# Math Glossary

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z #

## A

**Acute **

A positive angle measuring less than 90 degrees.

** **

**A****djacent **Two angles that share both a side and a vertex.

**Angles**

The union of two rays with a common endpoint, called the vertex.

** acute angle right angle **

** obtuse angle **

Two angles that share both a side and a vertex.

**A****rc** A portion (part) of the circumference of a circle.

**Area**

Area is the inside of a figure and you either count up the squares or multiply the

length and width.

If the length is 5 and the width is 2. A = 10 sq

**Associative Property of Addition** (a + b) + c = a + (b + c)

Example: 3 + 4 + 5 can be done either of the following two ways

a) (3 + 4) + 5

b) 3 + (4 + 5)

**Associative Property of Multiplication** (a x b) x c = a x (b x c)

Example: 3 x 4 x 5 can be done either of the following two ways

a) (3 x 4) x 5

b) 3 x (4 x 5)

**Average ** A number that represents the characteristics of a data set.

Example: A data set of the numbers 12, 17, 23, 29, and 34

1) Add all the numbers in the data set together

12

17 2) Take the sum of all the numbers and divide it by how many

23 numbers there are in the data set - for this example

29 there are five numbers

+34 115 ÷ 5 = 23

_____

115 3) Thus the average for this data set is 23

4) Remember that the average will always be

a number between the smallest number (in

this case the number 12 is smallest) and

the largest number (in this case the

number 34) - notice that our average 23

is between these two numbers.

## B

**Base ** The bottom of a plane figure or three-dimensional figure.

## C

**Chord ** A line segment that connects two points on a curve (not through the center).

**Circumference **

The distance around a circle.

**Common Multiple ** A multiple of two or more numbers.

**Commutative Property of Addition**

a + b = b + a

Example: 3 + 4 = 4 + 3

**Commutative Property of Multiplication**

a x b = b x a

Example: 3 x 4 = 4 x 3

**Complementary Angles**

**Two angles whose sum is 90 degrees.**

= angle, thus ABC is an angle that has points A, B, and C on it.

Example: FAB or FAD (same angle) is 45° and CAB is 90° then CAF is

also 45° which makes FAB and CAF complimentary angles since they add

to 90°

**Composite Number ** A natural number that is not prime. Which is any number that has factors of more than one

and itself. Such as 4 which has factors of (1, 2, 4) - 1x4 and 2x2.

**Cone** A three-dimensional figure with one vertex and a circular base.

**Congruent ** Figures or angles that have the same size and shape.

**Coordinate Plane** The plane determined by a horizontal number line, called the x-axis, and a

vertical number line, called the y-axis, intersecting at a point called the origin.

Each point in the coordinate plane can be specified by an ordered pair of

numbers.

**Cross Product ** A product found by multiplying the numerator of one fraction by the denominator of another

fraction and the denominator of the first fraction by the numerator of the second.

**Cube ** A solid figure with six square faces.

**Cylinder **

A three-dimensional figure having two parallel bases that are congruent circles.

## D

**Data ** Information that is gathered.

**Decimal Number ** The numbers in the base 10 number system, having one or more places to the

right of a decimal point.

Example: 12.38

**Decimals: Compare or Order -** (make sure the decimals are in the same place by

making equivalencies)

.9 .09 will become .90 > .09 as you make the decimals into the same place

3.80 3.8 will become 3.80 = 3.80

12.09 12.9 will become 12.09< 12.90

1.2 , 1.02, 11.2 , 12, 12.1 will become 1.20, 1.02, 11.20, 12.00, 12.10

When ordered least to greatest it will be 1.02, 1.20, 11.20, 12.00, 12.10

**Decimals: Converting to a Fraction and Percent -** (the denominator must be 100

and you do this by making an equivalent fraction)

.4 = 4/10 = 40/100 = 40%

.25 = 25/100 = 25%**Decimals: Counting** - (make sure you are in the same place as requested)

count by tenths

.8, .9 ,1.0. 1.1 etc....

count by hundredths

.98, .99, 1.00, 1.01 etc....

