###### Example1.2.21Quarters and Dimes

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

• $$\frac{1}{4}$$ of a dollar is a quarter, and so $$\frac{3}{4}$$ of a dollar is $$75$$ cents.

• $$\frac{1}{10}$$ of a dollar is a dime, and so $$\frac{2}{10}$$ of a dollar is $$20$$ cents.

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 $$\frac{19}{20}\text{.}$$)

in-context