5.6 Ratios and rate  (Page 3/10)

Write a rate as a fraction

Frequently we want to compare two different types of measurements, such as miles to gallons. To make this comparison, we use a rate    . Examples of rates are $120$ miles in $2$ hours, $160$ words in $4$ minutes, and $\text{\$5}$ dollars per $64$ ounces.

When writing a fraction as a rate, we put the first given amount with its units in the numerator and the second amount with its units in the denominator. When rates are simplified, the units remain in the numerator and denominator.

Find unit rates

In the last example, we calculated that Bob was driving at a rate of $\frac{\text{175 miles}}{\text{3 hours}}.$ This tells us that every three hours, Bob will travel $175$ miles. This is correct, but not very useful. We usually want the rate to reflect the number of miles in one hour. A rate that has a denominator of $1$ unit is referred to as a unit rate    .

Unit rates are very common in our lives. For example, when we say that we are driving at a speed of $68$ miles per hour we mean that we travel $68$ miles in $1$ hour. We would write this rate as $68$ miles/hour (read $68$ miles per hour). The common abbreviation for this is $68$ mph. Note that when no number is written before a unit, it is assumed to be $1.$

So $68$ miles/hour really means $\text{68 miles/1 hour.}$

Two rates we often use when driving can be written in different forms, as shown:

Another example of unit rate that you may already know about is hourly pay rate. It is usually expressed as the amount of money earned for one hour of work. For example, if you are paid $\text{\$12.50}$ for each hour you work, you could write that your hourly (unit) pay rate is $\text{\$12.50/hour}$ (read $\text{\$12.50}$ per hour.)

To convert a rate to a unit rate, we divide the numerator by the denominator. This gives us a denominator of $1.$