Vocab

• Variable (1-1): Letter(s) used to represent numbers; Change or unknown

• Evaluate(1-1): Find value of

x y z

Sections 1-1 to 1-5 Notes

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

)5(312

67

REMEMBER:

P Parenthesis or grouping symbols

E Exponents

MD Multiply or divide (left to right)

AS Add or subtract (left to right)

Ex 2)Evaluate

3

2yx 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)

18

24nmv

nm

15

10)4(6

312

xyx

xy

• Vocabulary

53

1-3 Exponential Notation PGS15-18

1-4 Associative Property pgs19-23

Examples6) 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 PowersSquared : 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..

means42 (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 644

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 = ________11) 40

12) (2x)0

13) (5x2y3z8)0 =

=

=

Negative Exponents

Negative exponents make __________(dividing by the base)14) 2-1 =

15) 4-2 =

16) 5-3 =

ExamplesEvaluate

17) 7n3 for n=2 18) (7n)3 for n=2

19) 5x2-x for x=3 2x

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

Like Terms(1-5):

Terms with the same ________and the same exact__________

• 2y and 4y _________like terms • 3x2 and 4x _________like terms

1-5 Distributive Property pgs24-28

Distributive Property: gets rid of __________________by distributing multiplication

• a(b+c) = ab + ac

• a(b-c) = ab – ac

• 3(4x + 2)=

Distribute21) 4(2x + 3)

22) 6(4x2 + 7)

23) ( x + 6 + 3y)(2)

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) aaa

5

2

5

3

Assignment

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