# PreAlgebra

## Terms

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What is Order of Operations?
1) Do all operations within grouping symbols first; start with the innermost group
2) Do all multiplication and Division from left to right.
3) Do all addition and subtraction from left to right
Define an algebraic expression.
A combination of variables, numbers and at least one operation.
What is a variable?
In algebra a placeholder is called a variable. Variables are usually letters.
Substitution Property of Equality
For all numbers a and b, if a=b, then a may be replaced by b.
The order in which numbers are added does not change the sum. 5+3=3+5
Commutative Property of Multiplication
The order in which numbers are multiplied does not change the product. 2*4=4*2
The way in which addends are grouped does not change the sum. (2+4)+6=2+(4+6)
Associative Property of Multiplication
The way in which factors are grouped does not change the product. (6*3)*7=6*(7*3)
Identity property of multiplication.
The product of a factor and 1 is the fsctor. 6*1=6
Distributive property
The sum of two addends multiplied by a number is the sum of the product of addend and the number.
a(b+c)=ab+ac and (b+c)*a=ba+ca
What are like terms?
Two or more terms with the same variable. 3st, 5st are like terms. So are 17d, 14d and 67d.
What is an equation? An Open sentence?
A mathematical sentence like 17+4=y is an equation. An equation containing variables is an open sentence. When variables in an open sentence are replaced by numbers the sentence may be true or false.
How do we locate points in mathematics?
Using a coordinate system
How is a coordinate system formed?
By the intersection of two number lines that meet at their zero points.
In a coordinate system what is origin?
The zero points where two number lines intersect.
In a coordinate system what are the horizontal and vertical axis called?
Horizontal is called the x-axis and vertical is called the y-axis
How do you graph a point in a coordinate sytem?
Using an ordered pair.
The first number in an ordered pair is the __ -axis and the second number is the __-axis.
x,y
The inverse operation of addition is______.
subtraction
The inverse operation of multiplication is _______.
division
Inverse operations are helpful for ____.
solving equations
What does it mean to define a variable?
Using an equation is an importnat problem solving strategy. The first step to writing an equation is to choose a vaiable and a quantity for the variable to represent. This is called defining a variable.
What is an inequality?
A mathematical sentence that contains < or >.
Which of these inequalities are true, false, or open? 18>3, 9<5, t<75
false, true, open until the variable is replaced by a number.
What is statistics?
collecting, analyzing, and presenting data
Bar graphs and frequency tables are used for what purpose in statistics?
To present data
In surveys where you want to represent the entire population without actually polling the entire population you can use a _____ group to represent the whole.
sample
An expression is in simplest form when it contains no ____ terms and no_____.
like, parentheses
What is a negative number?
A number less than zero.
What is absolute value? Give an example.
The distance the number is from the zero point on the number line.  is 4, [-4] is 4.
In statistics what are ouliers and what are clusters?
An outlier is data far apart from the rest of the data and clusters are data grouped closely together.
The coordinate plane can be seprated into four regions called ______?
What are the steps to adding integers with the same signs?
Add their absolute values and give the result the same sign.
What are the steps to adding integers with different signs?
Subtract their absolute values and give the result the same sign as the integer with the greater absolute value.
An integer and its opposite are additive inverses of each other.
The sum of an integer and its additive inverse is zero. 4+(-4)= 0. x+(-x)=0.
Describe the method for subtracting integers and give an example.
3-5=3+(-5), a-b=a+(-b)
Descibe the Fibonacci Sequence. What are the first ten numbers of the Fibonacci?
A pattern of numbers beginning with 1, 1 whose subsequent numbers are the sum of the previous two terms. 1,1,2,3,5,8,13,21,34,55.
The product of integers with differnet signs is always _______?
negative
The product of two integers with the same sign is _____?
positive
The quotient of two integers with different signs is ________?
negative
The quotient of two integers with the same sign is ______?
positive
What is a vertex?
a point where two sides of a polygon intersect.
How is eliminating possibilities different from guess and check?
By eliminating possible answers you can arrive at the correct answer which is different than substituting each answer into the equation to see which one is correct?.
What is the Subtraction Property of Equa;ity and when is it used?
It is used to solve equations. If you subtract the same number from each side of an equation, the two sides remain equal. If a=b, then a-c=b-c.
Some equations can be solved using the Addition property of equality. what is it?
If you add the same umber to each side of an equation, the two sides remain equal. If a=b, then a+b=b+c.
Division property of Equality
If you divide each side of an equation by the same nonzero number, the two sides remain equal.
if a=b, then a/c=b/c, where c does not equal 0
Multiplication Property of Equality
If you multiply teach side of an equation by the same number, the two sides remain equal. if a=b, then a*c = b*c.
What is a formula?
A formula shows the relationship among certain quantities.
What is the formula used to compute the miles per gallon achieved by a car?
miles/gallons=miles per gallon or
m/g=mpg
The distance around a geometric figure is called its _________?
perimeter
The measure of the surface enclosed by a geometric figure is its
area
What is the formula for the perimeter of a rectangle?
P=2(l+w), the perimeter is twice the length of the length and width
What is the formula for the area of a rectangle?
A=lw
Addition and Subtraction Properties of Inequalities
Adding or subtracting the same number from each side of an inequality does not change the truth of the inquality.
If a>b, then a+c>b+c and a-c>b-c
Multiplication and Division properties of Inequalities
When you multiply or divide each side of an inequality by a positive integer, the results remain true. if a.b, then a*c>b*c, where c>0 and a/c>b/c
What is the four step plan?
Explore What do we know and what do we need to find out,
Plan Translate words into equation and define variables,
Solve,
What are equivalent equations
Equations that have the same solution
atrium, atrio
atrium, entry hall
canis
dog
coquus
cook
cubiculum
bedroom
culina, culino
kitchen
est
is
filius
son
hortus, horto
garden
in
in, on
laborat
works, is working
mater
mother
pater
father
sedet
sits, is sitting
servus
slave
tablinum, tablino
study
triclinium, triclinio
dining room
via
street
dormit
sleep
bibit
drink
iratus
angry
circumspectat
look around
stat
stand
et
and
stertit
snoring
clamat
shout, exclaim
cibus
food
mensa
table
familia
family
in mensa
on the table
pestis
pest
furcifer
scoundrel
scribit
write
intrat
entering
spectat
looking
salit
jump
latrat
bark
surgit
rising
exit
exit
amicus
friend
ancilla
slave-girl
cena
dinner
dominus
master
gustat
taste
laetus
happy
laudat
praises
mercator
merchant
quoque
also, too
salutat
greets
toga
toga
tunica
tunic
visitat
visiting
villam
house
pecuniam
money
numerat
counting
argentarius
banker
salve
hello
respondet
replies
in lecto
on a couch
recumbit
reclines
cantat
singing
pavonem
peacock
coquit
is cooking
audit
hears, listens to
non est
is not
cenam
dinner
exspectat
is waiting for
vituperat
tells off, curses
portat
is carrying
vinum
wine
optimus
very good, excellent
suaviter
sweetly
delectat
mox
soon
videt
sees
consumit
eats
magnifice
in style, magificently
cenat
eats dinner, dines
laetissimus
very happy
paratus
anxius
anxious
vocat
call
non
no
irratissimus
very angry
bonus
good

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