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.
 Commutative Property of Addition
 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
 Associative Property of Addition
 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 Addition
 The sum of an addend and zero is the addend. 6+0=6
 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 xaxis and vertical is called the yaxis
 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. [4] 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 ______?
 quadrants
 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.
 What is an additive inverse?
 An integer and its opposite are additive inverses of each other.
 Additive Inverse property
 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.

To subtract an integer add its additive inverse.
35=3+(5), ab=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 ac=bc.
 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 ac>bc  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,
Examine check your answer.  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
 slavegirl
 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
 pleases
 mox
 soon
 videt
 sees
 consumit
 eats
 magnifice
 in style, magificently
 cenat
 eats dinner, dines
 laetissimus
 very happy
 paratus
 ready
 anxius
 anxious
 vocat
 call
 non
 no
 irratissimus
 very angry
 bonus
 good