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Mathematics-Theorems

Formula's

Number system

Traingles

Circles

Mislenious

Learn All Math Definitions

Introduction of Numbers...

Number System

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.   Continue Learning

Natural Numbers

The numbers that we use when, we can counting or ordering is called Natural number.    Continue Learning

Whole Numbers

The numbers that include natural numbers and zero. Not a fraction or decimal.    Continue Learning

Integer

A counting number, zero, or the negative of a counting number. No fractions or decimals.    Continue Learning

Decimal Number

Any number that contains a decimal point    Continue Learning

Rational Numbers

Can be expressed as a fraction. Include integers and fractions or decimals    Continue Learning

Irrational Numbers

Cannot be expressed as a fraction    Continue Learning

Positive

Greater than 0. x is positive if x > 0.    Continue Learning

Negative

Less than 0. x is negative if x < 0.    Continue Learning

Non-Negative

Greater than or equal to 0. x is non-negative if x — 0.    Continue Learning

Non-Positive

Includes negative numbers and 0.    Continue Learning

Even

An integer that is divisible by 2.    Continue Learning

  Odd

An integer that is NOT divisible by 2.    Continue Learning

  Place Value

It is the value of where the digit is in the number. Examples are units, tens, hundreds, thousands, ten thousands, hundred thousands, millions    Continue Learning

Equivalent

The Number Equal (=) to each other.    Continue Learning

Distinct

Not equal. x and y are distinct if x ≠ y.    Continue Learning

Constant

A number that does not change    Continue Learning

Consecutive (Evenly spaced)

In a row; without any missing; numbers or objects are consecutive if none of them are skipped.    Continue Learning

Learn Math Definitions of

Basic Operations...

Simplify

To make as short as possible    Continue Learning

Evaluate

To solve for a certain value    Continue Learning

Plus (Add)

To increase a number by another number (+)    Continue Learning

Sum

The result of adding (+) two numbers. Also Σ    Continue Learning

Minus (Subtract, Difference)

To decrease a number by another number (-)    Continue Learning

Difference

The positive result of subtracting (-) two numbers.    Continue Learning

Fewer than

To decrease by the original number (-)    Continue Learning

Multiply

To add a number to itself a certain number of times (x or •)    Continue Learning

Product

The result of multiplying (× or •) two numbers.    Continue Learning

Coefficient

A number in front of, or multiplying, a variable.    Continue Learning

Divide by

To cut up a number into a certain number of smaller parts (÷)    Continue Learning

Divided into

To use a number to cut another number into smaller parts (÷)    Continue Learning

  Divisor

The second number in a division; the number you are dividing by; the bottom number when division is written as a fraction.    Continue Learning

  Quotient

The result of dividing (÷ or /) two numbers.    Continue Learning

Numerator

The top number in a fraction. The numerator of 6/7 is 6    Continue Learning

Denominator

The bottom number in a fraction. The denominator of 6/7 is 7    Continue Learning

  Reciprocal

Switch the numerator and denominator of a fraction. The reciprocal of an integer n is the fraction 1/n. The reciprocal of 2/3 is 3/2.    Continue Learning

  Factor

A number that can be added to itself to reach another number. x is a factor of y if y/x is an integer.    Continue Learning

Greatest Common Factor

The largest factor that each number has. The greatest common factor of 24 and 36 is 12    Continue Learning

Multiple

The result when a number is added to itself. x is a multiple of y if x/y is an integer.    Continue Learning

   Least Common Multiple

The smallest number that is a multiple of each number. The least common multiple of 25 and 10 is 50    Continue Learning

  Prime

A positive integer that is divisible by exactly two positive numbers, 1 and itself. 1 is not a prime number, because it is divisible by only one positive number (itself).    Continue Learning

    Prime Factorization

Reducing a number into only its prime factors. The prime factorization of 72 is 23*32    Continue Learning

    Power (Exponent, Base)

An exponent tells you to multiply something by itself a particular number of times, in the same way that multiplication tells you to add something to itself a particular number of times. sometimes written as 2^5    Continue Learning

 Squared

To square a number is to multiply it by itself. A number x squared is written x2. Squaring a number means to raise it to the second power.    Continue Learning

 Cubed

To cube a number is to multiply it by itself three times. A number x cubed is written x3. Cubing a number means to raise it to the third power.    Continue Learning

