Fractions

5; 241; 74 are whole numbers or integers. ; ; 0.5; 0.102 are fractions. A fraction (from the Latin fractus, broken) is a number that represents part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or vulgar fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. An example is , in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.

A still later development was the fraction, now called simply a decimal, in which the denominator is a power of ten, determined by the number of digits to the right of a decimal separator, the appearance of which (e.g., a period, a raised period (•), a comma) depends on the locale). Thus for 0.75 the numerator is 75 and the denominator is 10 to the second power, i.e. 100, because there are two digits to the right of the decimal point. If 100 is divided by 3, the quotient is 33.33. In spoken English it is, ‘Thirty- three point three, three recurring’. If 100 is divided by 3, and the quotient is written 33.333, it is correct to three significant figures. If the quotient is written 33.33 it is correct to two significant figures.

A third kind of fraction still in common use is the percentage, in which the denominator is always 100. Thus 75% (read as “seventy five percent”) means .

Other uses of fractions are to represent ratios, and to represent division. Thus the fraction is also used to represent the ratio 3:4 (three to four) and the division 3 ÷ 4 (three divided by four).

In mathematics, the set of all common (vulgar) fractions is called the set of rational numbers, and is represented by the symbol Q.