In mathematics, a fraction is a way of expressing a quantity based on an amount that is divided into a number of equal-sized parts. For example, each part of a cake split into four equal parts is called a quarter (and represented numerically as ¼); two quarters is one half (½) of the cake, and eight quarters would make two cakes.
Mathematically, a fraction is a quotient of numbers, like ¾ (which is 3 divided by 4). More generally, a fraction is an element of a field of fractions.
In our cake example above, where a quarter is represented numerically as ¼, the bottom number, called the denominator, is the total number of equal parts making up the cake as a whole, and the top number, called the numerator, is the number of these parts we have. For example, the fraction ¾ represents three quarters.
The numerator and denominator may be separated by a slanting line called a solidus or slash, for example ¾, or may be written above and below a horizontal line called a vinculum: this is what fractions will look like in most math curriculum.
The numerator and denominator are the "terms" of the fraction. The word "numerator" is related to the word "enumerate," meaning to "tell how many"; thus the numerator tells us how many 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.). Note that because it is impossible to divide something into zero equal parts, zero can never be the denominator of a fraction.