FRACTION, a part of any integer (whole number), or unit. •For example, 'two and a means two units and that part of a unit which can be distinguished, as one-half, two-fifths and so on. In the fraction Y3 in a arithmetic, or — in algebra, the figure 1, or b a, is the numerator, and 3, or b, is the de nominator; and they represent that, if a whole number is divided into three or b parts, only 1 or a part is 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 de nominator) must then be added, when we have one whole fraction. Thus, if we want to add and %, we must find the least common mul tiple 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 these respective quotients and then add the two 'quantities together. Thus, Y3 added to % will 5 6 11 be equal to 15 15' The true definition of a fraction may be thus summed up: It is the division of its numerator by its denomina tor; as seven-eighths are equivalent to the whole number 7 divided by 8— whence a frac tion is obtained. Decimal fractions simplify
calculations greatly, as they are constructed on the principle of having one common denotnina tor — a multiple of 10; and thus fractions can be added, subtracted and divided without re peating over and over the tedious process of bringing them down to a common denominator.
The familiar form of numeral fraction is termed a °vulgar° fraction and where the erator is smaller than the denominator, as in 54, it is a proper fraction, but if the numerator is the larger, as 4it is an improper fraction.
Fractions of fractions are termed compound fractions and where either numerator or de nominator is itself a fraction, it is a complex fraction. For decimal fractions, see DECIMALS. See also ARITHMETIC.