Sections 1-1 to 1-5 Notes x y z Vocab Variable (1-1): Letter(s) used to represent numbers; Change or unknown Evaluate(1-1): Find value of

8/24/2012 Sets of Numbers Real Numbers (R)- set of rational and irrational numbers Rational Numbers (Q) –Can be written in form a/b (b ≠ 0) ( fractions- create decimals that repeat or terminate) Integers (Z)-(Neg integers, 0 , Positive integers ) Natural Numbers (N)- counting Whole Numbers (W)- 0 + N Irrational Numbers (I)- Cannot be written in the form a/b (roots- decimals that do not repeat or terminate)

Examples EX 1) Simplify Ex 2)Evaluate for x =2 and y=5 REMEMBER: P Parenthesis or grouping symbols E Exponents MD Multiply or divide (left to right) AS Add or subtract (left to right) EX 1) Simplify Ex 2)Evaluate for x =2 and y=5

Commutative Property(1-2): switches the order of the numbers being added or multiplied CPA CPM a + b = b + a ab=ba 3 + x + 4 = 3 + 4 + x 4*a*2 =4*2*a Helps us simplify expressions

Identity Property : A number stays the same (keeps its identity) if you add zero or multiply by one IPA IPM a + 0 = a 1x = x x+ 2+(-2) = x 4xy = 2x 2y We use this property when solving equations and simplifying fractions h + 3 - 3 is really h + 0 or h

Examples Simplify 3) 4) 5)

53 1-3 Exponential Notation PGS15-18 1-4 Associative Property pgs19-23 Vocabulary 53

Examples 6) 75 means 7) 2x3 means 8) (4y)2 means What is the difference in 7) and 8)?

Write the following in exponential form 9) 3∙3∙3∙3 10) 4∙4∙4 Are these the same? 34 = 43 =

Special Powers Squared : a base to the second power (squares have 2 dimensions: length and width) 62 : can be read “6 to the second power” or “6________” The area of the side of a square with a side of s is A = s2 so.. means 42 (4 squared) = 16 we are talking about the ______________!!!! 4

Cubed: a base to the third power (cubes have 3 dimensions (length-width-height) 53 : can be read 5 to the third power or 5______ The __________of a cube is V = S3 so the volume of this cube is V =43 (4 cubed) or 64 4

Zero / Negative Exponents 23 33 22 32 21 31 20 30 2-1 3-1 2-2 3-2 What is 70? What is 5-1?

Zero Power Any number to the zero power = ________ 40 (2x)0 13) (5x2y3z8)0 = = =

Negative Exponents Negative exponents make __________ (dividing by the base) 14) 2-1 = 15) 4-2 = 16) 5-3 =

Examples Evaluate 17) 7n3 for n=2 18) (7n)3 for n=2 5x2-x for x=3 2x

(a+b)+c+d= a+(b+c)+d (a*2)*3 =a*(2*3) Associative property (1-4): Changes the grouping of the parenthesis when adding or multiplying APA APM (1+2)+3 = 1+(2+3) 15*2*10 =15(2*10) (a+b)+c+d= a+(b+c)+d (a*2)*3 =a*(2*3)

Using commutative and associative property, write three equivalent expressions 20) (3x + 6) +y

1-5 Distributive Property pgs24-28 Like Terms(1-5): Terms with the same ________and the same exact__________ 2y and 4y _________like terms 3x2 and 4x _________like terms

a(b+c) = ab + ac a(b-c) = ab – ac 3(4x + 2)= Distributive Property: gets rid of __________________by distributing multiplication a(b+c) = ab + ac a(b-c) = ab – ac 3(4x + 2)=

8/24/2012 Distribute 21) 4(2x + 3) 22) 6(4x2 + 7) 23) ( x + 6 + 3y)(2)

Factoring- reverse distributive property (Use DIVIDING Factoring- reverse distributive property (Use DIVIDING!!!) make sure to get GCF greatest common factor Factor 24) 6x + 8 (what is gcf?) 25) 15a2 + 30ab + 5a (what is gcf?)

Collect like terms (Simplify) 26) 5x + 4 + 3x 27) 5(h + 3) + 2(4h + 3) 28)

Assignment Chapter 1 Rev/47-48/2-44e