Jack lives 6(1/2) miles from the library. If he walks 1/3 of the way and takes a break, what is the remaining distance to the library?
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Detailed Explanation
\(\frac{\mathrm{1} }{\mathrm{3}}\) of \(6\frac{\mathrm{1} }{\mathrm{2}}\) miles is \(\frac{\mathrm{1} }{\mathrm{3}}\) × \(6\frac{\mathrm{1} }{\mathrm{2}}\) =\(\frac{\mathrm{1} }{\mathrm{3}}\) × \(\frac{\mathrm{13} }{\mathrm{2}}\)= \(\frac{\mathrm{13} }{\mathrm{6}}\) miles walked.
The remaining distance is \(6\frac{\mathrm{1} }{\mathrm{2}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{13} }{\mathrm{2}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{39} }{\mathrm{6}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{26} }{\mathrm{6}}\) = \(\frac{\mathrm{13} }{\mathrm{3}}\)= \(4\frac{\mathrm{1} }{\mathrm{3}}\) miles.
The remaining distance is \(6\frac{\mathrm{1} }{\mathrm{2}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{13} }{\mathrm{2}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{39} }{\mathrm{6}}\) - \(\frac{\mathrm{13} }{\mathrm{6}}\) = \(\frac{\mathrm{26} }{\mathrm{6}}\) = \(\frac{\mathrm{13} }{\mathrm{3}}\)= \(4\frac{\mathrm{1} }{\mathrm{3}}\) miles.
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