ABSTRACT
Among the four arithmetic operations, multiplication and division were difficult compared with addition and subtraction. People invented doubling and halving operations a long time ago. These and similar operations were convenient for their lives, and made multiplication and division easier. Consequently, the fractions 1/2, 1/4, 1/8, 1/16, and so on became commonly used numbers in addition to natural numbers. Furthermore, the use of reciprocals of integers, such as 1/2, 1/3, 1/4, 1/5, 1/6, and so on, also became common and of great importance. The reciprocal of each nonzero natural number is called a unit fraction. They noticed that multiplications of unit fractions by integers were also useful for calculations. In this way, fractions appeared in ancient civilizations [7].
