Division (mathematics)

From Simple English Wikipedia, the free encyclopedia

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

If c times b equals a, written:

c \times b = a

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

\frac ab = c

For instance,

\frac 63 = 2

since

2 \times 3 = 6\,.

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

Division by zero (i.e. where the divisor is zero) is not defined.

[edit] 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

\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:

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:

ab .

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:

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").

[edit] External links