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BY:DURRELL WHITFIELD

BY:DURRELL WHITFIELD

PR

IME N

UM

BER

S

PR

IME N

UM

BER

S A prime number is a

A prime number is a whole number greater

whole number greater

than that has two

than that has two factors,1 and its self.

factors,1 and its self. Example: 2=2x1,

Example: 2=2x1, 3=3x1, 5=5x1, 7=7x1

3=3x1, 5=5x1, 7=7x1

Com

posi

te

Com

posi

te

num

bers

num

bers

A composite number is

A composite number is

a whole number

a whole number greater than 1 that

greater than 1 that has more than two

has more than two factors.factors.

Examples: 6=3x2 and

Examples: 6=3x2 and

1x6, 8=4x2 and 8x1,

1x6, 8=4x2 and 8x1,

10=5x2 and 1x10,

10=5x2 and 1x10, 12=6x2 and 1x12 and

12=6x2 and 1x12 and

3x4 3x4

Sim

plif

ying

Sim

plif

ying

fract

ions

fract

ions

When a fraction can be

When a fraction can be

written smaller or

written smaller or simplest form.

simplest form. Examples:6/24

Examples:6/24 First find common factor

First find common factor

of numerator and

of numerator and denominator.

denominator. 6=1,2,3,6 and 24=1,2,3,6.

6=1,2,3,6 and 24=1,2,3,6.

so GCF is 6so GCF is 6 Divide the 6 and 24 by 6

Divide the 6 and 24 by 6

and the new simplify

and the new simplify

fraction is 1/4

fraction is 1/4

Conve

rtin

g

Conve

rtin

g

betw

een p

erc

ent,

betw

een p

erc

ent,

deci

mals

, fr

act

ion

deci

mals

, fr

act

ion

A percent, decimals

A percent, decimals

and fractions are

and fractions are equivalent.equivalent. To convert between

To convert between decimals and percent

decimals and percent

all you need to do is

all you need to do is

multiply by 100 or

multiply by 100 or move the decimal

move the decimal place over two times.

place over two times.

Examples: 0.28 x 100

Examples: 0.28 x 100

= 28%, 0.25 x 100 =

= 28%, 0.25 x 100 =

25%, 0.14 x 100 = 14%

25%, 0.14 x 100 = 14%

Part

2 c

onve

rtin

g

Part

2 c

onve

rtin

g

betw

een d

eci

mals

,

betw

een d

eci

mals

, perc

ents

and

perc

ents

and

fract

ions.

fract

ions.

To convert percents

To convert percents into fractions you

into fractions you remove the percent

remove the percent sign, put the number

sign, put the number

over 100 then simplify.

over 100 then simplify. Examples: 28% =

Examples: 28% = 28/100 = 14/50 =

28/100 = 14/50 = 7/25, 25% = 25/100 =

7/25, 25% = 25/100 =

5/20 = 1/45/20 = 1/4

Part

3 c

onve

rtin

g

Part

3 c

onve

rtin

g

betw

een p

erc

ents

,

betw

een p

erc

ents

, deci

mals

and

deci

mals

and

fract

ions

fract

ions

To convert a percent

To convert a percent into a decimal and

into a decimal and then into a fraction

then into a fraction you take off the

you take off the percent and then you

percent and then you

move the decimal over

move the decimal over

two places. Then put

two places. Then put

the number over 100

the number over 100

and simplify.

and simplify. Examples 14% = 0.14

Examples 14% = 0.14

= 14/100 = 7/50.

= 14/100 = 7/50.

Ord

eri

ng r

ati

onal

Ord

eri

ng r

ati

onal

num

bers

num

bers

A rational number is a

A rational number is a

number that could be

number that could be

expressed as a

expressed as a fraction.fraction.

Examples: -2, -1 5/6, -

Examples: -2, -1 5/6, -

1 4/6, -1 3/6, -1 2/6, -1

1 4/6, -1 3/6, -1 2/6, -1

1/6, -11/6, -1

Unit

Rate

Unit

Rate

When a rate is

When a rate is simplified so that it

simplified so that it has a denominator of

has a denominator of

1 unit, it is called a

1 unit, it is called a unit rate.unit rate.

