GLOSSARY 
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Absolute Value  the absolute value of a number is the distance the number is from the zero point on the number line. The absolute value of a number or an expression is always greater than or equal to zero (i.e. nonnegative). see lesson 
Addition  a mathematical process to to combine numbers and/or variables into an equivalent quantity, number or algebraic expression 
Adding integers 
To ADD integers with the same sign, add their
absolute values. Give the
result the same sign as the integers.
To ADD integers with different signs, SUBTRACT the lesser absolute value from the greater absolute value. Give the result the same sign as the integer with the greater absolute value. 
Addition (and Subtraction) Property for Inequality 
For all numbers a, b, and c, the following are true: 1. If a > b, then a + c >
b + c 2. If a < b, then a + c <
b + c In words, if the same number or
expression is added or subtracted from both sides of a true inequality, the new
inequality is also true. 
Additive Identity Property 
For any number a, a + 0 = 0 + a In words, adding zero to a number leaves the number unchanged, hence the "identical" number. 
Additive Inverse Property 
For every number a, a + (a) = 0 e.g. 5 + ? = 0 5 + (5) = 0 17 + ? = 0 17 + 17 = 0 In words, if the opposite of a number is added to the original number, the sum is equal to zero. 
Algebra  a language that helps translate reallife situations into mathematical form so that we can analyze change and answer the question "What if?" 
Algebraic Expression  an expression consisting of one or more numbers and variables along with one or more arithmetic operations. 
Arithmetic Operation  a mathematical process of addition, subtraction, multiplication or division. 
Axes  Two perpendicular number lines that are used to locate points in a coordinate plane. By convention, the xaxis is the horizontal line and the yaxis is the vertical line. 
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BestFit Line 
A line drawn so it is close to most or all of the data points in a graph. A bestfit line is described as strong
or weak depending on how close the data
points are on average. 
Binomial  The sum of two monomials. 
Boundary  A boundary line of an inequality is a line that separates the coordinate plane into halfplanes. 
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Coefficient  The numerical factor in a term. In the term 4x, 4 is the coefficient. In the term ^{4x}/_{5 }; ^{4}/_{5} is the coefficient. Note that ^{4x}/_{5 }can also be written as ( ^{4}/_{5 })x. 
Complex fraction  A fraction that has one or more fractions in the numerator or denominator. 
Compound Event  A compound event consists of two or more simple events (i.e. the tossing of two or more coins). 
Compound Inequality  Two inequalities connected by AND or OR. 
Consistent  A system of equations is said to be consistent when it has at least one ordered pair that satisfies both equations. 
Constants  A monomial term that lacks a variable component. 
the plane containing the x and y axes.  
Counting Numbers  The set of counting (aka "natural") numbers can be expressed as {1,2,3,...}. This set is identical to the set of whole numbers, less the number zero. Counting numbers are not negative. 
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Degree of a monomial  The degree of a monomial is the sum of the exponents of its variables. 
Degree of a polynomial  The degree of a polynomial is the degree of the term of the greatest monomial degree. 
Dependent (equations)  A system of equations that has an infinite number of solutions 
Dependent Event  An occurrence or outcome that is affected by previous occurrences or outcomes. The probability of drawing a red or black card from a deck of cards is affected by the colors of cards previously drawn. see independent event 
Dependent Variable  When solving an equation for a given variable, that variable becomes the dependent variable. That is, its value depends upon the domain values chosen for the other variable. The dependent variable represents the range and is graphed on the yaxis (see independent variable). 
Difference  The result of a subtraction operation. Order matters! The difference of 6 and 3 equals 3. The difference of 3 and 6 equals 3. 
Difference of Squares  Two perfect
squares separated by a subtraction sign: a^{2}  b^{2}
& x^{2}  49 are both examples of the
difference of squares.
The difference of squares can easily be factored as follows: a^{2}  b^{2} = (a + b)(a
 b) 
Division Property for Inequality  
Domain  the set of all first (x) coordinates from the ordered pairs in a relation. 
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Element  A member of a set. 
