Common math symbols and terminology (2023)

Mathematical terminology and symbols can be confusing and a barrier to learning and understanding basic arithmetic.

Complementing our numerical literacy pages, this page provides a brief glossary of common mathematical symbols and terminology with concise definitions.

Are we missing something?let playto inform us.

common math symbols

+ Add, More, Positive

The plus sign + is often used to indicate that two or more numbers are to be added, for example 2 + 2.

The + symbol can also be used to indicate a positive number, although it is less common, for example +2. our page belowpositive and negative numbersexplains that an unsigned number is considered positive, so the plus sign is usually unnecessary.

See our page atadditivefor more.

− remainders, minus, negative

This symbol has two main uses in mathematics:

1. − is used when one or more numbers must be subtracted, for example 2 − 2.
2. The - symbol is also commonly used to indicate a negative or negative number, for example B-2.

See our page atSubtractionfor more.

× o * o . multiplication

These symbols have the same meaning; Commonly, × is used to mean multiplication when written by hand or used on a 2×2 calculator, for example.

The * symbol is used in spreadsheets and other computer applications to indicate multiplication, although in mathematics * has more complex meanings.

More rarely, multiplication can also be symbolized by a dot. or no icon. For example, if you see a number outside the brackets without any operator (symbol or character), it must be multiplied by the contents of the brackets: 2(3+2) is the same as 2×(3+2).

See our page atmultiplicationfor more.

÷ o / Division

These symbols are used to indicate division in mathematics. ÷ is commonly used in handwritten calculations and on calculators, for example 2 ÷ 2.

/ is used in spreadsheets and other computer applications.

See our page atdivisionfor more.

= same

The =equal symbol is used to indicate that the values ​​on both sides are equal. It is most commonly used to show the result of a calculation, e.g. 2 + 2 = 4, or in equations, eg. for example, 2 + 3 = 10 − 5.

You can also find other related symbols, although they are less common:

• ≠does not mean the same. For example 2+2≠5 - 2. In computer applications (eg Excel), the symbols <> mean different.
• ≡means identical to. This is similar but not exactly equal to equal. So when in doubt, stick with =.
• ≈means approximately the same or almost the same. The two sides of a relationship denoted by this symbolNObe precise enough to manipulate mathematically.

< Less than and > Greater than

this icon<means less than, for example 2 < 4 means 2 is less than 4.

this icon>means greater than, for example 4 > 2.

≤ ≥These symbols mean "less than or equal to" and "greater than or equal to" and are commonly used in algebra. In desktop applications, <= and >= are used.

≪ ≫These symbols are less common and mean much less or much more.

± more or less

This ± symbol means “more or less”. For example, it is used to indicate confidence intervals around a number.

The answer must be "plus or minus" another number, or in other words, within a range around the given answer.

For example, 5 ± 2 can be any number from 3 to 7 in practice.

∑ Soma

The ∑ symbol means sum.

∑ is the Greek capital sigma sign. It's commonly used in algebraic functions, and you might notice it in Excel as well: the AutoSum button has a sigma as a symbol.

° Grau

Degrees ° are used in many ways.

• As a rotation measure- the angle between the sides of a shape or the rotation of a circle. A circle measures 360° and a right angle 90°. See our section onGeometryfor more.
• A temperature measurement.Degrees Celsius or Centigrade are used in most parts of the world (except the US). Water freezes at 0°C and boils at 100°C. Fahrenheit is used in the US. On the Fahrenheit scale, water freezes at 32°F and boils at 212°F. See our page:measuring systemsfor more information.

∠ Store

The angle symbol ∠ is used as an abbreviation in geometry (the study of shapes) to describe an angle.

The expression ∠ABC is used to describe the angle at point B (between points A and C). Likewise, ∠BAC would be used to describe the angle at point A (between points B and C). See our pages for more information on angles and other geometric terms.Geometry.

√ Quadratwurzel

√ is the square root symbol. A square root is the number that, when multiplied by itself, gives the original number.

For example, the square root of 4 is 2 because 2 x 2 = 4. The square root of 9 is 3 because 3 x 3 = 9.

See our page:Special numbers and conceptsfor more information on square roots.

^norteViolence

A superscript integer (any integernorte) is the symbol for the power of a number.

for example 3², means 3 to the power of 2, which is the same as 3 squared (3 x 3).

4³means 4 increased to 3 or 4 cubic, so 4 × 4 × 4.

See our pages belowcalculation areajvolume calculationto see examples of when to use square numbers and cubes.

Powers are also used as abbreviations for large and small numbers.

big numbers

10⁶is 1,000,000 (one million).

