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Division

In mathematics division is an operation which is the opposite of multiplication.

If c times b equals a, written:

$\displaystyle{ c \times b = a }$

where b is not zero, then a divided by b equals c, written:

$\displaystyle{ \frac ab = c }$

For instance,

$\displaystyle{ \frac 63 = 2 }$

since

$\displaystyle{ 2 \times 3 = 6 }$.

In the above expression, a is called the dividend, b the divisor and c the quotient.

Division by zero

$\displaystyle{ \frac x0 =? }$

...is not defined.

Notation

Division is most often shown by placing the dividend over the divisor with a horizontal line, also called a vinculum, between them. For example, a divided by b is written

$\displaystyle{ \frac ab }$.

This can be read out loud as "a divided by b" or "a over b". A way to express division all on one line is to write the dividend, then a slash, then the divisor, like this:

$\displaystyle{ a/b.\, }$

This is the usual way to specify division in most computer programming languages since it can easily be typed as a simple sequence of characters.

A typographical variation which is halfway between these two forms uses a slash but elevates the dividend, and lowers the divisor:

a/b.

Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers (although typically called the numerator and denominator). A fraction is an accepted way of writing numbers. It is not always expected that the result of the division is written in decimals.

A less common way to show division is to use the obelus (or division sign) in this manner:

$\displaystyle{ a \div b. }$

But in elementary arithmetic this form is used rather often. The obelus is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator.

In some non-English-speaking cultures, "a divided by b" is written a : b. However, in English usage the colon is restricted to expressing the related concept of ratios (then "a is to b").