Complex Number Systemsand

Simplifying Algebraic Expressions

Critical Thinking Skill:Demonstrate Understanding of Concepts

Complex Number System

Whole Numbers: "counting numbers" and 0  0, 1, 2, 3, ...

Integers: positive and negative whole numbers and zero  ...-3, -2, -1, 0, 1, 2, 3, ...

Rational Numbers: any number that can be written in the form  -8, 0.7, fractions, decimals

Irrational Numbers: any number that cannot be written in the form  non-repeating decimals, π ,

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

Real Numbers: all rational and irrational numbers

Imaginary Numbers: square roots of negative numbers

True or False:

1). All real numbers are irrational. _________________

2). All integers are rational. ____________________

3). All natural numbers are integers. _________________

Combining Like Terms

Numerical Terms Variable Terms

3x

5.3

-34

2xy

x2

-367

643v25 5

.

Rules for Combining Like Terms

1). You CANNOT combine Variable Terms with Numerical Terms.

2). To combine Variable Terms:

a). Terms must have the EXACT same variable (letters and exponents)

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

1: 5x - 9x 2: 3y + 5x + 2y

3: 3x - 2 4: 9q + 4d + 2d

Combining like terms with subtraction.

4y - 3y + 6x - 5y

Try this one:

* Remember to change the subtraction to plus a negative and "clean up" your final answer.

4y - 3y + 6x - 5y

As you get better with combining like terms you may skip this step.

3: 2x2 - 6xy + 8y2

1.) 6r - 3s + 3r - 5r 2.) y + 7y + 6x - 2y

B: Simplifying variable expressions

~ Combination of distributive property and combining like terms

1.) 3x + 2(4x + 6) 2.) 10w + 3(5w + 1)

B: Distributing a negative number

~ remember to change the subtraction to plus a negative

ex 1: 5x - 7(3x + 9) ex 2: 3z - 2y - (4z + 5y)

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

5). 5a2 - 3a (7a - 6) 6). 4w2 - w(2w - 3)

Commutative Property of Addition and Multiplication: You can change the ORDER of the addends or factors without changing the sum or product. Ex. 6 + 4 = 4 + 6

ab = ba *Order does not matter!

Associative Property of Addition and Multiplication:

You can change the GROUPING of numbers without changing the sum or product. Ex.   (a + b) + c = a + (b + c) (ab)c = a(bc)

* Grouping does not matter