10⁹is 1,000,000,000 (billion).

10¹²is 1,000,000,000,000 (one trillion).

10¹⁰⁰handwritten would be 1 with 100 0 (a googol).

small numbers

10^-3is 0.001 (one thousandth)

10^-6is 0.000001 (one millionth)

The powers can also be written^Symbol.

10^6 = 10⁶= 1,000,000 (one million).

. For

. is the symbol for the decimal point, often referred to simply as a "dot". See our page atdecimalssee application examples.

, thousands separator

A comma can be used to divide large numbers to make them easier to read.

A thousand can be written as 1,000 and 1,000, and a million as 1,000,000 or 1,000,000. Larger numbers are separated into blocks of three by commas.

In most English-speaking countries, it has no mathematical function, just to make the numbers easier to read.

In some other countries, especially in Europe, a comma may be used instead of a decimal point, and indeed a decimal point may be used instead of a comma as a visual separator. This is explained in more detail in ourIntroduction to numbersbook page.

[ ], ( ) square brackets, square brackets

Parentheses ( ) are used to specify the order of a calculation dictated by theBODYRuler.

For example, parts of a calculation enclosed in parentheses are calculated first

• 5 + 3 × 2 = 11
• (5 + 3) × 2 = 16

% Percent

The % symbol means percentage or the number 100.

Learn all about percentages on our page:Introduction to percentages

pi

π or pi is the Greek character for the "p" sound. It is common in mathematics and is a mathematical constant. Pi is the circumference of a circle divided by its diameter and is equal to 3.141592653. It is an irrational number, that is, its decimals go to infinity.

∞ infinity

The ∞ symbol represents infinity, the concept that numbers last forever.

No matter how big your number is, you can always have a bigger one because you can always add one.

Infinity is not a number, that's itIdeaof numbers that last forever. You can't add one infinitely more than you can add one to a person or love or hate.

\(\bar x\) (bar x) means

\(\bar x\) is the mean of all possible values ​​of x.

Most of the time you will find this symbol in stats.

See our page atmediafor more information.

! Faculty

! is the symbol for factorial.

North! is the product (multiplication) of all numbers from n up to and including 1, that is, n × (n−1) × (n−2) × … × 2 × 1.

For example:

5! = 5 × 4 × 3 × 2 × 1 = 120

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 3.628.800

| sugar cane

pipe '|' It is also known as vertical bar, vbar, daub and has many uses in math, physics and computer science.

In basic mathematics, it used to be used for designationabsolute valueÖModulea real number, where \(\vert x \vert\) is theAbsolute value of the modulus of \(x\).

Mathematically this is defined as

$$\vert x \vert = \biggl\{\begin{eqnarray} -x, x \lt 0 \\ x, x \ge 0 \end{eqnarray}$$

Simply put, \(\vert x \vert\) is the non-negative value of \(x\). For example, the modulus of 6 is 6 and the modulus of -6 is also 6.

It is also used in probability, where P(Z|Y) denotes the probability of X given Y.

∝ Proportional

∝means "is proportional to' and is used to show something that varies in relation to something else.

For example, if x = 2y, then x ∝ y.

∴ therefore

∴ is a useful abbreviation for "therefore" used in math and science.

∵ well

∵ is a useful abbreviation for "because", not to be confused with "therefore".

Mathematical Terminology (A-Z)

Amplitude

When an object or point moves in a cyclic pattern or is subject to vibration or oscillation (for example, a pendulum), theAmplitudeis the maximum distance it moves from its center. The... seeIntroduction to Geometryfor more.

Apothem

Line connecting the center of a regular polygon to one of its sides. The line is perpendicular (at right angles) to the side.

Area

Geometric area is defined as the space occupied by a flat shape or the surface of an object. Area is measured in square units, such as square meters (m²). For more information, visit our page atArea, Area and Volume.

assumptota

An asymptote is a straight line or axis specifically related to a curved line. As the curved line extends (strains) to infinity, it approaches its asymptote without touching it (that is, the distance between the curve and the asymptote approaches zero). Occurs in geometry andTrigonometry.

axle

A reference line on which an object, point, or line is drawn, rotated, or measured. In a symmetric form, an axis is usually a line of symmetry.

coefficient

A coefficient is a number or quantity that multiplies another quantity. It is usually placed before aVariable. In expression 6x, 6 is the coefficient andxis the variable.

Scope

The perimeter is the length of the line around the edge of a circle. It is a species ofScopethis is unique to circular shapes. For more information, visit our page atcurved shapes.