    Root

The root of x is a number that when multiplied by itself a number of times will result in x. The number of times is the degree of the root. Another way to understand it is as an exponent that is a fraction. √    Continue Learning

    Perfect Square

A number whose square root is an integer    Continue Learning

Polynomial

An expression with more than one algebraic term    Continue Learning

Quadratic Equation

An equation with a variable to the second power    Continue Learning

   Absolute Value

The distance from 0. Always positive    Continue Learning

   Inequality

A relation between two values that are different instead of equal.
> means greater than
< means less than
— means greater than or equal to
— means less than or equal to    Continue Learning

 ( Braket

A relation between two values that are different instead of equal A way to express a range, but the point is not included    Continue Learning

 [ Big Braket

A way to express a range, but the point is included    Continue Learning

Percent

Another way of writing a fraction. x% is equal to the fraction x/100    Continue Learning

Average (Arithmetic Mean)

The result of adding all numbers and then dividing by the number of items.    Continue Learning

Median

The middle number of an ordered number of items. Make sure to put the list in order first. The median of 1, 10, and 11 = 10.    Continue Learning

Mode

The most common occurrence. There can be more than one mode if each occurs an equal number of times. The mode of 1, 2, 2, 3, 5, 5, 5 = 5    Continue Learning

  Standard Deviation

This is a measure of the spread of the data (i.e. how far away it is from the mean)    Continue Learning

  Ratio

A relationship between two amounts. This shows how many times bigger one is over the other. The ratio should be in the same order as the words. Expressed with ":"    Continue Learning

Proportion

When two ratios are equal    Continue Learning

Learn Math Definitions of

Geometry Operations...

Point

One single location. Usually a ●    Continue Learning

Line

Connects two points and continues forever in both directions    Continue Learning

Ray

Starts from one point and continue forever in only one direction    Continue Learning

Line Segment

Connects two points but does not continue beyond those points    Continue Learning

Endpoint

The end of a line segment or ray    Continue Learning

Midpoint

The point on a line that is of exactly equal distance from both endpoints    Continue Learning

Angle

The space between two intersecting lines. Usually measured in degrees or radians    Continue Learning

Degree of an Angle

The measurement of an angle. Usually between 0° and 360°    Continue Learning

Right Angle

An angle with a measure of 90°    Continue Learning

Acute

An angle with a measure of less than 90°    Continue Learning

Obtuse

An angle with a measure of more than 90°    Continue Learning

Complementary

Two angles whose sum is 90°    Continue Learning

Supplement

Two angles whose sum is 180°    Continue Learning

Bisect

To cut an angle or line exactly in half    Continue Learning

Tangent

To touch at only one point    Continue Learning

Parallel

Two lines that never touch    Continue Learning

Perpendicular

Two lines that touch and form four 90° angles    Continue Learning

To Scale

When a picture is drawn as it looks. If something is not drawn to scale, it might not correctly represent the actual picture.    Continue Learning

Polygon

An enclosed figure with 3 or more lines    Continue Learning

Vertex

Where two lines of a polygon touch    Continue Learning

Quadrilateral

A four-sided polygon. The sum of interior angles is 360°    Continue Learning

Parallelogram

A four-sided polygon such that opposite sides are parallel    Continue Learning

Rhombus

A four-sided polygon such that all sides are equal and such that opposite angles are equal    Continue Learning

Rectangle

A four-sided polygon such that opposite sides are equal, such that opposite sides are parallel, and such that all angles equal 90°    Continue Learning

Square

A four-sided figure such that all sides are equal, such that opposite sides are parallel, and such that all angles equal 90°    Continue Learning

Trapezoid

A quadrilateral with two sides that are parallel    Continue Learning

Triangle

A three-sided figure. The sum of interior angles is 180°    Continue Learning

Isosceles Triangle

A triangle with 2 equal sides. The angles opposite the equal sides are equal.    Continue Learning

Equilateral Triangle

A triangle with 3 equal sides. Each angle is 60°    Continue Learning

Right Triangle

A triangle with one 90° angle    Continue Learning

Hypotenuse

The longest side of a right triangle (opposite the right angle).    Continue Learning

Pythagorean Theorem

An equation for the relationship of the sides of a right triangle    Continue Learning

  Similar Triangles

Triangles that have equal angle measures. Usually the triangles are of different size, but the ratios of each side of one triangle to the matching side of the other triangle are the same.    Continue Learning