Examples 160 beats/2

Examples 160 beats/2

minutes = 80 beats/1

minutes = 80 beats/1

minute or 80 beats per

minute or 80 beats per

minute.minute.

Proport

ions

Proport

ions

A proportion is an

A proportion is an equation stating that

equation stating that

two rations on rates

two rations on rates are equation.

are equation.

Examples : ½ = 3/6 ,

Examples : ½ = 3/6 ,

4/8, 5/10 4/8, 5/10

Perc

ent

of

a

Perc

ent

of

a

num

ber

num

ber

To find percent of a number you can

To find percent of a number you can

do 2 different ways.

do 2 different ways.

The first one is to write the percent

The first one is to write the percent

as a fraction. The second way is to

as a fraction. The second way is to

write the percent as a decimal.

write the percent as a decimal. If the question is : What is 5% of

If the question is : What is 5% of

300? You can solve it in 2 ways

300? You can solve it in 2 ways Example number one: 5% = 5/100 or

Example number one: 5% = 5/100 or

1/201/201/20 of 300 = 1/20 x 300 =

1/20 of 300 = 1/20 x 300 =

15 15

Example number two:5%=5/100 or

Example number two:5%=5/100 or

0.050.050.05 of 300 = 0.05 x 300=15

0.05 of 300 = 0.05 x 300=15

Consu

mer

Consu

mer

Math

em

ati

cs

Math

em

ati

cs

Consumer mathematics is

Consumer mathematics is

using math to buy stuff.

using math to buy stuff.

You need to know sales tax,

You need to know sales tax,

discounts, total costs and

discounts, total costs and

other stuff.other stuff.

Sales tax is added to the

Sales tax is added to the

price of something to get

price of something to get

the final price of something

the final price of something

you buy.you buy. the phone costs $138 and

the phone costs $138 and

tax is 8.5%. You have to

tax is 8.5%. You have to

multiply them and you get

multiply them and you get

$11.33 . Then you add

$11.33 . Then you add

$11.33 to $138 and the

$11.33 to $138 and the

total cost is $149.73

total cost is $149.73

Consu

mer

Consu

mer

math

em

ati

cs

math

em

ati

cs

Some times people

Some times people give discounts.

give discounts. If the phone was on

If the phone was on

sale for 25% off you

sale for 25% off you

multiply 0.25 x138

multiply 0.25 x138 and you get $34.50

and you get $34.50

off. The discount price

off. The discount price

is $103.5is $103.5With sales tax At

With sales tax At 8.5% the final price on

8.5% the final price on

the phone is $103.50

the phone is $103.50

+ $8.80=$112.30

+ $8.80=$112.30

consu

mer

consu

mer

math

em

ati

cs

math

em

ati

cs

Some times you have

Some times you have

to find the original

to find the original price from the sale

price from the sale price if a phone is on

price if a phone is on

sale for30% off and

sale for30% off and the sale price is

the sale price is $150,what is the

$150,what is the original price?

original price?

Consu

mer

Consu

mer

math

em

ati

cs

math

em

ati

cs To figure this out you

To figure this out you

ask $130 is 70% of?

ask $130 is 70% of? To solve you multiply

To solve you multiply

$130/0.7=$143

$130/0.7=$143

Posi

tive

inte

gers

Posi

tive

inte

gers

A positive integer are

A positive integer are

greater then 0.

greater then 0. Example:58, 26, 12

Example:58, 26, 12

Negati

ve

Negati

ve

inte

gers

in

tegers

A negative integer are

A negative integer are

less then 0 and they

less then 0 and they have a negative sign .

have a negative sign .

Examples: -14, -18, -

Examples: -14, -18, -125125

Ord

er

of

Ord

er

of

opera

tion

opera

tion

My cousin who is the

My cousin who is the

greatest cousin in the

greatest cousin in the

world taught me about

world taught me about

PEMDAS. PEMDAS.

