 # Math Dictionary

absolute value  The absolute value of a number is the distance that number is from zero. The absolute value of a positive number or zero is that number.  The absolute value of a negative number is the opposite of that number, and the absolute value of zero is zero which is neither positive or negative

acre A unit of area often used to measure plots of land. One acre is equivalent to exactly 43,560 square feet, or 4,840 square yards, or 1/640 of a square mile, or about 4,047 square meters.

acute angle   An angle whose measure is between 0° and 90º. We like to think of them as the "cute" skinny angles.

additive identity  The number zero. When you add zero to any number, you do not change its identity, thus the name, additive identity.

Additive Identity Property For any number n: n + 0 = n. If you add zero to any other number, you do not change its identity.

Additive Inverse The number, which when added to a number, gives a sum of 0. The additive inverse of n is denoted -n. Also called opposite.

adjacent angles Two nonstraight and nonzero angles with a common side interior to the angle formed by the noncommon sides.

adjacent sides In a polygon, two sides with an endpoint in common.

adjacent vertices In a polygon, endpoints of a side.

algebraic expression  An expression that contains a variable alone or with numbers and operation symbols.

angle  The union of two rays with the same endpoint.

area  Measure of the space inside a two-dimensional figure. Area is measured in square units.

Area Model for Multiplication  The area of a rectangle with length l and width w is l times w or a = lw.

arthmetic mean The result of adding the n numbers in a data set and dividing the sum by n. Also called the average or mean.

Associative Property of Addition For any numbers a, b, and c:
( a + b)
+ c = a + ( b + c ) = a + b + c. The positions of the numbers do not change, the placement of the grouping symbols changes.

Associative Property of Multiplication   For any numbers a, b, and c:
a( bc ) = ( ab )c = abc
. The positions of the numbers do not change, the placement of the grouping symbols changes.

average A number representing a set of other numbers determined by taking the sum of those numbers and dividing by the number of them. Also called mean or arithmetic mean.

axis A line of reference in a coordinate system. Plural: axes.

bar graph A graph in which information is represented using bars of various lengths to show values of a particular category.

base of a triangle  The side of a triangle to which an altitude is drawn.

bases of a trapezoid The parallel sides of a trapezoid.

base angles of an isosceles triangle Two angles of an isosceles triangle whose vertices are the endpoints of the base of the triangle.

base angles of a trapezoid Two angles whose vertices are the endpoints of a base of the trapezoid.

base of an isosceles triangle The side opposite the vertex angle.

bilateral symmetry A space figure has bilateral symmetry if and only if there is a plane over which the reflection image of the figure is the figure itself.

billion  A word name for 1,000,000,000 or .

billionth  A word for 0.000000001 or x^-9.

box A a right prism whose faces are rectangles.

brackets [ ] Grouping symbols which serve the same role as parentheses.

capacity The number of unit cubes or parts of unit cubes that can be fit into a solid. Also called volume.

cartesian plane Name given to the plane containing points identified as ordered pairs of real numbers. Also called coordinate plane.

center of a circle The given point from which the set of points of the circle are all at the same distance.

center of a regular polygon The point equidistant from the vertices.

center of a sphere  The given point from which the set of points of the sphere are all the same distance.

center of symmetry For a rotation-symmetric figure, the center of a rotation that maps the figure onto itself.

.centi-  A prefix meaning 1/100.

centimeter  1/100 of a meter.

certain event  An event with a probability of 1.

chord A segment whose endpoints are on a given circle.

circle  The set of points in a plane that are equidistant from a given point known as its center.

circle graph A graph in which information is represented using a circle that is cut into sectors to show values of a particular category. Also called a pie graph.

circumference The perimeter of a circle, which is found by multiplying its diameter times pi.

clockwise  The direction around a circle in which the hands on a clock usually move.

clockwise rotation The direction in which the hands move on a nondigital clock, designated by a negative magnitude.

coefficient  The number by which a certain variable in a term is multiplied.

coincide  To occupy the same position.

column  A vertical line of objects in a rectangular array.

common denominator  A multiple of all the denominators in a problem.