  Congruent

A traingle that is Identical to each other    Continue Learning

Perimeter

Distance around the edges. Add all of the sides    Continue Learning

Area

Amount of space inside. Usually multiply two sides that form a right angle.    Continue Learning

Circle

Round figure – all of the outside is the same distance from the center    Continue Learning

Radius

The distance from the center of a circle to the outside (plural: radii)    Continue Learning

Diameter

The distance between two points on a circle that passes through the center    Continue Learning

Chord

A line that connects two points on the circle. It does not have to pass through the center.    Continue Learning

Circumference

The measure of the distance around the outside of a circle    Continue Learning

Arc

A part of the circumference    Continue Learning

Sector

Part of the area of a circle enclosed by two radii. Looks like a piece of pizza.    Continue Learning

Central Angle

The angle at the center of a circle that is enclosed by two radii (angle of a sector)    Continue Learning

Cube

A 3-dimensional square – all sides are equal.    Continue Learning

Rectangular Solid

A 3-dimensional rectangle.    Continue Learning

Cylinder

A circle with height – like a can of soda    Continue Learning

Sphere

A 3-dimensional circle – like a ball    Continue Learning

Volume

The space inside a 3-dimensional figure    Continue Learning

Surface Area

The area of the outside of a 3-dimensional figure    Continue Learning

Inscribed

When a figure is drawn inside another such that their boundaries touch    Continue Learning

Learn Math Definitions of

Coordinate Geometry Operations...

Coordinate Plane

A graph in which each point can be represented by a set of coordinates    Continue Learning

Axis

The lines that make up a coordinate plane. (plural: axes) There is usually an x and a y axis    Continue Learning

Ordered Pair

A set of numbers that indicates location on a graph (x, y)    Continue Learning

Intercept

The point at which a line goes through another line or axis    Continue Learning

Y-Intercept

The point at which a line crosses the y-axis. (0, y)    Continue Learning

X-Intercept

The point at which a line crosses the x-axis. (x, 0)    Continue Learning

Slope

The gradient or steepness of a line. It is how far the line moves up whenever the line moves one to the right.    Continue Learning

Domain

The set of numbers that are allowed in a function or line on a graph    Continue Learning

Range

The potential output of a function or line on a graph    Continue Learning

Parallel (graphing)

Two lines with the same slope    Continue Learning

Perpendicular (graphing)

Two lines with slopes that are negative reciprocals of each other    Continue Learning

Translation

Movement of a line or shape such that the result is the same but in a different location    Continue Learning

Rotation

To turn an object in a circular motion around a fixed point    Continue Learning

Reflection

To flip a line or shape over a line (axis)    Continue Learning

Symmetry

When rotating or reflecting a shape results in the same shape    Continue Learning

Look Common Symbols

Common Symbols use in various...

Symbol

Definition

Examples

How to Say it

$

Dollars. U.S. money

$5.00

Five dollars

+

Addition. Usually read as “plus”

2 + 7

Two plus seven

-

Subtraction. Usually read as “minus”

5 – 2

Five minus two

*

Multiplication. Usually read as “times”

3 * 4

Three times four

÷

Division. Usually read as “divided by”

8 ÷ 2

Eight divided by two

/

Division. Usually read as “divided by”

6 / 3

Six divided by three

=

Equals

1 + 1 = 2

One plus one equals two

Approximately (almost equals)

9.95 ≈ 10

 

Less than

2 < 4

Two is less than four

Greater than

5 > 3

Five is greater than three

Less than or equal to

x ≤ 10

x is less than or equal to ten

Greater than or equal to

x ≥ 2

x is greater than or equal to two

^

Exponents. Usually read as “to the power of”

3^2 = 32 = 9

x to the power of two

Root

√4 = 2

The square root of four is two

%

Percent

50% = 50/100

Fifty percent

Infinity

 

 

Pi

3.14159…

 

 

 

Summation

3

∑ 2i = 2(1) + 2(2) + 2(3) = 11

i = 1

 

{ … }

Set

{ 2, 3, 5, 7, 11, 13, …}

The set of                       numbers

[ , ]

Defines an inclusive range

[5, ∞)

x ≥ 5

( , )

Defines an exclusive range or

a coordinate point on a graph

(-∞, 2)

x < 2