Division (mathematics)

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In mathematics, the word "division" means the operation which is the opposite of multiplication. The symbols for division are the slash () and the fraction line, as in:

or

where each of the three expressions means "6 divided by 3", with 2 as the answer. The first number is the dividend (6), and the second number is the divisor (3). The result (or answer) of a division is the quotient, where any left-over amount as whole numbers is called the "remainder".[1] For example, gives quotient 3 with remainder 2, all expressed as the mixed number or 3.5).

The numbers involved in division can be very big, such as the case with two hundred: , or with 7 billion: (where the quotient is equal to 7 million).

With multiplication[change | change source]

If times equals , written as:

where is not zero, then divided by equals , written as:

[2]

For instance,

since

.

In the above expression, is called the dividend, the divisor and the quotient.[2]

Division by zero, as in

is not defined.

Notation[change | change source]

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

This can be read 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:

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 (in which case, the two numbers are typically referred to as 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.

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

Related pages[change | change source]

References[change | change source]

  1. "Division". www.mathsisfun.com. Retrieved 2020-08-26.
  2. 2.0 2.1 Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.

Other websites[change | change source]