Commutative Property of Addition   For any numbers a and b:

Commutative Property of Multiplication   For any numbers a and b: ab = ba. Notice the positions of the numbers switch, but the quantities are still equal.

compass An instrument for drawing circles.

composite number  Any positive integer exactly divisible by one or more positive integers other than itself and 1.

conclusion The "then" clause of a condition. The result of a deduction in a proof. Also called consequent.

cone The surface of a conic solid whose base is a circle.

congruent figures  Figures with the same size and shape. Figures which are the image of each other under a reflection, rotation, or translation, or combination of these.

conjecture An educated guess or opinion.

consequent The "then" clause of a conditional, also called the conclusion.

construction A drawing which is made using only an unmarked straightedge and a compass following certain prescribed rules.

continuous A figure made up of points with no space between them.

conversion factor A factor by which one unit can be converted to another.

coordinate The number or numbers associated with the location of a point on a line, a plane, or in space.

coordinate axes A pair of perpendicular coordinatized lines in a plane that intersect at the point with coordinate 0; three mutually perpendicular coordinatized lines in space that are concurrent at the point with coordinate 0.

coordinate graph  Displaying points as ordered pairs of numbers.

coordinate plane Name given to the plane containing points identified as ordered pairs of real numbers. Also called cartesian plane.

corresponding parts Angles or sides that are images of each other under a transformation.

corresponding sides  Any pair of sides in the same relative positions in two similar figures.

count  A number of particular things.

counterclockwise  The direction around a circle opposite from that in which the hands of a clock move.

counterclockwise rotation The direction opposite that which the hands move on a nondigital clock, designated by a  positive magnitude.

counterexample A specific case of a conditional for which the antecedent is true but the consequent is false. An example which shows a conjecture to be false.

counting unit The name of the particular things being tallied in a count.

cube A three-dimensional figure with six faces, each face being a square

cubic units Units for measuring volume.

cylinder The surface of a cylindric solid whose base is a circle.

cylindric solid The set of points between a region (its base) and its translation image in space, including the region and its image.

decagon A ten-sided polygon.

decimal notation  The notation in which numbers are written using ten digits and each place stands for a power of ten.

decimal system  The system in which numbers are written in decimal notation.

degree A unit of measurements equal to 1/360 of a complete circle.

denominator  The divisor, or bottom number, in a fraction.
b in the fraction a/b.

diameter of a circle or sphere A segment connecting two points on the circle or sphere and containing the center of the circle or sphere, also the length of that segment.

difference The answer to a subtraction problem.

digit One of the ten symbols, 0 1 2 3 4 5 6 7 8

dimensions  The lengths of the sides of a rectangle. The number of rows and the number of columns in a rectangular array.

dimensions of a box The lengths of three edges of the box which meet at the same vertex. Usually referred to as length, width, and height.

dimensions of a rectangle The lengths of two sides of the rectangle which meet at a single vertex. Usually referred to as length and width.

irection of translation The direction given by the vector from any preimage point to its image point in a translation.

directly congruent Figures which are congruent and have the same orientation.

Distributive Property of Multiplication over Addition For any numbers a, b, and x : ax + bx = ( a + b )x and x( a + b) = xa + xb. Also called distributivity.

Distributive Property of Multiplication over Subtraction   For any numbers a, b, and x : ax + bx = ( a - b )x and ( a - b ) = ax - bx. Also called distributivity.

dividend  The number in a quotient which is being divided; a is the dividend in a/b.

divisor The number by which you divide in a quotient; b is the divisor in a/b.    Also a number that exactly divides into another number, referred to as a factor.

edge Any side of a polyhedron's faces.

endpoint A point at the end of a segment or the starting point of a ray.

endpoint of a ray   The starting point of a ray.

Equal Fractions Property If the numerator and denominator of a fraction are both multiplied ( or divided ) by the same nonzero number, then the resulting fractions are equal.

equally likely outcomes Outcomes in a situation where each outcome is assumed to occur as often as every other outcome.

equation A sentence with an equal sign.

