Transcript Prime vs. Composite Numbers

Prime vs. Composite Numbers
• A prime number is a whole number
greater than 1 that has exactly two
factors 1 and itself.
• 2,3,5,7 are whole prime numbers
Ex: The number 17 has only two factors
1 and itself, so its prime.
Prime vs. Composite Numbers
• Prime Factorization is a composite number
that can be written as a product of prime
numbers. Factor Trees are used to find the
prime factorization.
60
6 x 10
2x 3x 2x5
The prime factorization of 60 is 2x2x3x5.
Prime vs. Composite Numbers
• A Composite Number is a whole number
grater than 1 that has more than 2
factors.
• 4,6,8,9,10 are whole composite numbers
Ex: The number 12has six factors:1,2,3,4,6
and 12, so its composite.
Simplifying Factions
• A fraction is simplest form when the GCF
of the numerator and denominator is 1.
• Equivalent fractions have the same value.
Method 1:
6 over 24 divided by the CF which is 2 will
bring you to 3/12 which is simplified but
not in simplest form so you’d divide again
by 3 and you’d get and get ¼.
Simplifying Fractions
Method 2:
First find the GCF of the numerator and
denominator.
Factors of 6:1,2,3,6
The GCF of 6 and
Factors of 24:1,2,3,4,6
24 is 6.
Then divide the numerator and denominator
by the GCF,6.
6/24 divided by 6 which
equals ¼
Converting between percents,
decimals, fractions
• Percents, decimals, and fractions can all be
•
•
•
turned into each other. They all came from
whole numbers.
Percents are basically out of 100.
Fractions are out of what ever the denominator
is and the numerator should never be bigger
than the denominator.
Decimals are whole numbers with extra left over.
Converting between Percents,
Decimals and Fractions
• Percents turned into fractions:
190%=190/100 then take off the extra
zero’s and make it 19/10 or 1 9/10 this is
called an improper fractions
• Fractions turned into percents:
¼ =25%, ½ =50%,3/4 =75%
Converting between Percents,
Fractions, and Decimals
Fractions turned into decimals:
89/100,000 = n/100
8,900=100,000n
8,900/00,000 = 100,000n/100,000
n=0.089 Write a proportion, find the
cross products, divide each side by
100,000
Fractions turned into decimals:
¼ = 0.25 ¾ = 0.75 ½ = 0.5
Ordering Rational Numbers
• A rational number is a number that can be
expressed as a fractions.
Least to Greatest:
-5,3,-3,7,-1 = -5,-3,-1,3,7
6.8,7.2,1,0.94,6 = -6,0.94,1,6.8,7.2
Greatest to Least:
12,6,-4,0,-5,-3 = 12,6,0,-3,-4,-5
10,6.8,4.9,0.1,0.1,10.6=10.6,10,6.8,4.9,0.1, -0.1
Unit Rate
• Unit Rate-the quantity per 1 unit (30mph)
• To find the unit rate ,your denominator
must be 1.
Ex:$280 a week, what is your hourly wage
if you work 40 hrs per week?
$280 divided by $40=$7hr
Proportions
• Proportion- an equation stating that 2
ratios are equal.
Ex:2/3= 10/15
• Cross product-to multiply diagonally.
Ex:20 40
20x10=200
y
=
5x40=200
5
10
Proportions
Ex: 6
24
7x24=168
y
=
6x29=174 no
7
29
Ex: 5
x
6x=18.5 multiply
y
=
6x=90 divide
6
18
6
6 (x=15 solution)
Ex:6/c=24/28 24c=6x28=168 24 divided by
7=168
24c=7x2 c=7
Percent of a Number
To find 5% of 300, you can use either
method.
Method 1:Write the percent as a fraction
5%=5/100 or 1/20
1/20 of 300=1/20x300 or 15
Method 2:Write the percent as a decimal
5%=5/100 or 0.05
0.05 of 300=o.05x300 or 15 so 5% of 300
is 15
Consumer Mathematics
List price-Original prize
Sales tax-Amount added to the original price
Total price-LP+ Sales tax
Sales Tax
Sales tax= LP x rate
What is the sales tax?, on $110 @ 5% sales tax?
$110x0.05=$5.50
In Arizona the sales tax is 6.5%. What is the sales
tax on a $239 DVD player?
239x0.065=$15.535=$15.54
Consumer Mathematics
Total Cost:
What is the total cost the of groceries if they are
listed @ $74.50 and there is a 7% sales tax?
$74.50x7=52.150=52.2
74.50+52.2=$79.72
Discount-The amount by which the list is reduced
Sales price-LP-D
Rate of Discount-the percent of discount
Tent-$50 @ 17% discount. D=LP x Rate
D=50 x 0.17 D=$8.50
Consumer Mathematics
$310 @ 25% discount; 6% sales tax
D=LP x R
ST=LP x R
D=310x0.25
ST=232.50x0.06
D=$77.50
ST=$13.95
SP=LP-D
TC=LP + ST
SP=310-77.50 TC=23.50 + 13.95
SP=$232.50
TC=$246.45
Integers
Integers are numbers that are either
positive or negative.
