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spndsh
if (x/y) =(3/4) and (x/z)=(1/8), then (y/z)=?
\[\left(\frac{x}{z} \div \frac{x}{y}\right) =\left(\frac{x}{z} \dot\ \frac{y}{x}\right) = \frac{y}{z} \] \[\left(\frac{1}{8} \div \frac{3}{4}\right) =\left(\frac{1}{8} \dot\ \frac{4}{3}\right) = \frac{4}{24} \] or, when simplified \[\frac{1}{6}\]
To check perform the following steps to get back to x/y: \[\left(\frac{x}{z} \div \frac{y}{z}\right) = \left(\frac{x}{z} \dot\ \frac{z}{y}\right) =\frac{x}{y}\] \[\left(\frac{1}{8} \div \frac{1}{6}\right) = \left(\frac{1}{8} \dot\ \frac{6}{1}\right) =\frac{6}{8}\] or \[\frac{3}{4}\] when simplified