.equilateral polygon A polygon with all sides of equal length.

equilateral triangle A triangle in which all the sides have the same length.

equivalent formulas  Formulas in which the same numbers work.

equivalent sentences  Sentences that have exactly the same solutions.e

stimate  A number which is near another number. Also called approximation.

evaluating an expression Finding the value of an algebraic expression by substituting a value for the variable(s) and then applying the order of operations, PEMDAS (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

evaluating a numerical expression Working out the arithmetic in a numerical expression. The order of operations, PEMDAS (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right), must be followed when evaluating any numerical expression

event A collection of possible outcomes of an experiment.

exponent  In the power x^n, n is the exponent.

factor A number that divides another number exactly. Also called divisor.

figure A set of points.

finite decimal  A decimal that ends. Also called terminating decimals.

flip A transformation in which each point is mapped onto its reflection image over a line or plane.

flow chart A diagram that shows a step-by-step progression through a procedure or system.

foot (ft) A unit of length in the U.S. system of measurement equal to 12 inches. Also 1 foot = 30.48 cm, 3 feet = 1 yard, 5,280 feet = 1 mile.

formula A sentence in which one variable is written in terms of other variables.

fraction A number written in the form a/b, where b is non zero.

fraction bar  A grouping symbol separating the numerator and denominator of a fraction and standing for division.

gallon (gal) A unit of capacity in the U.S. system of measurement equal to 4 quarts.

gram  A unit of mass in the metric system. A gram weighs about as much as a medium sized paperclip.

graph A picture of numbers on a number line or coordinate system. See also network.

grouping symbols Symbols such as parentheses ( ), brackets [ ],
braces { }, and fraction bars /, that group numbers and, or variables together.

half turn A turn of 180°.

height In a triangle or trapezoid, the segment from a vertex perpendicular to the line containing the opposite side; also, the length of that segment. In a prism or cylinder, the distance between the bases. In a pyramid or cone, the length of a segment from the vertex perpendicular to the plane of the base. Also called altitude.

height of a trapezoid   The perpendicular distance between the bases of a trapezoid.

height of a triangle The perpendicular distance from any vertex of a triangle to the side opposite that vertex. Also called altitude.

hemisphere The half of a sphere on one side of a great circle.
*Remember that a great circle is the intersection of a sphere and a plane that contains the center of the sphere.

heptagon A seven-sided polygon.

hexagon A six-sided polygon.

horizontal line A line with an equation y = k on the coordinate plane. No matter what value "x" may assume, the "y" value for every point on this line is locked at the value "k".

image The result of applying a transformation to an original figure or preimage. Transformations can be reflections, as seen in the example below, rotations, translations or "slides", and glide reflections.

impossible event An event with a probability of 0 .

inch ( in)  The base unit of length for the US system of measurement.
1 in is exactly equal to 2.54 centimeters.

inequality A sentence with one of the following symbols:

infinite decimal A decimal that goes on forever to the right of the decimal point. Some of these decimals repeat and some do not. The ones which do not are called irrational numbers examples of which are pi and the square root of two.

infinite repeating decimal A decimal in which a digit or group of digits to the right of the decimal point repeats forever.

integer A number which is a positive whole number, a negative whole number, or zero.

irrational number  A number that cannot be written as a simple fraction. It is an infinite and nonrepeating decimal. Examples are "pi" and the square root of two.

isosceles trapezoid A trapezoid with a pair of non parallel sides the same measure. In an isosceles trapezoid, the base angles will be congruent.

isosceles triangle A triangle with two sides equal in length.

justification A definition, postulate, or theorem which enables a conclusion to be drawn.

key in   To press keys or enter information into a calculator.

key sequence A set of instructions for what to key in on a calculator. When writing out a key sequence, operations and symbols like parentheses are typically drawn in rectangles indicating what hey to press.

kilo A prefix meaning 1000.

line segment  The points A and B along with the points on segment between A and B. Also called segments.

line symmetry A figure is said to posses line symmetry if it can be reflected onto of itself over a given line.

length The distance between two points measured along the segment or an arc joining them. A dimension of a rectangle or rectangular solid.

limit The value to which the terms of an infinite sequence get closer and closer as one goes further and further out in the sequence.

line An undefined geometric term. See Point-Line-Plane Postulate.

line of reflection The line over which a preimage is reflected. Also called reflecting line or mirror.

liter  A volume or capacity in the metric system equal to 1000 cubic centimeters.

