Vulgar fraction

In algebra, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. The fraction "three divided by four" or "three over four" or "three fourths" or "three quarters" can be written as

Related Topics:
Algebra - Integer - Divided by

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

: rac{3}{4}       or       3 ÷ 4       or       3/4       or       3⁄4

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In this article, we will use the last of these notations. The first quantity, the "number on top" of the fraction, is called the numerator, and the other number is called the denominator.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The numerator and denominator are the terms of the fraction. The word "numerator" is related to the word "enumerate." To enumerate means to "tell how many"; thus the numerator tells us how many fractional parts we have in the indicated fraction. To denominate means to "give a name" or "tell what kind"; thus the denominator tells us what kind of parts we have (halves, thirds, fourths, etc.).

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The denominator can never be zero because division by zero is not defined. All vulgar fractions are rational numbers and, by definition, all rational numbers can be expressed as vulgar fractions, although the representation is not unique. (For example, 3⁄4 = 6⁄8.)

Related Topics:
Zero - Division by zero - Rational number

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Consider this article a gentle introduction to fractions: for a more theoretical treatment see rational numbers. There is also a fraction article which can serve as a guide to different kinds of fractions.

Related Topics:
Rational number - Fraction

~ ~ ~ ~ ~ ~ ~ ~ ~ ~