Prime vs. Composite Prime vs. Composite NumbersNumbers

• A prime number is a whole A prime number is a whole number greater than 1 that has number greater than 1 that has exactly two factors 1 and itself.exactly two factors 1 and itself.

• 2,3,5,7 are whole prime numbers2,3,5,7 are whole prime numbers

Ex: The number 17 has only two Ex: The number 17 has only two factors 1 and itself, so its prime. factors 1 and itself, so its prime.

Prime vs. Composite Prime vs. Composite NumbersNumbers• Prime Factorization is a composite number Prime Factorization is a composite number

that can be written as a product of prime that can be written as a product of prime numbers. Factor Trees are used to find the numbers. Factor Trees are used to find the prime factorization. prime factorization.

60 60

6 x 10 6 x 10

2 x 3 x 2 x 52 x 3 x 2 x 5

The prime factorization of 60 is 2x2x3x5. The prime factorization of 60 is 2x2x3x5.

Prime vs. Composite Prime vs. Composite Numbers Numbers

• A Composite Number is a whole A Composite Number is a whole number grater than 1 that has more number grater than 1 that has more than 2 factors. than 2 factors.

• 4,6,8,9,10 are whole composite 4,6,8,9,10 are whole composite numbersnumbers

Ex: The number 12has six Ex: The number 12has six factors:1,2,3,4,6 and 12, so its factors:1,2,3,4,6 and 12, so its composite.composite.

Simplifying FactionsSimplifying Factions

• A fraction is simplest form when the GCF A fraction is simplest form when the GCF of the numerator and denominator is 1. of the numerator and denominator is 1.

• Equivalent fractions have the same Equivalent fractions have the same value. value.

Method 1:Method 1:

6 over 24 divided by the CF which is 2 will 6 over 24 divided by the CF which is 2 will bring you to 3/12 which is simplified but bring you to 3/12 which is simplified but not in simplest form so you’d divide not in simplest form so you’d divide again by 3 and you’d get and get ¼. again by 3 and you’d get and get ¼.

Simplifying FractionsSimplifying Fractions

Method 2: Method 2:

First find the GCF of the numerator and First find the GCF of the numerator and denominator. denominator.

Factors of 6:1,2,3,6 The GCF of 6 and Factors of 6:1,2,3,6 The GCF of 6 and

Factors of 24:1,2,3,4,6 24 is 6. Factors of 24:1,2,3,4,6 24 is 6.

Then divide the numerator and Then divide the numerator and denominator by the GCF,6. 6/24 denominator by the GCF,6. 6/24 divided by 6 which equals ¼ divided by 6 which equals ¼

Converting between percents, Converting between percents, decimals, fractionsdecimals, fractions

• Percents, decimals, and fractions can all Percents, decimals, and fractions can all be turned into each other. They all came be turned into each other. They all came from whole numbers. from whole numbers.

• Percents are basically out of 100. Percents are basically out of 100. • Fractions are out of what ever the Fractions are out of what ever the

denominator is and the numerator should denominator is and the numerator should never be bigger than the denominator. never be bigger than the denominator.

• Decimals are whole numbers with extra Decimals are whole numbers with extra left over. left over.

Converting between Percents, Converting between Percents, Decimals and FractionsDecimals and Fractions

• Percents turned into fractions: Percents turned into fractions:

190%=190/100 then take off the extra 190%=190/100 then take off the extra zero’s and make it 19/10 or 1 9/10 this zero’s and make it 19/10 or 1 9/10 this is called an improper fractions is called an improper fractions

• Fractions turned into percents: Fractions turned into percents:

¼ =25%, ½ =50%,3/4 =75% ¼ =25%, ½ =50%,3/4 =75%

Converting between Percents, Converting between Percents, Fractions, and DecimalsFractions, and Decimals Fractions turned into decimals: Fractions turned into decimals: 89/100,000 = n/100 89/100,000 = n/100 8,900=100,000n 8,900=100,000n 8,900/00,000 = 100,000n/100,000 8,900/00,000 = 100,000n/100,000 n=0.089 Write a proportion, find n=0.089 Write a proportion, find

the cross products, divide each side the cross products, divide each side by 100,000 by 100,000

Fractions turned into decimals: Fractions turned into decimals: ¼ = 0.25 ¾ = 0.75 ½ = 0.5¼ = 0.25 ¾ = 0.75 ½ = 0.5

Ordering Rational NumbersOrdering Rational Numbers• A rational number is a number that A rational number is a number that

can be expressed as a fractions. can be expressed as a fractions. Least to Greatest: Least to Greatest: -5,3,-3,7,-1 = -5,-3,-1,3,7 -5,3,-3,7,-1 = -5,-3,-1,3,7 6.8,7.2,1,0.94,6 = -6.8,7.2,1,0.94,6 = -