1Liter 1.06 quarts.lowest terms A fraction written with the smallest possible whole numbers.

mean A number that describes a set of other numbers. You get a mean, or average, as it is commonly called, by taking the sum of the numbers being examined and then dividing that sum by how many numbers were added.

measure The dimension or amount of something, usually in a system of units.

meter  The basic unit of length in the metric system.
1 meter
1.09 yards 39.4 inches.

metric system of measurement A system of measurement based on the decimal system. Also called the international system of measurement.

midpoint of a segment The point on the segment equidistant from the segment's endpoints.

mile ( mi ) A unit of length in the US system of measurement equal to 5,280 feet. 1 mile 1.609 km.

milli  A prefix meaning 1/1000.

million  A word name for 1,000,000.

millionth  A word name for 0.000001 or 10-6.

minuend The number a in a - b.

mirror A line over which a figure is reflected. Also called reflecting line.

mixed number A symbol consisting of a whole number with a fraction next to it, when written like this it means the numbers are being added.

mode The number which appears most often in a data set. The mode of the following data set is 6 : 15, 6, 2, 6, 42, 6.It is possible to have more than one mode as in the set 1, 1, 3, 12, 4, 4. It is possible to have no mode if no values appear more than once as in the set 1, 2, 3, 4.

Multiplication of Fractions Property for all numbers a, b, c, and f with b and f not equal to 0:

Multiplication Property of Zero  For any real number x: x times 0 = 0.

Multiplicative Identity Property of One    For any number n:
n times 1 = n
. *We like to say that multiplying a number by one causes it to retain its identity.

multiplicative inverse The number by which a given number can be multiplied resulting in a product equal to 1. Also called reciprocal.

natural number Any one of the numbers 1, 2, 3, ... . Also called positive integer. These are sometimes called "counting numbers".

n-gon A polygon with n sides.negative integer    Any one of the numbers -1, -2, -3, ... .

negative number  A number which is the opposite of a positive number.

nonagon  A nine-sided polygon.

number line  A line in which the points, in order, correspond to numbers in order.

numerator  a in the fraction a/b.  Remember that a fraction is a division problem. The top number, the numerator, is the number being divided, the fraction bar is the division symbol, and the bottom number, the denominator, is the number of equal parts that you are dividing the top into.

numerical expression  A collection of numbers and operation symbols, without an equal sign, that represents a number.

octagon An eight-sided polygon.

one-dimensional A space in which all points are collinear. Basically a single line.

opposite  When a given number is added to its opposite you always get ZERO. The opposite of a number n is denoted -n. Also called additive inverse.

ordered pair  A pair of numbers ( x, y ) in which x is the first coordinate and y is the second coordinate.

order of operations  Rules for evaluating an expression: work first within parentheses, then calculate all exponents, then do multiplication and division together as they appear in the problem from left to right; then do addition and subtraction as they appear from left to right.

orientation The order of the designation of the vertices of a polygon, either clockwise or counterclockwise.

origin The point where the x and y axes intersect denoted by ( 0, 0 ).

ounce (oz) A unit of weight in the U.S. system of measurement equal to 1/16 of a pound. 1 ounce 29.574 milliliters.

overlapping figures Figures which have some interior points in common.

parallel lines Two lines in a plane are parallel if they have no points in common or are identical.

parallelogram A quadrilateral with two pairs of parallel sides.

parentheses ( )  Grouping symbols which indicate the order of operations that should be followed in evaluating an expression; the work inside them should be done first.

pattern  A general form for which there are many examples.

pentagon A five-sided polygon.

percent  % means times 1/100 or .01, one one-hundredth.

perimeter  The sum of the lengths of the sides of a polygon.... or the length of the boundary of a closed region.

perimeter of a polygon The sum of the lengths of its sides.

perimeter of a rectangle  2l + 2w where l is the length and w is the width of a rectangle.

perpendicular The name given to rays, segments, or lines that form right angles.

pie graph A graph in which information is represented using a circle that has been cut into sectors to show values of a particular category. Also called circle graph.

pint A unit of  capacity in the U.S system of measurements equal to two cups, or 1/2 a quart, or 16 ounces, or 0.473 liters.

place value  The numbers that each digit stands for in a decimal.
In the illustration below, if you think of the one's place and the decimal point as the center, the names correspond on either side. Remember, the numbers to the right of the decimal point always end in "ths".

plane An undefined geometric term. In Euclidean Geometry, a plane is understood to be a flat surface that extends infinitely in all directions..

plane figure A set of points that are all in one plane.

point An undefined geometric term. In Euclidean Geometry, a point can be thought of as a dot that represents a location on a plane or in space. These points have no size.

polygon  A union of three or more coplanar segments (its sides) such that each segment intersects exactly two others, one at each of its endpoints (its vertices).

positive integer  Any one of the numbers 1, 2, 3, ... . Also called natural numbers. Remember that 0 is neither positive nor is it negative.

pound (lb.)  A unit of weight in the U.S. system of measurement equal to 16 ounces. 1 pound 0.4536 kilograms.

power  The answer to a problem . In this power, "a" is called the base and "b" is called the exponent.

preimage The original figure in a transformation.

prime number  A positive integer whose only positive integer divisors are itself and one.

prism To create a prism, start with a polygon base, then translate this base to a parallel plane, then connect the corresponding vertices of the two bases.

probability A number from 0 to 1 which indicates how likely something is to happen. A probability of 0 means the event cannot happen. A probability of 1 means it will definitely happen. A probability of 0.5 means you have a 50% chance of it happening.

product The resulting of doing a multiplication.

pyramid A polyhedron in which all but one of the polygonal faces intersect at a single point known as the vertex of the pyramid. The side which does not intersect at the vertex is called the "base".

quadrant  One of the four parts into which the coordinate plane is divided by the x-axis and y-axis. Quadrants are labeled with Roman Numerals as shown below.

quart (qt) A unit of volume in the U.S. system of measurement equal to 2 pints or 4 cups. One quart = 32 ounces. One quart 0.946 liters.

quotient  The result of dividing one number by another.

radius of a circle or sphere A segment connecting the center of a circle or a sphere with a point on that circle or sphere, also, the length of that segment. Plural is radii.

rational number A number that can be written as a simple fraction. These numbers can also be written as terminating or repeating decimals.

ray  A part of a line which begins at some point and goes on forever in a particular direction. The ray with endpoint A containing B is denoted .

real numbers A number that can be written as a decimal. The set of Real numbers is made up of all rational numbers as well as all irrational numbers.

rectangle  A quadrilateral with four right angles.

rectangular array  An arrangement of objects into rows and columns.

rectangular solid  A box. The union of a box and its interior.

reflecting line The line over which a preimage is reflected. Also called mirror line or line of reflection.

reflection A transformation in which each point is mapped onto its reflection image over a line or plane.

reflection image   The image of a figure reflected over a line.

regular polygon   A convex polygon whose sides all have the same length and angles all have the same measure.

regular prism A right prism whose base is a regular polygon.

regular pyramid A right pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles.

Repeated Addition Model for Multiplication  If n is a positive integer, then nx = x + x + . . . + x. ( n addends)

revolution  A turn of 360°. Also called full turn.

rhombus  A quadrilateral with all sides of the same length.

right angle An angle whose measure is 90°. A right angle will always be drawn with a small square at its vertex. This removes all doubt that it is a 90 degree angle. If you don't see the square you cannot assume that it is a right angle.

rotation A transformation in which every point of the preimage is rotated by a given angle about a point (in two dimensions) or a line (in three dimensions).

rounding down  Making an estimate that is smaller than the exact value.

rounding to the nearest Making an estimate to a particular decimal place by either rounding up or rounding down depending on which estimate is closest to the exact value.

rounding up  Making an estimate that is bigger than the exact value.

row  A horizontal line of objects in a rectangular array.

scalene triangle A triangle with no two sides of the same length.

segment On a line, the set consisting of the distinct points A and B (its endpoints) and all points between A and B. Also called line segment.
side
One of the segments which makes up a polygon. One of the rays of an angle. One of the faces of a solid.

side of a polygon One of the segments whose union is a polygon; also, the length of that segment.