Elimination  The elimination method of solving a system of equations is a method that uses addition or subtraction to eliminate one of the variables to solve for the other variable. 
Equal (also Equivalent) 
a term used to indicate that two or more quantities are of the same value. 
Equation  a mathematical sentence that compares two expressions linked by an equals sign (=). 
Evaluate  To find the value of an expression when the value of the variables are known. 
Exponent  In an expression of the form x^{n}, the exponent is n. The exponent represents the number of times the base (in this case, x) is multiplied by itself. The expression x^{n} is called a power. 
Expression  see Algebraic Expression 
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Factors  In
a multiplication expression, the quantities being multiplied are called
factors.
In the monomial term 3bc, there are three factors: 3, b and c. In the algebraic expression 3(m+5) there are two factors: 3 and (m+5). 
FOIL Method  To
multiply two binomials, find the sum of the
products of:
F
the first terms, 
Formula  an equation that states a rule for the relationship between certain quantities. The formula for distanceratetime problems is d=rt. 
Function
(see vertical line test) 
a function is a relation in which each element of the domain is paired with exactly one element of the range. 
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Graph  To draw or
plot the points named by: 1) certain numbers on a number line or 2) certain ordered pairs on a coordinate plane. 
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HalfPlane  The region on a graph on one side of a boundary is called a halfplane. 
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Inconsistent  A system of equations is said to be inconsistent when it has no ordered pair that satisfies both equations. 
Independent (equations)  A system of equations is said to be independent if the system has exactly one solution. 
Independent Event  An occurrence or outcome that is not affected by previous occurrences or outcomes. The probability of tossing a coin heads or tails is an independent event. see dependent event 
Independent Variable  The domain contains values represented by the independent variable. The domain values are graphed on the xaxis (see dependent variable). 
Inequality  A mathematical sentence comparing two expressions that are linked by one of the following: <, <, >, or >. 
Integer  The set of numbers represented as {..., 3, 2, 1, 0, 1, 2, 3,...}. 
Intersection (of sets)  The intersection of two sets A and B is the set of elements common to both A and B. 
Inverse of a Relation  Relation Q is the inverse of Relation S if and only if for every ordered pair (a,b) in S, there is an ordered pair (b,a) in Q. For example, the inverse of (2, 5) is (5, 2). 
Irrational number  A number that cannot be expressed in the form (a/b) where a and b are integers and b <> 0. 
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Like Terms  terms that contain the same variables, where the corresponding variables also are of the same power (exponent). 
Linear Equation  An equation whose graph is a line. 
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Mathematical Sentence  see Open Sentence 
Monomial  A monomial is a number, a variable, or a product of a number and one or more variables. 
Multiplication (and Division) Property for Inequality 
For all numbers a, b, and c, the following are true: IF c is POSITIVE: 1. If a > b, then ac >
bc the same holds true for DIVISION where c is not equal to zero. + + + + + + + + + + + + For all numbers a, b, and c, the following are true: IF c is NEGATIVE: 1. If a > b, then ac <
bc the same holds true for DIVISION where c is not equal to zero. 
Multiplicative Identity Property 
For any number a,
a ^{.} 1 = 1 ^{. }a =
a 
Multiplicative Inverse Property 
For every nonzero number a/b,
there is exactly one number b/a such that (a/b) ^{.} (b/a) = 1 In words, a number multiplied by its reciprocal will always equal zero. 
Multiplicative Property of Zero 
For any number a,
a ^{. }0 = 0 ^{. }a =
0 In words, any number or expression multiplied by zero will equal zero. 
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Natural Numbers  see counting numbers. 
Negative Correlation  There
is a negative correlation between x and y if the values are related in
an opposite way  i.e. as x increases, y decreases or as x decreases, y
increases. see lesson 
Negative Exponent  For any
nonzero number a
and any integer n: a^{n} = ^{1}/_{a}n 
Negative Number  Any number that is less than zero. 
Number  an element of a mathematical system used to represent known quantities, both standalone and in mathematical sentences. 
Number Line  A line with equal distances marked off to represent numbers. 
Numerical Expression  an expression consisting of one or more numbers along with one or more arithmetic operations. 
