math 156
posted by Karen on .
Post your response to the following: How are the concepts of the Greatest Common Factors (GCF), divisibility, and Lowest Common Multiple (LCM) used when computing fractions? Provide an example and demonstrate how the concepts are used.

Example of application to fractions:
5/6+ 7/15
= 25/30 + 14/30 ..... (1)
= 39/30
= 13/10 .... (2)
= 1 3/10
(1) LCM of denominators 6 and 15 is 30
(2) To simplify a fraction to simplest terms, both numberator and denominator are divided by the GCF.
In order to find the GCF or the LCM, divisibility is needed to factorize the numbers.
However, divisibility is not required to find LCM or GCF if the extended Euclidean algorithm is used.
http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm