that you can multiply by that will not change the value or identity of what you started with is 1.   (a)(1)=a

Additive Identity-  The number that you can add to a number and not change the value or identity of what you started with is 0 .   a + 0 = a

Multiplicative Inverse or Reciprocal is the number you multiply a given number by to get the answer 1