Data

Data is a collection of values, information or characteristics, often numerical in nature. They can be collected through scientific experiments or other observational methods. you can bequantitativelyÖqualitativeVariables A data item is a single value of a single variable. See our page atdata typefor more.

diameter

Diameter is a term used in geometry to define a straight line passing through the center of a circle or sphere and touching the circumference or surface at both ends. The diameter is twice as largeRadio.

extrapolate

Extrapolation is a data analysis term. Refers to extending a graph, curve, or range of values ​​into an area for which no data exists, deriving the unknown data values ​​from trends in the known data.

Factor

A factor is a number that we multiply by another number. A factor divides another number by an integer. Most numbers have an even number of factors. FORsquare numberhas an odd number of factors. FORPrime numberhas two factors: itself and 1. AFirst factoris a factor that is a prime number. For example, the prime factors of 21 are 3 and 7 (because 3 × 7 = 21 and 3 and 7 are prime).

Mean, median and mode

ANDmean(Average) of a data set is calculated by adding all the numbers in the data set and then dividing by the number of values ​​in the data set. If the record is sorted from smallest to largest, theMedianit's the middle. The mode is the number that occurs most frequently.

Operation

A mathematical operation is a step or phase in a calculation, or a mathematical "action". The basic arithmetic operations are addition, subtraction, multiplication and division. The order in which operations are performed in a calculation is important. The order of operations is known asBODY.

Mathematical operations are often referred to as "additions". Strictly speaking, a 'sum' is an addition operation. By SYN we mean operations and calculations, but in colloquial speech you often hear the general term "sum" which is incorrect.

Scope

The perimeter of a two-dimensional shape is the solid line (or the length of the line) that defines the shape's outline. The perimeter of a circular shape is specifically referred to as itsScope. . . . our page upScopeexplains this in more detail.

Part

Proportion is relative to ratio. Proportion compares one part to another, and proportion compares the part to the whole. Example: "3 out of 10 adults in England are overweight". The ratio refers tofractions.

Pythagoras

Pythagoras was a Greek philosopher who is credited with a number of important mathematical and scientific discoveries, perhaps the most significant of which is known astheorem of Pythagoras.

It's an important rule that only applies to right triangles. It states that "the square of the hypotenuse is equal to the sum of the squares of the other two sides".

quantitatively and qualitatively

quantitative dataThey are numerical variables or values ​​that can be expressed numerically, i.e. how much, how many, how often, and are obtained by counting or measuring.

qualitative dataare variables of the type that do not have a numerical value and can be expressed descriptively, that is, by means of a name or symbol, and obtained by observation.

See our page atdata typefor more.

radians

The radian is the SI unit for measuring an angle. A radian is the angle subtended at the center of a circle by an arc of the same length as the radius. A radian is slightly less than 57.3 degrees. One complete rotation (360 degrees) is equal to 2π radians.

Radio

The term radius is used in connection with circles and other curved shapes. It is the distance from the center of a circle, sphere, or arc to its outer edge, surface, orScope. ANDdiameteris twice the radius. For more information, visit our page atcurved shapes.

Area

In statistics, the range of a given set of data is the difference between the largest and smallest values.

Relationship

Ratio is a mathematical term used to compare the size of one part to another. Ratios are usually displayed as two or more numbers separated by colons, for example 7:5, 1:8, or 5:2:1.

standard deviation

The standard deviation of a data set measures how much the data deviates from the mean, i. H. is a measure of the fluctuation or spread of a set of values. When data variability is small and all values ​​are close to the mean, the standard deviation is small. A high standard deviation indicates that the data is spread over a larger range.

Expression

A term is a single mathematical expression. It can be a single number, a single variable (ex.x) or multiple constants and multiplied variables (e.g. 3xtwo). Terms are usually separated by addition or subtraction operations. A term can contain addition or subtraction operations, but only enclosed in parentheses, for example 3(2-x3).

Variable

A variable is aFactorin a mathematical expression, arithmetic relationship, or scientific experiment that is subject to change. An experiment usually has three types of variables: independent, dependent, and controlled. In expression 6x, 6 is thecoefficientjxis the variable.

Difference

Variance is a statistical measure that indicates the dispersionbetween membersin a registry. It measures how far each member of the set is from the mean, and therefore from all other members of the set.

Vector

Vectors describe mathematical quantities that have magnitude and direction. Vectors appear in many mathematical and physical applications, e.g. the study of motion in which velocity, acceleration, force, displacement, and momentum are vector quantities.

Volume

Volume is the three-dimensional space occupied by a solid or hollow shape. It is quantified by the cubic measure of the space enclosed by its surfaces. Volume is measured in cubic units, e.g. subway³.