.9 would need to be changed to .90 before you could count by hundredths

**Decimals: Equivalent** (zeros to the right of decimal)

0.7 = 0.70

1.9 = 1.90

13.503 = 13.503 (can't remove zero when trapped by digit to right)

**Decimals: Place Value**

1,234.56789

1 = thousands

2 = hundreds

3 = tens

4 = ones

5 = tenths

6 = hundredths

7 = thousandths

8 = ten thousandths

9 = hundred thousandths**Decimals: Rounding - **(is usually to the nearest whole number unless indicated

otherwise)

1.25 = 1 3.09 = 3 1.9 = 2

**Degree ** A unit of measure of an angle.

**Denominator ** The bottom part of a fraction.

**Diameter ** The line segment joining two points on a circle and passing through the center of the circle.

**Difference ** The result of subtracting two numbers.

**Digit ** The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 215 has three

digits: 2, 1, and 5.

**Distributive Property of Multiplication**

** **Example: 34 x 56

1) way 1:( 30 + 4 ) x ( 50 + 6 )

(30 x 50) + (30 x 6) + (4 x 50) + (4 x 6)

2) way 2: (30 + 4) x 56

(30 x 56) + (4 x 56)

3) way 3: 34 x (50 + 6)

(34 x 50) + (34 x 6)

4) way 4: (40-6 ) x 56

(40 x 56) - (6 x 56)

**Dividend ** In

**a**÷

**b = c**,

**a**is the dividend. In the problem the 56 is the dividend.

**Division**

DMSB or dad, mother, sister, brother, is an acronym we use to help us divide.

It stands for divide, multiply, subtract and bring down.

Does McDonalds Serve Cheese Burgers Daily in another acronym. Does =

Divide, McDonalds = Multiply, Serve = Subtract, Cheese = Check (check to make

sure subtraction answer is lower than number dividing by), Burgers Daily = Bring

Down.

**Divisor ** In

**a**÷

**b = c**,

**b**is the divisor. In the problem the 8 is the divisor.

## E

**Equation **

A mathematical statement that says that two expressions have the same value;

any number sentence with an =. Examples: 3 + 4 = 7, 5 x 8 = 40, a - b = c

**Evaluate** To substitute number values into an expression. If a = 4, b = 2, substitute the

numbers for the letters in the expression. a + b = c, 4 + 2 = 6 so c = 6

**Even Number **

A natural number that is divisible by 2.

**Exponent** (see also power)

A number that indicates the operation of repeated multiplication.

## F

**Face **

A flat surface of a three-dimensional figure.

**Factor **

One of two or more expressions that are multiplied together to get a product.

**Factoring** To break a number into its factors.

**Formula ** A equation that states a rule or a fact.

**Fraction ** A number used to name a part of a group or a whole. The number below the bar is

the denominator, and the number above the bar is the numerator.

**Fractions: Addition & Subtraction of Fractions with Like Denominators** - Add the numerators and keep the denominators the same.

4/5 + 1/5 = 5/5 = 1 1 2/5 + 2/5 = 1 4/5 3 2/4 - 1/4 = 31/4

**Fractions: Adding & Subtraction of Fractions with Unlike Denominators** - Must first find common denominator before adding or subtracting

- The following is an example - the numbers would change depending on the

problem.

**Fractions: Close to 0, 1/2, 1 or more than 1** - close to zero if numerator and denominator are far apart 2/20

- close to one if numerator and denominator are close to together 19/20

- exactly one if numerator and denominator are the same 7/7

- over one if the numerator is biggier than the denominator 5/4

**Fractions: Comparing & Ordering**

unit fractions have same numerator 1/20 1/5 1/25 1/8

In this case the bigger the denominator the smaller the piece

1/25 1/20 1/8 1/5 = least to greatest

same denominator fractions 3/6 2/6 1/6 5/6

In this case the bigger the numerator the bigger the piece

1/6 2/6 3/6 5/6

when comparing fractions use cross multiplication

4 8

12 < 9

multiply 4 x 9 = 36 and 12 x 8 = 96 so 8/9 is bigger

**Fractions: Equivalent** Fractions that reduce to the same number. 10/15 = 2/3

**Fractions: Numerator**= number above the fraction bar (division bar) (the 3 in

this fraction)

**Fractions: Fraction of a Whole**

whole number times numerator divided by denominator

4/5 of 20 = 4 x 20 = 80 80 divided by 5 = 16

** **

1.2 = 1 2/10 = one and two tenths

13.09 = 13 9/100 = 13 and 9 hundredths

0.54 = 53/100 = fifty three hundredths

**Fractions: Whole Set and in Word Problems**

- (a b a) what fraction is vowels? = 2/3

- If I have 6 cookies and 9 people, how much will each person get of the cookies? =

6/9

**Frequency** The number of times a particular item appears in a data set.

## G

**Graph **

A type of drawing used to represent data.

