Can a complex fraction become a simple fraction?
Yes, it can! The goal of simplifying complex fractions is to rearrange them into equivalent simple fractions which are in simplest form. And can a simple fraction be simplified? You should already know it can. The goal of simplifying a simple fraction is to obtain an equivalent fraction that looks simpler (i.e. it has less terms in its numerator and denominator). Sometimes the numerator and denominator of a complex fraction are just single simple fractions themselves. Then, for the first step in simplifying the complex fraction, we just use the wellknown invert and multiply rule: multiply the fraction in the numerator by the reciprocal of the fraction in the denominator: You see that the initial complex fraction on the left has been turned into a single simple fraction on the right. This step is justified only if the numerator and denominator of the original complex fraction are both single simple fractions. When the pattern in the box above is valid, all that is left to do in simplify
