1. Complex Number Systems and Simplifying Algebraic Expressions Critical Thinking Skill: Demonstrate Understanding of Concepts

2. 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

5. True or False: 1). All real numbers are irrational. _________________ 2). All integers are rational. ____________________ 3). All natural numbers are integers. _________________

6. Combining Like Terms Numerical Terms Variable Terms 3x 5.3 -34 2xy x2 -367 643v 25 5.

7. 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

8. 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.

9. 3: 2x2 - 6xy + 8y2 1.) 6r - 3s + 3r - 5r 2.) y + 7y + 6x - 2y

10. B: Simplifying variable expressions ~ Combination of distributive property and combining like terms 1.) 3x + 2(4x + 6) 2.) 10w + 3(5w + 1)

11. 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)

12. 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