# Operation (mathematics) - Simple English Wikipedia, the free encyclopedia

In mathematics, an **operation** is a function which takes one or more inputs (called operands) and produces an output. Some of the most common operations include addition, subtraction, multiplication and division,^{[1]}^{[2]} all of which take two inputs and produce an output. These are called binary operations,^{[3]}^{[4]} and are often used when solving math problems. Other types of operations are called unary operations,^{[5]} which take only one input and produce an output.

There are more operations than these, including raising numbers to exponents, taking the root and applying the logarithm.

Below is a list of the most used operations.

## List of mathematical operations[change | change source]

### Addition[change | change source]

Addition is the first arithmetic operation and hyperoperation. It is the inverse operation of subtraction. The terms in an addition are called *addends*, and the result of an addition is called a *sum*.

The symbol for addition is **+**

Examples of additions:

Any number plus zero is the same number (). This is called the *additive identity*.

For example:

Changing the order of the addends in an addition does not change its sum. This is called the *commutative property of addition*.

For example:

Changing how addends are grouped in an addition does not change its sum either. This is called the *associative property of addition*.

For example:

#### Additive inverses (opposites)[change | change source]

The opposite of a number is . A number plus its opposite is always equal to 0:

For example, the opposite of 5 is -5, because

The absolute value of two opposite numbers is always the same.

### Subtraction[change | change source]

Subtraction is the second arithmetic operation and the inverse operation of addition. The number that is being subtracted is the *subtrahend* and the number it is subtracted from is the *minuend*. The result of a subtraction is called a *difference*.

The symbol for subtraction is **−**

Examples of subtractions:

Because of the *additive identity*, any number minus zero is the same number ().

In a subtraction of two terms, switching the minuend and the subtrahend changes the sign of the answer, meaning subtraction is anticommutative.

For example: and

### Multiplication[change | change source]

Multiplication is the third arithmetic operation and the second hyperoperation. It is the inverse operation of division. The terms in a multiplication are called *factors*, and the result of a multiplication is called a *product*.

Multiplication is repeated addition.

The symbol for multiplication is **×** (• in algebra and * in most programming languages)

Examples of multiplications:

Any number times one is the same number (). This is called the *multiplicative identity*.

For example:

Changing the order of the factors in a multiplication does not change its product. This is called the *commutative property of multiplication*.

For example:

Changing how factors are grouped in a multiplication does not change its product either. This is called the *associative property of multiplication*.

For example:

Multiplication can also be implied. For example, means , and means .

With the Hindu-Arabic numerals, putting two digits next to each other could be misunderstood (e.g. 235 is read as "two hundred and thirty-five" and not ). Instead, one of the numbers (typically the second) is put in brackets.

For example:

#### Multiplicative inverses (reciprocals)[change | change source]

The reciprocal of a number is . A number times its reciprocal is always equal to 1:

For example, the reciprocal of 3 is 1/3, because

To get the reciprocal of a fraction, switch the numerator and the denominator: the reciprocal of is

### Division[change | change source]

Division is the fourth arithmetic operation and the inverse operation of multiplication. The number that is being divided is the *dividend* and the number it is divided by is the *divisor*. The number on top of a fraction is called the *numerator* and the number at the bottom is called the *denominator*. The result of a division is called a *quotient*.

Division is repeated subtraction.

The symbol for division is **/** or a fraction.

Examples of divisions:

Because of the *multiplicative identity*, any number divided by one is the same number ().

Division by zero is undefined ().

In a fraction, switching the numerator and the denominator gives the reciprocal of the fraction.

For example:

### Exponentiation[change | change source]

Exponentiation is the fifth arithmetic operation and the third hyperoperation. It is one of the inverse operations of roots and logarithms. The number that is being multiplied is the *base* and the number of times it is multiplied is the *exponent*. The result of an exponentiation is called a *power*.

Exponentiation is repeated multiplication or division.

The symbol for exponentiation is the superscript (x^{y}) or the caret (**^**).

Examples of exponentiations:

Because of the *multiplicative identity*, the first power of any number is the same number, and the zeroth power of any number is one ( and ).

### Roots[change | change source]

Roots are the sixth arithmetic operation and one of the inverse operations of exponentiation and logarithms. The first term is called the *index*, and the second term is called the *radicand*. The result of a root is called a *base*. When there is no index, this means it is a square (2) root.

The symbol for roots is the radical ().

Examples of roots:

The first root of any number is the same number ().

### Logarithms[change | change source]

Logarithms are the seventh arithmetic operation and one of the inverse operations of exponentiation and roots. The first term is called the *base*, and the second term is called the *power*. The result of a logarithm is called an *exponent*. When there is no base, this means it is a base 10 logarithm.

The symbol for logarithm is **log**_{b}(a)

Examples of logarithms:

The logarithm of 1 () is 0 in every base. This is because

The logarithm base e, or natural logarithm, is written as .

### Modulation[change | change source]

Modulation is the eighth arithmetic operation. It gives the remainder of a division. The first term is called the *modulend* and the second term is called the *modulator*. The result of a modulation is called a *modulus*.

The symbol for modulation is **\**

Examples of modulations:

\

\

\

\

\

\ is always equal to zero, because zero can be divided by any number ().

### Factorial[change | change source]

Factorial is a function which gives the number of ways to arrange objects. The term is called the *index*. The result of a factorial is also called a factorial.

The symbol for factorial is **!**

The first factorials are:

is equal to one because there is exactly one way of arranging 0 objects. Factorials are undefined for negative integers. Factorials of fractional numbers can be calculated using the Gamma function.

### Absolute value[change | change source]

Absolute value is a function which gives the distance from zero (or magnitude) of a number.

The symbol for absolute value is

Examples of absolute values:

The absolute value of is the same as the absolute value of (). This is because subtraction is anticommutative.

## Related pages[change | change source]

## References[change | change source]

- ↑ "Definition of Operation (Illustrated Mathematics Dictionary)".
*mathsisfun.com*. Retrieved 2021-10-21. - ↑ "Order of Operations".
*mathsisfun.com*. Retrieved 2021-11-21. - ↑ Weisstein, Eric W. "Binary Operation".
*mathworld.wolfram.com*. Retrieved 2020-08-26. - ↑ "Definition of Binary Operation (Illustrated Mathematics Dictionary)".
*mathsisfun.com*. Retrieved 2021-11-21. - ↑ "Definition of Unary Operation (Illustrated Mathematics Dictionary)".
*mathsisfun.com*. Retrieved 2021-11-21.