The Multiplication and Division of Simple Continued Fractions

Abstract

The finite =  and infinite  simple continued fractions for (rational and irrational) are considered. The multiplication of two simple continued fractions  and  for (m = n, m ¹ n) are discovered. Also, the multiplicative inverse and the division of the simple continued fractions are showed. The most important that we will do in this paper, we exploring how the simple continued fractions can be used to calculate the numbers ,  and . Many definitions and examples that we used of these low are presented.