Verticle Bar Horizontal Bar Line Circle or Pie Pictograph

Graph Graph Graph Graph

**Greatest Common Factor (GCF)** The largest number that divides two or more numbers evenly.

Example: The GCF of 12 and 15 is 3 because it is the largest number that both

can be divided by

## H

**Horizontal** A line with zero slope.

## I

**Improper Fraction **

A fraction with a numerator that is greater than the denominator.

**Inequality ** A mathematical expression which shows that two quantities are not equal.

**Integers ** The set of numbers containing zero, the natural numbers, and all the negatives of the natural numbers.

**Intersecting Lines ** Lines that have one and only one point in common.

**Inverse ** Opposite. -5 is the additive inverse of 5, because their sum is zero. 1/3 is the

multiplicative inverse of 3, because their product is 1.

**Inverse operations ** Two operations that have the opposite effect, such as addition and subtraction.

## J

## K

## L

**Least Common Denominator (LCD)**

The smallest multiple of the denominators of two or more fractions.

**Least Common Multiple (LCM)** The smallest nonzero number that is a multiple of two or more numbers

**Like Fractions (common denominator)** Fractions that have the same denominator.

**Line ** A straight set of points that extends into infinity in both directions.

** Line of Symmetry ** Line that divides a geometric figure into two congruent portions.

**Lines**

**parallel lines**

**perpendicular lines**

**intersecting lines**

**line segment** has two points

**line** has two arrows

**ray** has one arrow

**Logic ** The study of sound reasoning.

**Lowest Terms ** Simplest form; when the GCF of the numerator and the denominator of a

fraction is 1.

## M

**Mean** (see Average)

**Median**

** ** Example: Data Set: 1,4,7,2,8,2,7,9,7

1) place in order from least to greatest 1,2,2,4,7,7,7,8,9

2) Median = the number in the middle (when there is an equal number of

numbers in the data set the two middle numbers are averaged

to find the median (see average)

**Minuend** The number to be subtracted from.

**Mixed Number ** A number written as a whole number and a fraction.

**Mode**

Example: Data Set: 1,4,7,2,8,2,7,9,7

1) place in order from least to greatest 1,2,2,4,7,7,7,8,9

2) Mode= the number that is written down the most often (there can be

more than one mode in a data set)

**Multiple** A multiple of a number is the product of that number and any other whole number.

Zero is a multiple of every number.

## N

**Natural Numbers **

The counting numbers.

**Negative Number ** A real number that is less than zero.

**Number Line ** A line on which every point represents a real number.

**Numerator ** The top part of a fraction.

## O

**O btuse Angle **

** ** An angle that is greater than 90 degrees

** **

**Obtuse Triangle ** A triangle with an obtuse angle.

**Octagon ** A polygon with 8 sides.

**Odd Number ** A whole number that is not divisible by 2.

**Operation** Addition, subtraction, multiplication, and division are the basic arithmetic operations.

**Opposites ** Two numbers that lie the same distance from 0 on the number line but in opposite

directions.

## Example: 8 and -8 also -3/4 and 3/4

**Order of Operations**

**PEMDAS** is an acronym that shows what to do first in an equation: p stands for

parenthesis, m for multiplication, d for division, a for addition, and s for subtraction.

You solve a problem using this order.

The multiplication and division are reversable

- do whichever comes first, also the addition and subtraction are also reversable -

do whichever comes first.

example: 32 ÷ (4 + 4) x 2 You would do addition first to get 8 because it is in the

parenthesis, then the division to get 4, and then finally the multiplication to get 8.

**Ordered Pair** Set of two numbers in which the order has an agreed-upon meaning, such as the

Cartesian coordinates (x, y), where the first coordinate represents the horizontal

position, and the second coordinate represents the vertical position.

**Outcome ** In probability, a possible result of an experiment.

## P

**Parallel **

Two lines are parallel if they are in the same plane and never intersect.

**Parallelogram ** A quadrilateral with opposite sides parallel.

**Pentagon ** A five-sided polygon.

**Percent ** A fraction, or ratio, in which the denominator is assumed to be 100. The symbol %

is used for percent.

