Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

Complex Number System,Combining Like Terms

andSimplifying Algebraic Expressions

Essential Skill:Demonstrate Understanding of Concepts

Complex Number  System

Whole Numbers:  natural numbers and 0              0, 1, 2, 3, ...      

Integers:  whole numbers and their opposites             ...­3, ­2, ­1, 0, 1, 2, 3, ...     

Natural Numbers:  "counting numbers"              1, 2, 3 ...     

Real Numbers:  all rational and irrational numbers                 

Rational Numbers: any number that can be written in the form                 ­8, 0.7, √9  , .3      

Irrational Numbers: any number that cannot be written in form a                                  non­terminating non­repeating decimals                                          π, √3                                                                                                

abterminating decimals

repeating decimals

Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

True or False:

1)  All real numbers are irrational.  _________________

2)  All integers are rational.  ____________________

3)  All natural numbers are integers.  _________________              

Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

variable:  a letter that represents an unknown quantity               

algebraic expression:  an expression that contains at least one variable               substitute:  replacing a variable with a number               evaluate:  substitute and simplify               simplify:  make less complicated               

Algebraic Vocabulary               

coefficient:  the number multiplied to a variable in a term               terms:  parts of an expression that are added/subtracted to each other               

Numerical Terms Variable Terms3x

5.3

-34

2xy

x2

-367

643v

25x5

Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

Rules for Combining Like Terms1) Combine your Numerical Terms using your basic operations ( +, -).

2) You CANNOT combine Variable Terms with Numerical Terms.

3) To combine Variable Terms:

a) Terms must have the EXACT same variable portion (letters and exponents)---coefficients can be different.

b) To combine, you just + or - the coefficients.

ex 1: 5x - 9x ex 2: 4y - 3y + 6x -5y

ex 3: 3x - 2 ex 4: 2x2 - 6xy + 8x2

Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

Simplifying Variable Expressions

ex 1: 5x - 2(3x + 9) ex 2: 3z - 2y - (4z + 5y)

ex 3: -2 ( e -f) + 4 (2e + 5f) ex 4: a2 + 3(a2 - 9)

Complex Number Sys, CLT, Simplifying.notebook August 30, 2016

Pick at least two to try...1) 7u - 3(7u + v)

2) (-5x + 2) - ( -2x - 3)

3) 12y - (2y - 1)

4) 5a2 - 3a (7a - 6)

5) 4w2 - w(2w - 3)