Collier's New Encyclopedia (1921)/Fraction

FRACTION, a part of any magnitude, integer (whole number), or unit. For example, "two and a fraction" means two units and that part of a unit which can be distinguished, as one-half, two-fifths, and so on. In the fraction ⅓ in arithmetic, or a/b in algebra, the figure 1, or a, is the numerator, and 3, or b, is the denominator; and they represent that, if a whole number is divided into three or b parts, only one or a parts are taken. In the addition of fractions, the fractions must be brought down to the same denominator, and their numerators (as expressed in the value of their new denominator) must then be added, when we have one whole fraction. Thus, if we want to add ⅓ and 2-5, we must find the least common multiple of 3 and 5, which is found to be 15; then, as 3 goes 5 times into 15, and 5 goes 3 times into the same number, we multiply the numerators of the different fractions by those respective quotients, and then add the two quantities together. Thus, ⅓ added to 2-5 will be 5 added to 6 fifteenths. The true definition of a fraction may be thus summed up: It is the division of its numerator by its denominator; as seven-eighths are equivalent to the whole number 7 divided by 8—whence a fraction is obtained. Decimal fractions simplify calculations greatly, as they are constructed on the principle of having one common denominator—a multiple of 10; and thus fractions can be added, subtracted, and divided without repeating over the tedious process of bringing down to a common denominator. See Arithmetic; Decimal Fraction.