6,0.94,1,6.8,7.2 6,0.94,1,6.8,7.2 Greatest to Least: Greatest to Least: 12,6,-4,0,-5,-3 = 12,6,0,-3,-4,-5 12,6,-4,0,-5,-3 = 12,6,0,-3,-4,-5 10,6.8,4.9,-10,6.8,4.9,-

0.1,0.1,10.6=10.6,10,6.8,4.9,0.1, -0.10.1,0.1,10.6=10.6,10,6.8,4.9,0.1, -0.1

Unit RateUnit Rate

• Unit Rate-the quantity per 1 unit Unit Rate-the quantity per 1 unit (30mph) (30mph)

• To find the unit rate ,your To find the unit rate ,your denominator must be 1. denominator must be 1.

Ex:$280 a week, what is your hourly Ex:$280 a week, what is your hourly wage if you work 40 hrs per week? wage if you work 40 hrs per week?

$280 divided by $40=$7hr$280 divided by $40=$7hr

ProportionsProportions

• Proportion- an equation stating that 2 Proportion- an equation stating that 2 ratios are equal. ratios are equal.

Ex:2/3= 10/15 Ex:2/3= 10/15

• Cross product-to multiply diagonally. Cross product-to multiply diagonally.

Ex:20 40 20x10=200 Ex:20 40 20x10=200 y y = 5x40=200 = 5x40=200

5 105 10

ProportionsProportions

Ex: 6 24 7x24=168 Ex: 6 24 7x24=168 y = 6x29=174 no y = 6x29=174 no

7 29 7 29

Ex: 5 x 6x=18.5 multiply Ex: 5 x 6x=18.5 multiply y = 6x=90 divide y = 6x=90 divide

6 18 6 6 (x=15 solution) 6 18 6 6 (x=15 solution)

Ex:6/c=24/28 24c=6x28=168 24 divided by Ex:6/c=24/28 24c=6x28=168 24 divided by 7=168 24c=7x2 c=77=168 24c=7x2 c=7

Percent of a NumberPercent of a Number

To find 5% of 300, you can use either To find 5% of 300, you can use either method. method.

Method 1:Write the percent as a fraction Method 1:Write the percent as a fraction 5%=5/100 or 1/20 5%=5/100 or 1/20

1/20 of 300=1/20x300 or 15 1/20 of 300=1/20x300 or 15 Method 2:Write the percent as a Method 2:Write the percent as a decimal decimal

5%=5/100 or 0.05 5%=5/100 or 0.05

0.05 of 300=o.05x300 or 15 so 5% of 0.05 of 300=o.05x300 or 15 so 5% of 300 is 15 300 is 15

Consumer MathematicsConsumer MathematicsList price-Original prize List price-Original prize

Sales tax-Amount added to the original price Sales tax-Amount added to the original price

Total price-LP+ Sales tax Total price-LP+ Sales tax

Sales TaxSales Tax

Sales tax= LP x rate Sales tax= LP x rate

What is the sales tax?, on $110 @ 5% sales What is the sales tax?, on $110 @ 5% sales tax? $110x0.05=$5.50 tax? $110x0.05=$5.50

In Arizona the sales tax is 6.5%. What is the In Arizona the sales tax is 6.5%. What is the sales tax on a $239 DVD player? sales tax on a $239 DVD player? 239x0.065=$15.535=$15.54 239x0.065=$15.535=$15.54

Consumer MathematicsConsumer MathematicsTotal Cost: Total Cost: What is the total cost the of groceries if they are What is the total cost the of groceries if they are

listed @ $74.50 and there is a 7% sales tax? listed @ $74.50 and there is a 7% sales tax? $74.50x7=52.150=52.2 $74.50x7=52.150=52.2

74.50+52.2=$79.72 74.50+52.2=$79.72 Discount-The amount by which the list is Discount-The amount by which the list is

reduced reduced Sales price-LP-D Sales price-LP-D Rate of Discount-the percent of discount Rate of Discount-the percent of discount Tent-$50 @ 17% discount. D=LP x Rate Tent-$50 @ 17% discount. D=LP x Rate D=50 x 0.17 D=$8.50 D=50 x 0.17 D=$8.50

Consumer MathematicsConsumer Mathematics

$310 @ 25% discount; 6% sales tax $310 @ 25% discount; 6% sales tax

D=LP x R ST=LP x R D=LP x R ST=LP x R

D=310x0.25 ST=232.50x0.06 D=310x0.25 ST=232.50x0.06

D=$77.50 ST=$13.95 D=$77.50 ST=$13.95

SP=LP-D TC=LP + ST SP=LP-D TC=LP + ST

SP=310-77.50 TC=23.50 + 13.95 SP=310-77.50 TC=23.50 + 13.95

SP=$232.50 TC=$246.45SP=$232.50 TC=$246.45

Integers Integers

Integers are numbers that are either Integers are numbers that are either positive or negative. positive or negative.

