Encyclopedia > Denominator

  Article Content


Redirected from Denominator

In algebra, a fraction consists of one quantity divided by another quantity. The fraction "three divided by four" or "three over four" or "three fourths" can be written as
<math> \frac{3}{4} </math>
or 3 ÷ 4
or 3/4

In this article, we will use the latter notation. Other typical fractions include -2/7 and (x+1)/(x-1). The first quantity, the number "on top of the fraction", is called the numerator, and the other number is called the denominator. The denominator can never be zero. A fraction consisting of two integers is called a rational number.

Several rules for the calculation with fractions are useful:

Cancelling. If both the numerator and the denominator of a fraction are multiplied or divided by the same number, then the fraction does not change its value. For instance, 4/6 = 2/3 and 1/x = x / x2.

Adding fractions. To add or subtract two fractions, you first need to change the two fractions so that they have a common denominator; then you can add or subtract the numerators. For instance, 2/3 + 1/4 = 8/12 + 3/12 = 11/12.

Multiplying fractions. To multiply two fractions, multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator. For instance, 2/3 × 1/4 = (2×1) / (3× 4) = 2 / 12 = 1 / 6.

Dividing fractions. To divide one fraction by another one, flip numerator and denominator of the second one, and then multiply the two fractions. For instance, (2/3) / (4/5) = 2/3 × 5/4 = (2×5) / (3×4) = 10/12 = 5/6.

In abstract algebra, these rules can be proved to hold in any field. Furthermore, if one starts with any integral domain R, one can always construct a field consisting of all fractions of elements of R, the field of fractions of R.

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article
Dennis Gabor

...     Contents Dennis Gabor Dennis Gabor (Gábor Dénes) (1900-1979) was a Hungarian physicist. He invented holography in 1947, for whic ...

This page was created in 117.8 ms