Explanation:
The integers (from the Latin integer, literally
"untouched", hence "whole": the word entire comes from the same origin, but
via French) are formed by the natural numbers including 0 (0, 1, 2, 3, ...) together with the negatives of the non-zero natural numbers
(−1, −2, −3, ...). Viewed as a subset of the real numbers, they are numbers
that can be written without a fractional or decimal component, and fall within
the set {..., −2, −1, 0, 1, 2, ...}. For example, 21, 4, and
−2048 are integers; 9.75 and 5½ are not integers.
http://en.wikipedia.org/wiki/Integer
Division (mathematics)
In mathematics, especially in
elementary arithmetic division (÷) is an arithmetic
operation. Specifically, if c times b equals a,
written:
where b is not zero
then a divided by b equals c,
written:
For instance,
Since
.
In the above expression, a is
called the dividend, b the divisor and c the quotient.
(Our solved example in mathguru.com uses this concept)
Notation
Division is often shown in algebra and science by placing the dividend over the divisor with a horizontal line, also called a vinculum or fraction
bar, between them. For example, a divided by b is written
This can be read out loud as "a divided by b", "a
by b" or "a over b". A way to express division all on one line
is to write the dividend,
or numerator then a slash, then
the divisor, or
denominator like this:
Division
of integers
Division of integers is not closed.
Apart from division by zero being undefined, the quotient will not be an
integer unless the dividend is an integer multiple of the divisor; for example
26 cannot be divided by 10 to give an integer. In such a case there are four
possible approaches.
1. Say
that 26 cannot be divided by 10; division becomes a partial function.
2. Give
the answer as a decimal fraction or a mixed
number, so or This is the approach usually taken in
mathematics.
3. Give
the answer as an integer quotient and a remainder, so
4. Give
the integer quotient as the answer, so This is sometimes called integer division.
http://en.wikipedia.org/wiki/Division_(mathematics)
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative
Commons Attribution- ShareAlike 3.0 Unported License.