Positive integers are numbers above zero. Positive integers are numbers above zero.

012345678910012345678910

Negative integers are numbers below zero. Negative integers are numbers below zero.

-1-2-3-4-5-6-7-8-9-10 -1-2-3-4-5-6-7-8-9-10

IntegersIntegers

Add and Integers Add and Integers

Rule 1: If they have the same sign, add Rule 1: If they have the same sign, add them and use their sign. them and use their sign.

Ex: 3+1=4 -3+(-1)=-4 Ex: 3+1=4 -3+(-1)=-4

Rule 2: If they have different signs, Rule 2: If they have different signs, subtract (big-small) and use the sign subtract (big-small) and use the sign of the bigger number of the bigger number

Ex:15+-35=-20 Ex:15+-35=-20

IntegersIntegersAbsolute value-the distance a number Absolute value-the distance a number

is from zero on the number line. is from zero on the number line. *Absolute value is always positive. *Absolute value is always positive. Ex: -9 =9Ex: -9 =9Compare and order Integers Compare and order Integers -100,35,-32,-33,-1=-100,-33,-32,-1,35 -100,35,-32,-33,-1=-100,-33,-32,-1,35 Subtracting Integers Subtracting Integers Rule: Keep, change, flip Rule: Keep, change, flip

IntegersIntegers

Multiply and Divide Integers Multiply and Divide Integers Positive: Pos x Pos, Negative x Positive: Pos x Pos, Negative x

Negative, Pos divided by a Pos, Negative, Pos divided by a Pos, Negative divided by a Negative Negative divided by a Negative

Negative: Pos x Negative, Negative x Negative: Pos x Negative, Negative x Pos, Pos divided by a Negative, Pos, Pos divided by a Negative, Negative divided by a Pos. Negative divided by a Pos.

2x3=6 -2x-3=6 5x-2=-10 -5x2=10 2x3=6 -2x-3=6 5x-2=-10 -5x2=10 20 divided by -2=10 -20 divided by 20 divided by -2=10 -20 divided by

2=-10 2=-10

Order of OperationsOrder of Operations

• Parenthesis ( ) Parenthesis ( )

• Exponents Exponents

• Multiplication or Division (left to right) Multiplication or Division (left to right)

• Add or Subtract (left to right) Add or Subtract (left to right)

Ex:5(3-1)+6 to the second power Ex:5(3-1)+6 to the second power

1.(3-1) 2.6 to the second power 3.5x2 1.(3-1) 2.6 to the second power 3.5x2 4.36+104.36+10

One and Two Step One and Two Step OperationOperation

Inverse Operations- Opposite Inverse Operations- Opposite Operation, add/subtract; Operation, add/subtract; multiply/divide. multiply/divide.

Ex: a+4= 7 c-8=3 Ex: a+4= 7 c-8=3

-4 -4 +8 +8-4 -4 +8 +8

a=3 c=11a=3 c=11

One and Two Step One and Two Step OperationOperation

Step 1-Add or Subtract Step 1-Add or Subtract

Step 2-Multiply or divide Step 2-Multiply or divide

Ex: 2a+4=16 Ex: 2a+4=16

-4 -4 -4 -4

2a=12 2a=12

2 2 2 2

a=6a=6

Coordinate GraphingCoordinate Graphing

PointCoordinateQuadrantPointCoordinateQuadrant

II (-,+) (+,+)I v -8,0 x-axisII (-,+) (+,+)I v -8,0 x-axis

v X-AXIS v X-AXIS

III (-,-) (+,-)IVIII (-,-) (+,-)IV

Y-AXISY-AXIS

Middle- origin Order pair=(x, y)Middle- origin Order pair=(x, y)

PropertiesProperties

Commutative Property-In addition and Commutative Property-In addition and multiplication, the order dose not multiplication, the order dose not matter. matter.

Ex:9x8=72 3+5=8 a+ b= b+ a Ex:9x8=72 3+5=8 a+ b= b+ a

8x9=72 5+3=8 ax b= b x a 8x9=72 5+3=8 ax b= b x a

Associative Property-Grouping numbers Associative Property-Grouping numbers together that are easy to work with. (t together that are easy to work with. (t and x) Ex:3+61+7=(3+7)+61 and x) Ex:3+61+7=(3+7)+61

PropertiesProperties

Distribute Properties-Distribute your Distribute Properties-Distribute your number through the problem using number through the problem using multiplication. multiplication.

