Example 1.2.23 Quarters and Dimes

Find the sum \(\frac{3}{4}+\frac{2}{10}\text{.}\) Does this seem intimidating? Consider this:

So if you know what to look for, the expression \(\frac{3}{4}+\frac{2}{10}\) is like adding \(75\) cents and \(20\) cents, which gives you \(95\) cents. As a fraction of one dollar, that is \(\frac{95}{100}\text{.}\) So we can report

\begin{equation*} \frac{3}{4}+\frac{2}{10}=\frac{95}{100}\text{.} \end{equation*}

(Although we should probably reduce that last fraction to \(\frac{19}{20}\text{.}\))