Writing 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.

Definition: Rate

A rate compares two quantities of different units. A rate is usually written as a fraction.

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.

Example

Bob drove his car $525$ miles in $9$ hours. Write this rate as a fraction.

Solution

	$\text{525 miles in 9 hours}$
Write as a fraction, with 525 miles in the numerator and 9 hours in the denominator.	$\frac{\text{525 miles}}{\text{9 hours}}$
	$\frac{\text{175 miles}}{\text{3 hours}}$

So $525$ miles in $9$ hours is equivalent to $\frac{\text{175 miles}}{\text{3 hours}}.$

Optional Video: Rates and Unit Rates

This lesson is part of:

Introducing Decimals

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	\(\text{525 miles in 9 hours}\)
Write as a fraction, with 525 miles in the numerator and 9 hours in the denominator.	\(\frac{\text{525 miles}}{\text{9 hours}}\)
	\(\frac{\text{175 miles}}{\text{3 hours}}\)