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Odds  a ratio of the number of ways a certain event can occur to the number of ways it cannot occur. see lesson 
Open Sentence  a statement in which numbers, variables, arithmetic operations and other symbols (i.e. =, <, %) are used to calculate or compare various quantities. 
Ordered Pair  a pair of numbers used to locate points in the coordinate plane. 
Organize data  Organizing data is useful before solving a problem. Some ways to organize data are to use tables, charts, different types of graphs, or diagrams. 
Origin  the point of intersection of the two axes in the coordinate plane. 
Outcomes  Outcomes are all possible combinations of a counting problem. Positive and negative outcomes are the basis of many probability problems. see lesson 
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Percent  A percent is a ratio that compares a number to 100. see lesson 
Percent of Decrease  The ratio of an amount of decrease to a previous amount, expressed as a percent. 
Percent of Increase  The ratio of an amount of increase to a previous amount, expressed as a percent. 
Perfect square  A rational number whose square root is a rational number. 
Pointslope form of a linear equation 
For a given point (x_{1}, y_{1}) on a nonvertical line having slope m, the pointslope form is: y  y_{1} = m(x  x_{1}) 
Polynomial  A polynomial is a monomial or a sum of monomials. 
Positive Correlation  There is a positive correlation between x and y if the values are related in the same way  i.e. as x increases, y also increases or as x decreases, y decreases. see lesson 
Power of a Monomial 
For any numbers a and b and any integers m, n, and p: (a^{m}b^{n})^{p} = a^{mp}a^{np} 
Power of a Power  For any number
a, and
all integers m
and n:
(a^{m})^{n} = a^{mn} 
Power of a Product 
For any numbers a and b and any integers m: (ab)^{m} = a^{m}b^{m}

Principal square root  The nonnegative square root of an expression. 
Probability  a ratio of the number of ways a certain event can occur to the number of possible outcomes. see lesson 
Product  The result of a multiplication operation. Order does NOT matter. The product of 6 and 3 equals 18. The product of 3 and 6 also equals 18. 
Product of Powers  For any number
a, and
all integers m
and n:
a^{m}a^{n} = a^{m+n} 
Proportion  an equation stating that two ratios, rates or fractions are equivalent. 
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Quadrant  One of the four regions into which the x and y axes separate the coordinate plane. 
Quantity  the way in which a person, place or thing is measurable for purposes of assignment or comparison. For example, a person could be measured in height, weight or intelligence. A town could be measured in population, square miles, or tax revenue. A building could be measured in height, floor space or storage capacity. Each measurement can be represented as a quantity. 
Quotient  The result of a division operation. Order matters! The quotient of 6 and 3 equals 2. The quotient of 3 and 6 equals 1/2 (or 0.5). 
Quotient of powers  For any
nonzero number a,
and all integers m
and n:
a^{m}/a^{n} = a^{mn} 
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Radical sign  The symbol
, indicating the principal square root of an expression. 
Range  the set of all second (y) coordinates from the ordered pairs in a relation. 
Rate 
The relationship ^{a}/_{b} of two quantities a and b that are measured in different units. For example, a car that travels 100 miles in 2 hours has a unit RATE of speed of 50 miles per hour, or ^{50 miles}/_{1 hour} 
Ratio  a comparison
of two quantities or numbers that are measured in
the same units. A ratio can be expressed as: 1) ^{a}/_{b} 2) a:b 3) a to b Recipe ingredients are often expressed as ratios to a unit of measure such as a cup or tablespoon. see lesson 
Rational Number  a number that can be expressed as a ratio of two integers, except that the denominator cannot be equal to zero. 
Real number  The set of rational numbers and irrational numbers together form the set of real numbers. 
Reflexive Property of Equality 
For any number a,
a = a 
Relation  a set of ordered pairs. 
Replacement Set  A set of numbers from which replacements for a number may be chosen. 
Rise  The vertical (up and down) change in a line graphed in the coordinate plane. 
Run  The horizontal (left and right) change in a line graphed in the coordinate plane. 
