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:
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". 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:
In the above expression, is called the dividend, the divisor and the quotient.
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:
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]
- Divisor, another meaning as a number which evenly divides an amount
- Division by two
- Long division
- Modular arithmetic
References[change | change source]
- ↑ "Division". www.mathsisfun.com. Retrieved 2020-08-26.
- ↑ 2.0 2.1 Weisstein, Eric W. "Division". mathworld.wolfram.com. Retrieved 2020-08-26.
Other websites[change | change source]
- Division on a Japanese abacus selected from Abacus: Mystery of the Bead
- Chinese Short Division Techniques on a Suan Pan
- Rules of divisibility Archived 2015-05-03 at the Wayback Machine