similar figures Two figures that have the same shape, but not necessarily the same size.

simple closed curve A figure that is closed and does not intersect itself.

simple fraction  A fraction with an integer in the numerator and a nonzero integer in the denominator.

slide A translation of a given preimage. This occurs when given numbers are added to every "x" coordinate and or "y" coordinate of the preimage. The result is that the image appears to "slide" away from the preimage.

slide image The result of adding the same number to the coordinates of the point in a figure. Also called translation image.

solid The union of a surface and the region of space enclosed by the surface.

solution  A value of a variable that makes an open sentence true.

solving an open sentence  Finding value(s) of the unknown(s) in an open sentence that make it true.

space The set of all points in a geometry.

space figure A figure whose points do not all lie in a single plane. Also called a three-dimensional figure.

sphere  The set of points in space at a fixed distance (its radius) from a point (its center). s

quare  A four-sided figure with four right angles and four sides of equal length. A rectangle with the same length and width.

square root  If A = s^2 , then s is called a square root of A.

square units  Units for measuring area.

straight angle An angle whose measure is 180°.

straightedge An instrument for drawing the line through two points which has no marks for determining length. S

ubstitution Principle  If two numbers are equal, then one may be substituted for the other in any computation without changing the results of the computation.

subtrahend  b in the subtraction a - b.

sum The result of an addition.

surface The boundary of a three-dimensional figure.

surface area  The sum of the areas of the faces of a solid.

symmetric figure  A figure that coincides with its reflection image over a line.

symmetry line For a figure, a line m such that the figure coincides with its reflection image over m. See above the heart figure with the symmetry line down its center.

table  An arrangement of data in rows and columns.

terms  Numbers or products of numbers and variables that are added.

three-dimensional figure A figure whose points do not all lie in a single plane.

transformation  The movement of a figure in a plane from its original position, the preimage, to a new position, the image. Also called a map. Transformations can occur when there is a reflection, a rotation, a translation, or a glide reflection of the original image.

translation A transformation in which every point of the preimage moves in the same direction by the same amount to form the image. A translation is also referred to as a "slide".

trapezoid A quadrilateral that has (at least) one pair of parallel sides.

trial and error  A problem-solving strategy in which various solutions are tried until the correct solution is found.

triangle A polygon with three sides.

turn A transformation in which every point of the preimage is rotated by a given angle about a point (in two dimensions) or a line (in three dimensions).They are also called rotations.

two-dimensional Pertaining to figures that lie in a single plane, or to their geometry. This is "flat land" so to speak.

unit cost  The cost per one unit of an object.

unknown A variable which can be assigned different values.

U.S system of measurement A measurement system in common use in the United States today, based on inches and pounds. Also called the customary system of measurement.

value of an algebraic expression The number that is the result of evaluating an algebraic expression.

value of a variable  A number that is substituted for a variable.

variable  A symbol that can stand for any one of a set of numbers or other objects.

vertex (plural vertices) The point two sides of a polygon have in common. The point of intersection of the sides of an angle.

vertical line A line with an equation x = h on the coordinate plane.

volume Measurement of the space inside a three-dimensional, or solid figure. The number of unit cubes or parts of unit cubes that can be fit into a solid. Also called capacity.

whole number Any of the numbers 0, 1, 2, 3,

width (of a rectangle) A dimensional of a rectangle or rectangular solid taken at right angles to the length.

x-axis  The horizontal number line in a coordinate graph. The line in the coordinate plane or in space, usually horizontal, containing those points whose second coordinates (and third, in space) are 0.

x-coordinate  The first coordinate of an ordered pair or an ordered triple.

y-axis The vertical number line in a coordinate graph. The line in the coordinate plane, usually vertical, or in space, containing those points whose first coordinates (and third, in space) are 0.

y-coordinate   The second coordinate of an ordered pair or ordered triple.

yard (yd)  A unit of length in the U.S system of measurement equal to 3 feet or 36 inches.

Zero property of multiplication Any number multiplied by zero will equal zero.

The website that the dictionary came from also has a good bit of examples.

Math Z website: http://www.themathlab.com/dictionary/zwords/zwords.htm