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Scatter Plot  In a scatter plot, two sets of data are plotted as ordered pairs in the coordinate plane. see lesson 
Scientific Notation  A number is
expressed in scientific notation when it is in the form: a × 10^{n}, where 1 < a < 10 and n is an integer. 
Sequence  A set of numbers in a specific order. 
Set  A collection of objects or numbers. 
Setbuilder Notation  A notation used to describe the members of a set. For example { y  y< 17 } represents the set of all numbers y such that y is less than 17. see lesson 
Simple Events  A single event in a probability problem (i.e. the tossing of one coin). 
Simplest Form  an algebraic expression is in simplest form when it contains no parentheses or like terms. 
Slope  The slope m of a line is the ratio of the change in the ycoordinates to the corresponding change in the xcoordinates. Also described as "rise over run" or "the change in y over the change in x". see lesson 
Slopeintercept form 
Given the slope m
and the y = mx + b 
Solution  A replacement for the variable(s) in an open sentence that results in a true sentence. 
Solution Set  The set of all replacements for the variable(s) in an open sentence that result in a true sentence. 
Square root  One of two identical factors of a number. 
Standard Form  The Standard Form of a linear equation is: Ax + By = C where A, B, and C
are integers, A > 0 and A and B are both
not equal to 0.

Substitution  The substitution method of solving a system of equations is a method that uses substitution of one equation into the other equation to solve for the other variable. 
Substitution Property of Equality 
Given that a and b are numbers or expressions, if a = b, then a may be replaced by b in any expression. 
Subtracting Integers 
To subtract a number, add its additive inverse. For any numbers a and b; a  b = a + (b) 
Subtraction (and Addition) Property for Inequality  
Sum  The result of an addition operation. Order does not matter. The sum of 6 and 3 equals 9. The sum of 3 and 6 also equals 9. 
Symmetric Property of Equality 
For any numbers
a
and
b,
if a = b, then b = a 
System of equations  A set of
equations (two or more) with the same variables.
With respect to a system of two linear
equations, we can say the system has either: 
System of inequalities  A set of inequalities (two or more) with the same variables. 
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Term (of an algebraic expression)  a number, a variable, or a product of numbers and variables. 
Term (2) (of a sequence)  a number in a sequence. 
Transitive Property of Equality 
For any numbers
a, b,
and
c,
if a = b and
b = c, then a = c 
Tree Diagram  A diagram used to show the total number of all possible outcomes for two or more independent events. 
Trinomial  A trinomial is the sum of three monomials, assuming that like terms have been combined. 
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Uniform Motion  When an object moves at a constant speed (or rate) it is said to be in uniform motion. The formula distance = rate * time ( d = rt ) is used to solve uniform motion problems. see lesson 
Union  The union of two sets A and B is the set of elements contained in both A and B. 
Unit Cost  The cost of one unit of something. For example if 12 bagels cost $3.60, the unit cost for one bagel is $0.30 or 30 cents, which is the quotient of (3.60)/(12). 
Unit Rate  A rate where the denominator is expressed as a single whole unit, i.e. miles per (one) hour, price per (one) pound, words per (one) minute, etc.. A rate can be converted to unit rate by using a proportion. 
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Value  a numerical quantity that is assigned or is determined by calculation or measurement. 
Variable  a symbol, typically a lower case letter, that is used to represent an unspecified number. 
Vertical Line Test for a Function  if any vertical line passes through no more than one point of the graph of a relation, then the relation is a function. 
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Whole numbers  The set of whole numbers can be expressed as {0,1,2,3,...}. This is the set of counting (aka "natural") numbers and zero. Whole numbers are not negative. 
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xcoordinate  the first number of an ordered pair. It corresponds to the numbers on the xaxis. 
xintercept  The coordinate at which a graph intersects the xaxis. 
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ycoordinate  the second number of an ordered pair. It corresponds to the numbers on the yaxis. 
yintercept  The coordinate at which a graph intersects the yaxis. 
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Zero Product Property  For all numbers a and b, if ab=0 then either a=0, b=0 or both a and b equal 0. 
Zero exponent  For any
nonzero number a:
a^{0} = 1 