Positive integers are numbers above zero.
012345678910
Negative integers are numbers below zero.
-1-2-3-4-5-6-7-8-9-10
Integers
Add and Integers
Rule 1: If they have the same sign, add
them and use their sign.
Ex: 3+1=4 -3+(-1)=-4
Rule 2: If they have different signs, subtract
(big-small) and use the sign of the bigger
number
Ex:15+-35=-20
Integers
Absolute value-the distance a number is
from zero on the number line.
*Absolute value is always positive.
Ex: -9 =9
Compare and order Integers
-100,35,-32,-33,-1=-100,-33,-32,-1,35
Subtracting Integers
Rule: Keep, change, flip
Integers
Multiply and Divide Integers
Positive: Pos x Pos, Negative x Negative, Pos
divided by a Pos, Negative divided by a
Negative
Negative: Pos x Negative, Negative x Pos,
Pos divided by a Negative, Negative
divided by a Pos.
2x3=6 -2x-3=6 5x-2=-10 -5x2=10
20 divided by -2=10 -20 divided by 2=-10
Order of Operations
• Parenthesis ( )
• Exponents
• Multiplication or Division (left to right)
• Add or Subtract (left to right)
Ex:5(3-1)+6 to the second power
1.(3-1) 2.6 to the second power 3.5x2
4.36+10
One and Two Step Operation
Inverse Operations- Opposite Operation,
add/subtract; multiply/divide.
Ex: a+4= 7
c-8=3
-4 -4
+8 +8
a=3
c=11
One and Two Step Operation
Step 1-Add or Subtract
Step 2-Multiply or divide
Ex: 2a+4=16
-4 -4
2a=12
2 2
a=6
Coordinate Graphing
II (-,+)
v
III (-,-)
(+,+)I
PointCoordinateQuadrant
v
-8,0
x-axis
X-AXIS
(+,-)IV
Y-AXIS
Middle- origin
Order pair=(x, y)
Properties
Commutative Property-In addition and
multiplication, the order dose not matter.
Ex:9x8=72
3+5=8
a+ b= b+ a
8x9=72
5+3=8
ax b= b x a
Associative Property-Grouping numbers
together that are easy to work with. (t and
x) Ex:3+61+7=(3+7)+61
Properties
Distribute Properties-Distribute your number
through the problem using multiplication.
Ex:5(8x3)=5x8+5x3=40+15=55
Identity Properties-The sum of an addend
and 0 is the addend. The product of a
factor and 1 is the factor. A + 0=A
Probability
Simple Events:
Probability-number of successful outcomes
divided by a total number outcomes
Event: Roll a number cube
P(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(9)=0/6=0 impossible
Probability
Sample Space and Probability
Sample space-the set of all possible
outcomes in a probability experiment.
Tree diagram-used to display the sample
space.
A couple decided to have two children. Find
the sample space of the children's gender
if having a boy is equally likely as having a
girl. Answer: girl, girl, girl, boy, boy, boy,
girl, boy.
Probability
Sample space and Probability
Amy has two choices of bread and 3 choices
for lunchmeat.
Ham
Outcomes=6
Wheat Turkey
Roast beef
Ham
Sourdough Turkey
Roast beef
Fundamental Counting Principle
We use the FCP to determine how many out
comes there are in an event.
Ex: Day of the week then month of a year. 84
Toss a coin roll a cube choose a letter in math.
48
Pants
Shirt
Shoes Socks
Pink skinnies Hello kitty Boots Knee highs
School pants Halter top Boots w/ fur dirty socks
Short shorts Toga 54
Probability
Permutations-in a permutation the order is not
important. How many different ways can 5
people line up. 5x4x3x2x1=120
Combinations-not important number
Ex: 2 toppings Method 1: Make a list
ham
hp ph sh bh oh
pineapple
hs ps sp bp op
salami
hb pb sb bs os
bacon
ho po so bo ob
onion
10 choices
Probability
Combinations:
Method 2-Formula
5x4/2x1=20/2=10
Ex: You choose 3 out of 7 stickers
7x6x5/3x2x1=35
Probability
Compound Events- two or more simple
events.
Independent Events-the outcome of one
event doses
NOT affect the next outcome. (with
replacement)
2 Ex: flip a coin and roll a cube
Probability
Compound Events:
Dependent Event-The outcome of the first
event will affect the probability of the next
event. (without replacement)
Ex: P (g, b)=4/105
Venn diagrams
Sprite-5
Both-10
Pepsi-8 Neither-2
10 represents the people that like both
Sprit and Pepsi.
2 represents the people who do not like
either Sprite or Pepsi.
5 represents the people who like Sprite
only.
8 represents the people who like Pepsi only.