Example: 34% = 34 parts of 100

**Perimeter**

The perimeter is the outside of a figure and you add up all the sides.

If the length is 5 and the width is 2. P = 14

**Perpendicular ** Two lines are perpendicular if the angle between them is 90 degrees.

**Pi ** The ratio of the circumference of a circle to its diameter.

**Place Value**

expanded form = 300,000 + 20,000 + 3,000 + 400 + 60 + 9

written form = three hundred twenty three thousand four hundred sixty nine

3,456,789

value of 3 = 3,000,000

place value of 3 = million

**Plane ** A flat surface that stretches into infinity.

**Point ** A location in a plane or in space, having no dimensions.

**Polygons ** - are many sided figures

*triangle is a three sided figure *quadrilaterial is a four sided figure

*pentagon is a five sided figure *hexagon is a six sided figure

*heptagon is a seven sided figure *octagon is a eight sided figure

*nonagon is a nine sided figure *decagon is a ten sided figure

**CLICK HERE** for more about regular polygons

**Polyhedron** A three-dimensional solid that is bounded by plane polygons.

**Positive Number ** A real number greater than zero.

**Power (also see exponent)** A number that indicates the operation of repeated multiplication.

**Prime Number ** A number whose only factors are itself and 1. Such as 3 - 1x3, 5 - 1x5, 7 - 1x7,

11 - 1x11, and 13 1x13, ect.

**Probability ** For an experiment, the total number of successful events divided by the total

number of possible events.

a,4,a,b,3,4,6,7

Probability of pulling out an "a" from above list is 2/8 and unlikely

Probability of pulling out a "number" from the above list is 5/8 and likely

The words we use are impossible, unlikely, maybe, likely, and certain.

**Product ** The result of two numbers being multiplied together.

**Proper Fraction ** A fraction whose numerator is less than its denominator.

**Pyramid ** A three-dimensional figure that has a polygon for its base and whose faces are

triangles having a common vertex.

## Q

**Quadrant ** One of the quarters of the plane of the Cartesian coordinate system (coordinate

grid)

**Quadrilaterals ** - are four sided figures

trapezoid has one set of parallel lines

parallelogram has two sets of parallel sides

rectangle has two sets of parallel and equal sides with right angles

rhombus has all sides equal

**Quotient ** The answer to a division problem.

## R

**Radius ** The distance from the center to a point on a circle; the line segment from the

center to a point on a circle.

**Range**

Example: Data Set: 1,4,7,2,8,2,7,9,7

1) place in order from least to greatest 1,2,2,4,7,7,7,8,9

2) Range = highest number minus lowest number 9-1 = 8

**Rate **

A ratio that compares different kinds of units.

Example: 10 km per 2 hours or 5 km per hour - comparing km to hours

**Ratios**

girls 13 boys 15 (written 3 ways for each)

ratio of girls to boys is 13 to 15 or 13/15 or 13:15

ratio of girls to total is 13 to 28 or 13/28 or 13:28

**Ray ** part of a line, with one endpoint, and extending to infinity in one direction.

**Reciprocal ** The number which, when multiplied times a particular fraction, gives a result of 1.

Example: 3/4 x 4/3 = 12/12 which equals 1

**Rectangle ** A quadrilateral with four 90-degree angles.

regular rectangle square which is a

special rectangle

**Reflection ** A transformation resulting from a flip.

**Right angle**

** **An angle that is exactly 90 degrees

** **

**Rhombus ** A parallelogram with four equal sides.

**Right Angle** An angle whose measure is 90 degrees.

**Right Triangle ** A triangle that contains a right angle.

**Rotation ** A transformation in which a figure is rotated through a given angle, about a point.

## S

**Scale Drawing ** A drawing that is a reduction or an enlargement of the original.

**Scalene Triangle ** A triangle with three unequal sides.

**Scientific Notation ** A method for writing extremely large or small numbers compactly in which the number is

shown as the product of two factors.

**Shapes: Analyzing**

Students will need to be able to analyzse a figure to see if it has certain

characteristics. For example:a trapezoid has parallel lines and in this

case obtuse and acute angles.

Students will need to be able to analyse a figure to see what other shapes can be

found in the figure. For example: a trapezoid could be made up of

three triangles or a rectangle with two triangle.

**Shapes:** **Congruency & Similarity**

Congruent is the same size and shape

Similar is the same shape

**Shapes:** **Nets**

There may be more than one net for each figure.

