Tammy D.

whole #'s

no fractions

no decimals

no negatives

what is a prime #?

NOT #1

#'S >1

#'s only divisible by itself

(odd #'s except for the #2)

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only even prime #

2

what is a composite #?

>1

divisible by a # other than itself AND #1

natural #

≥ 1, counting #'s

no remainders

no fractionsno decimals

K H D M D C M

3 spots to right is mcg!

1 mile = ? km

1.6 km

3 is 60% of what?

of ^{-} 100

x ^{•} 100 = 60 = 5

fraction to %

(5/8)

5÷8=0.625

0.625×100=62.5

62.5%

decimal to %

move decimal 2 spaces **left**

OR

÷100

% to decimal

2 places to left OR

×100

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\3×/2×↑2=12^{3}

prime factorization

factor tree

(use all #'s)

12=2^{2}•3

Calculate GCD or GCF

factor tree then

use smallest COMMON exponents

Calculate LCM

use ALL & largest #'s

how to calculate absolute value

spaces to get to 0

||3|=3 ^{-}|^{-}8|=^{-}8

|0|=0

integers

1717 - (^{-}11) = 28

dble negative =positiveintegers^{}

sign of larger #

integers ^{}

dbl neg = **+**

integers multiply rule

same sign=?

always positive^{}^{- }× ^{- }= ^{+}

integers multiply rule

diff sign=?

always negative^{}^{- }× ^{+ }= ^{-}

integers multiply rule

> 2 #'s

odd qty of #'s= ^{-}

even qty of #'s= ^{+}^{}

integer rules with parentheses

(^{-}6)^{2}=36^{-}6^{2}=^{-}36 ^{-}just moves

→no ( )=just move ^{-}

integers division rules same sign

same sign=^{+}

integers division rules

diff sign

diff sign=negative

what is a quotient of integers?

a fraction

what is a mixed #?

fraction=8 2/5

what is a rational #?

fraction or whole #

→whole # can be written over 1 as a fraction

what is an improper fraction?

fraction __42__

5

converts to 8 2/5

(mixed number)

negative just moves over^{-}29/8=^{-}3 5/8

When do denominators have to be the same?

only when adding or subtracting

what is negative exponent rule?

b^{-m}=1/b^{m}

8^{-2}=1/64

_{ -2 }__ 1 __ __ 1 __ __ 1 __

8 = 8^{2} = 8•8 = 64

how do you multiply fractions?

multiply strait across__2__ _{. }__3__ __2•3__ __ 6 __

8 9 ^{=} 8•9 ^{=} 72

how do you divide fractions?

when you multiply flip & don't ask why__7__ __21__ __7__ __8__ __56__

4 ^{÷} 8 ^{=} 4 ^{•} 21 ^{=} 84

mixed fraction to improper fraction

5 ¾ →

5•4+3=__23__

5

decimal as quotient of integers

0.5=5/10=½

0.75=75/100=¾

decimal as quotient of integers TIP

denom=decimal place

0.5=tenth= 5/10

0.75=100th= 75/100

0.777=1000th= 777/1000

repeating decimal as quotient of integers TIP

denom=decimal place in 9's

0.5=tenth= 5/10-1= 5/9

0.75=100th= 75/100-1= 75/99

0.777=1000th= 777/1000-1= 777/999

SETS

Roster Method

P={1,2,3,4,5,6}

SETS

word description

Set P is numbers 1 through 6.

SETS

Set-Builder notation

P={x|x is numbers 1 thru 6}

SETS

empty/null set

{ } or ∅

NOT

{0} or {∅}

SETS

not defined

5 worst presidents

what is ∈?

"is an element of"

14={2,4,6,8,...,30}

what is ∉?

"not an element of"

11 ∉ {2,4,6,...,30}

13 ∉ {a,b,c,...,z}

define equal & equivalent

equal=exact

•ignore duplicate elements

equivalent=same # of elements

SUBSETS

define ⊂

"is a proper subset"

A={1,3} ⊂ B={1,3,5}

A is a proper subset of B

NOT exact ∅ ⊂ ⊆ {2,4,6}

SUBSETS

define ⊆

"is a subset of"

A={cat} ⊆ B={black cat}

A is a subset of B

NOT exact { } ⊆ ∅

{man, woman} ⊆ {person}

SUBSETS

define
"is NOT a subset of"

A={p,r,o,f} __⊄__ B={r,o,f}

A is NOT a subset of B

{ } __⊄__ {1,2,3} {2,4,6} __⊄__ ∅

Set & subsets TIPS

•must have { }

•watch for words "set" or "#"

SUBSETS

# of subsets & proper subsets

{1,2,3,4,5,6,7,8,9}

subsets =2^{9}= 512

proper subsets

=2^{9}-1=511

→512, 511

SETS

Cardinal #

# of elements

{a,e,i,o,u}

n(A)=5

"n of A has 5 elements"

find # half way tween 2 fractions

adjusting recipes

recipe amt ^{•} amount ^{=}

5 dozen^{ •} 1 ^{=} 5 = 14÷5 = 2 4/5 eggs

Scientific notation

decimal after 1st #

26**.**1×10^{5} -^{ }incorrect

2**.**6 × 10^{5} - correct

→260,000**.**

(decimal notation)

Exponents

(3^{4})^{5}

(3

Multiply exponents before applying

(3^{4})^{5}=3^{4}•^{5}=3^{20}

(3

Subtract exponents

5^{12-4}=5^{8}

5

Exponents

13^{0}

13

13^{0}=1 always

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