# Unit Rates

A rate is a ratio that compares quantities in different units. Rates are commonly found in everyday life. The prices in grocery stores and department stores are rates. Rates are also used in pricing gasoline, tickets to a movie or sporting event, in paying hourly wages and monthly fees.

A unit rate is a rate where the second quantity is one unit , such as $34$ per pound, $25$ miles per hour, $15$ Indian Rupees per Brazilian Real, etc.

$\begin{array}{|l|}\hline 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{minute}=60\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{seconds}\hfill \\ 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hour}=60\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{minutes}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{or}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}3600\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{seconds}\hfill \\ 1\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{day}=24\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{hours}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(\text{or}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}1440\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{minutes}\hfill \\ \hline\end{array}$

Example 1:

A motorcycle travels $230$ miles on $4$ gallons of gasoline. Find the average mileage per gallon.

For this problem, simply divide $230$ by $4$ .

$\frac{230\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{miles}}{4\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{gallons}}=57.5\frac{\text{miles}}{\text{gallon}}$

The motorcycle gets $57.5$ miles per gallon.

Example 2:

A copy machine makes $45$ copies in $25$ second. Find the unit rate of copies per second.

Divide $45$ by $25$ to find the unit rate.

$\begin{array}{l}\frac{45}{25}=\frac{\overline{)5}\cdot 9}{\overline{)5}\cdot 5}\\ =1.8\end{array}$

The copy machine makes $1.8$ copies per second.