Ord

er

of

Ord

er

of

opera

tions

opera

tions

PEMDAS stands for :

PEMDAS stands for : P=PARENTHESIS

P=PARENTHESIS E=EXPONENTS

E=EXPONENTSM=MULTIPLY

M=MULTIPLYD=DIVIDED=DIVIDEA=ADD

A=ADD S=SUBTRACT

S=SUBTRACT

0R

DER

OF

0R

DER

OF

OPERATIO

NS

OPERATIO

NS

Example:5x3+(12-3)=

Example:5x3+(12-3)= 5x3+9

5x3+9 15+9=2415+9=24

One a

nd t

wo

One a

nd t

wo

step o

pera

tions

step o

pera

tions One step operations

One step operations can be solve in one

can be solve in one step.step. Examples:9x7=63,

Examples:9x7=63, 11x7=7711x7=77

One a

nd t

wo

One a

nd t

wo

step o

pera

tions

step o

pera

tions A two step problem

A two step problem can be solve in two

can be solve in two steps.steps. Examples:79-(9x3)=

Examples:79-(9x3)= 79-27=52

79-27=52

Coord

inate

Coord

inate

gra

phin

ggra

phin

g

To graph coordinates

To graph coordinates

you have to have an x-

you have to have an x-

axis and a y-axis.

axis and a y-axis. When these two cross

When these two cross

it = 0.it = 0. The y-axis goes up in

The y-axis goes up in

down and the x-axis

down and the x-axis goes side to side

goes side to side

Coord

inate

Coord

inate

gra

phin

ggra

phin

g

Quadrant one has

Quadrant one has positive numbers.

positive numbers.Quadrant two has

Quadrant two has positive and negative

positive and negative

numbers.numbers.Quadrant three only

Quadrant three only has negative numbers.

has negative numbers.

Quadrant four has

Quadrant four has positive numbers.

positive numbers.

Coord

inate

Coord

inate

gra

phin

ggra

phin

g To graph you need

To graph you need ordered pairs.

ordered pairs.An example: (3, 2).

An example: (3, 2). The three goes on the

The three goes on the

x-axis and the two

x-axis and the two goes on the y-axis

goes on the y-axis

Com

muta

tive

Com

muta

tive

pro

pert

ypro

pert

y

The commutative

The commutative property of

property of multiplication is no

multiplication is no matter what order you

matter what order you

multiply the numbers

multiply the numbers

you get the same

you get the same product.product. example:3x5=5x3

example:3x5=5x3

Ass

oci

ati

ve

Ass

oci

ati

ve

pro

pert

ypro

pert

y

The associative

The associative property of

property of multiplication is when

multiplication is when

three or more

three or more numbers are grouped

numbers are grouped

and there product has

and there product has

not change.

not change. Examples:5x(6x7)=(5x

Examples:5x(6x7)=(5x

6)x76)x7

Dis

trib

uti

ve

Dis

trib

uti

ve

pro

pert

ypro

pert

y The distributive

The distributive property has both

property has both addition and

addition and multiplication.

multiplication. Examples:3x(4+6)=3x

Examples:3x(4+6)=3x

4+3x64+3x6

Inve

rse p

ropert

y

Inve

rse p

ropert

y The inverse property

The inverse property

of multiplication have

of multiplication have

a product of one the

a product of one the inverse of a number is

inverse of a number is

called the reciprocal.

called the reciprocal. Exmple:3/4 x 4/3 = 1

Exmple:3/4 x 4/3 = 1

pro

babili

typro

babili

ty

The probability is a

The probability is a chance of an event

chance of an event happening.happening. P=number of

P=number of favorable favorable outcomes/number of

outcomes/number of

possible outcomes

possible outcomes

pro

babilt

ypro

babilt

y Examples: what is the

Examples: what is the

probability of rolling

probability of rolling an odd number n a

an odd number n a dice with 1,2,3,4,5,6

dice with 1,2,3,4,5,6 P=3/6=1/2

P=3/6=1/2

Venn d

iagra

ms

Venn d

iagra

ms

Venn diagrams

Venn diagrams overlapping circles to

overlapping circles to

show how common

show how common elements among sets

elements among sets

of numbers or objects

of numbers or objects

are related.

are related. If 2 circles overlap, the

If 2 circles overlap, the

middle area shows the

middle area shows the

common elements.

common elements. The outside areas show

The outside areas show

uncommon elements.

uncommon elements.