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Example: Based on Property of Division by Integers

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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.




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,



In the above expression, a is called the dividendb the divisor and c the quotient. (Our solved example in mathguru.com uses this concept)



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.




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.