**cube **

**cone**

**cyclinder**

**CLICK HERE** for many more nets that can be printed and made

**Shapes: Plotting**

Students will ned to be able to plot a geometry figure or line on a coordinate grid.

The trapezoid is at points (2,1) and (4,1) and (5, 4) and (1, 4).

**Similar** Two polygons are similar if their corresponding sides are proportional.

**Simplifying ** Reducing to lowest terms.

**Solution ** The value of a variable that makes an equation true.

Example: 4a - 3 = 21 solving for the variable a gets the solution a = 6

**Square Root ** The square root of x is the number that, when multiplied by itself, gives the

number, x.

**Statistics ** The science of collecting, organizing, and analyzing data.

**Stem and Leaf Plot ** A technique for organizing data for comparison.

**Straight Angle ** An angle that measures 180 degrees.

**Subtrahend** The number to number to be subtracted.

**Supplementary Angles ** Two angles are supplementary if their sum is 180 degrees.

**Surface Area ** For a three-dimensional figure, the sum of the areas of all the faces.

## T

**Transformation ** A change in the position, shape, or size of a geometric figure.

**Translation ** A transformation, or change in position, resulting from a slide with no turn.

**Trapezoid**

A quadrilateral that has exactly two sides parallel.

**Tree Diagrams**

I have three flavors of ice cream: vanilla, chocolate, and praline. I have two types

of cones: sugar and plain. I have two toppings: nuts and fruit. How many

combinations can I make? 3 x 2 x 2 = 12 combinations

1) vanilla: sugar: nuts

2) vanilla: sugar: fruit

3) vanilla: plain: nuts

4) vanilla: plain: fruit

5) chocolate: sugar: nuts

6) chocolate: sugar: fruit

7) chocolate: plain: nuts

8) chocolate: plain: fruit

9) praline: sugar: nuts

10) praline: sugar: fruit

11) praline: plain: nuts

12) praline: plain: fruit

**Triangles** three sided figures

1) Triangles based on their angles:

-**acute triangle** has all acute angles

-**obtuse triangle** has one obtuse angle

-**right triangle** has one right angle

2) Triangles based on their sides:

-**isosceles triangle** has two sides the same length

-**equalateral triangle** has all sides the same length

-**scalene triangle** has no sides the same length

## U

**Unit Price ** Price per unit of measure.

## V

**Variable ** A letter used to represent a number value in an expression or an equation.

Examples: r - 3 = 12, 4b = 16, 8 + s = 24, 40 ÷ y = 5, 3r + 4 = 22

**Vertex ** The point on an angle where the two sides intersect.

**Vertex Edge Graphing**

vertex = a point on a graph ( blue )

edge = a line segment or curve connecting two vertices ( black lines )

path = a connected sequence of edges that starts at a vertex

and ends at a vertex

circuit = a path that begins and ends at the same vertex

graph coloring = assigning colors to the vertices of a graph so that adjacent

vertices are assigned different colorsdegree of vertex = the number of edges that

come off of a vertex.

Example: If 1 is green then 5 and 2 can not be green, but 4 should be green. If

5 is yellow than 6 and three should be yellow. 2 must be a new

color. In other words you want to try to color with the fewest colors

without having the same color next to each other.This is called

chromatic coloring.

cycle graph = a graph where the vertices can be arranged in a circle so that each

vertex is adjacent to the vertices that come before and after it

disconnected graph = a graph that contains two or more vertices that are not

connected

The following are some applied problems using the concept of wieghted vertex

edge graphs.

a)

b)

**CLICK HERE** for more information on Vertex Edge Graphing

**Vertical Angles ** A pair of opposite angles that is formed by intersecting lines.

**Volume ** A measurement of space, or capacity.

## W

**Whole Numbers ** The set of numbers that includes zero and all of the natural numbers.

**Word Problems: Key words that signal x, ÷** **, + and - **

product x increase or decrease by -

quotient / how many more -

area x difference -

total x or + er word like taller or smaller -

times x sum +

split evenly / perimeter +

share evenly /

## X

**X-Axis ** The horizontal axis in a Cartesian coordinate plane.

**X-Axis**

## Y

**Y-Axis ** The vertical axis in a Cartesian coordinate system.

**Y-Axis**

## Z

**Zero Property of Multiplication** The product of zero and any number is zero.

Example: 3,458 x 0 = 0

## #