A fraction from the Latin fractus, is a number that can represent part of a whole.

The earliest fractions were reciprocals of integers, symbols representing one half, one third, one quarter, and so on. A much later development were the common or “vulgar” fractions which are still used today, and which consist of a numerator and a denominator. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 parts, and the denominator, 4, tells us that 4 parts make up a whole.

A still later development was the decimal fraction, now usually called simply a “decimal”, in which the denominator is a power of ten, determined by the number of digits to the right of a the decimal point. Thus in 0.75 the numerator is 75 and the denominator is 10 to the second power because there are two digits to the right of the decimal and thus the denominator is 100.

Music Notation

Other uses for fractions are to represent ratios, to represent division, and in musical scores.

Thus the fraction 3/4 is also used to represent the ratio 3:4 (three to four) and the division 3 ÷ 4 (three divided by four). In a musical score, a fraction is used to give the time signature. A time signature of 3/4 means that there are 3 beats to a measure, and a quarter note is one beat.

Ancient Egyptians

The ancient Egyptians only used fractions. They were able to write any fraction as a sum of unit fractions where all the unit fractions were different. It is much easier to compare fractions using Egyptian fractions than it is by using our present-day notation for fractions.