Ex:5(8x3)=5x8+5x3=40+15=55 Ex:5(8x3)=5x8+5x3=40+15=55

Identity Properties-The sum of an addend Identity Properties-The sum of an addend and 0 is the addend. The product of a and 0 is the addend. The product of a factor and 1 is the factor. A + 0=A factor and 1 is the factor. A + 0=A

ProbabilityProbability

Simple Events: Simple Events:

Probability-number of successful outcomes Probability-number of successful outcomes divided by a total number outcomes divided by a total number outcomes

Event: Roll a number cube Event: Roll a number cube

P(5)=1/6 not likely P (not 1)=5/6 likelyP(5)=1/6 not likely P (not 1)=5/6 likely

P (odd)=3/6=1/2 equal P(6)=6/6=1 definite P (odd)=3/6=1/2 equal P(6)=6/6=1 definite

P(9)=0/6=0 impossible P(9)=0/6=0 impossible

ProbabilityProbabilitySample Space and Probability Sample Space and Probability Sample space-the set of all possible Sample space-the set of all possible

outcomes in a probability experiment. outcomes in a probability experiment. Tree diagram-used to display the sample Tree diagram-used to display the sample

space. space. A couple decided to have two children. A couple decided to have two children.

Find the sample space of the children's Find the sample space of the children's gender if having a boy is equally likely gender if having a boy is equally likely as having a girl. Answer: girl, girl, girl, as having a girl. Answer: girl, girl, girl, boy, boy, boy, girl, boy.boy, boy, boy, girl, boy.

Probability Probability Sample space and ProbabilitySample space and ProbabilityAmy has two choices of bread and 3 Amy has two choices of bread and 3

choices for lunchmeat. choices for lunchmeat. Ham Outcomes=6Ham Outcomes=6Wheat Turkey Wheat Turkey Roast beef Roast beef HamHam Sourdough Turkey Sourdough Turkey Roast beefRoast beef

Fundamental Counting Fundamental Counting PrinciplePrincipleWe use the FCP to determine how many out We use the FCP to determine how many out

comes there are in an event. comes there are in an event.

Ex: Day of the week then month of a year. 84Ex: Day of the week then month of a year. 84

Toss a coin roll a cube choose a letter in Toss a coin roll a cube choose a letter in math. 48 math. 48

Pants Shirt Shoes SocksPants Shirt Shoes Socks

Pink skinnies Hello kitty Boots Knee highs Pink skinnies Hello kitty Boots Knee highs

School pants Halter top Boots w/ fur dirty School pants Halter top Boots w/ fur dirty sockssocks

Short shorts Toga 54Short shorts Toga 54

ProbabilityProbabilityPermutations-in a permutation the order is not Permutations-in a permutation the order is not

important. How many different ways can 5 important. How many different ways can 5 people line up. 5x4x3x2x1=120 people line up. 5x4x3x2x1=120

Combinations-not important number Combinations-not important number

Ex: 2 toppings Method 1: Make a listEx: 2 toppings Method 1: Make a list

ham hp ph sh bh oh ham hp ph sh bh oh

pineapple hs ps sp bp oppineapple hs ps sp bp op

salami hb pb sb bs os salami hb pb sb bs os

bacon ho po so bo ob bacon ho po so bo ob

onion 10 choices onion 10 choices

ProbabilityProbability

Combinations:Combinations:

Method 2-Formula Method 2-Formula

5x4/2x1=20/2=10 5x4/2x1=20/2=10

Ex: You choose 3 out of 7 stickers Ex: You choose 3 out of 7 stickers

7x6x5/3x2x1=357x6x5/3x2x1=35

ProbabilityProbability

Compound Events- two or more simple Compound Events- two or more simple events. events.

Independent Events-the outcome of Independent Events-the outcome of one event doses one event doses

NOT affect the next outcome. (with NOT affect the next outcome. (with replacement) replacement)

2 Ex: flip a coin and roll a cube 2 Ex: flip a coin and roll a cube

ProbabilityProbability

Compound Events:Compound Events:

Dependent Event-The outcome of the Dependent Event-The outcome of the first event will affect the probability first event will affect the probability of the next event. (without of the next event. (without replacement) replacement)

Ex: P (g, b)=4/105 Ex: P (g, b)=4/105

Venn diagramsVenn diagrams

Sprite-5 Both-10 Pepsi-8 Sprite-5 Both-10 Pepsi-8 Neither-2Neither-2

10 represents the people that like both 10 represents the people that like both Sprit and Pepsi. Sprit and Pepsi.

2 represents the people who do not like 2 represents the people who do not like either Sprite or Pepsi. either Sprite or Pepsi.

5 represents the people who like Sprite 5 represents the people who like Sprite only.only.

8 represents the people who like Pepsi 8 represents the people who like Pepsi only. only.