; AD,
; AE,
. Thus, a fraction is denoted by two numbers parted by a horizontal line; the lower, called the denominator, denotes the number of equal parts into which the integer is divided; and the upper, called the numerator, denotes the number of these equal parts which are taken. Hence it follows, that if the numerator be less than the denominator, the fraction is less than unity. If the numerator be equal to the denominator, the fraction is equal to unity; and if greater than the denominator, it is greater than unity. It is evident that a fraction is an abstract quantity—that is, that its value is independent of the nature of the integer which is divided.
2. If we divide each of the equal parts AC, CD, DE, EB into two equal parts, the whole, AB, will be divided into eight equal parts; and we see that AC =
; AD =
; AE =