PreAlgebra
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- What is Order of Operations?
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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
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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. [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.
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To subtract an integer add its additive inverse.
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
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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?
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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
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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?
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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
- 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
- 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