# Percents and Fractions

The word percent means “hundredths” or “divided by $100$ .”  The symbol $%$ is used to represent percent.

$39%$ means $39$ divided by $100$ or $\left(\frac{39}{100}\right)$

This shows how to convert a percent to a fraction . Sometimes you may need to reduce the resulting fraction to lowest terms.

$\begin{array}{l}5%=\frac{5}{100}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{1\cdot 5}{20\cdot 5}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{1}{20}\end{array}$

If the percent is not a whole number, you may need to use a denominator greater than $100$ .

For example, if you have a percent written as a mixed number like $4\frac{1}{2}%$ , you can convert to a decimal first. Then, since you have one decimal place, use a denominator of $1000$ instead of $100$ .

$\begin{array}{l}4\frac{1}{2}%=4.5%\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{45}{1000}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{9\cdot 5}{200\cdot 5}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{9}{200}\end{array}$

Example 1:

Write $\frac{1}{3}%$ as a fraction in lowest terms.

This may seem confusing, since $\frac{1}{3}%$ already looks like a fraction. But remember that $%$ means "divided by $100$ ", just as always:

$\begin{array}{l}\frac{1}{3}%=\frac{\left(\frac{1}{3}\right)}{100}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\frac{1}{300}\end{array}$