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Convert rates with compatible units

A rate can be expressed in different but compatible units by multiplying or dividing by an equivalent conversion factor, while preserving the relationship between the two quantities—for example, converting miles per hour to feet per hour or miles per minute. The conversion applies appropriately to the numerator, denominator, or both, with units tracked to verify the result; this builds fluency with equivalent rates, unit rates, measurement, and proportional reasoning without extending to incompatible or compound-unit conversions.

Detailed Explanation: Convert rates with compatible units

A rate can be written in different compatible units without changing the relationship it describes. To convert a rate, multiply by a conversion factor equal to 11, and make sure the unwanted units cancel.

Example: Convert 33 miles per hour to feet per hour.

  1. Start with the rate:

3mileshour3\frac{\text{miles}}{\text{hour}}

  1. Use the fact that 11 mile (=5,280)(=5{,}280) feet. Write the conversion factor so that miles cancel:

3mileshour×5,280 feet1 mile3\frac{\text{miles}}{\text{hour}}\times\frac{5{,}280\text{ feet}}{1\text{ mile}}

  1. Cancel the miles:

3×5,280feethour3\times 5{,}280\frac{\text{feet}}{\text{hour}}

  1. Multiply:

16,840feethour16{,}840\frac{\text{feet}}{\text{hour}}

So,

3 miles per hour=16,840 feet per hour\boxed{3\text{ miles per hour}=16{,}840\text{ feet per hour}}

The time unit stayed the same, so only the distance unit needed to be converted.

Learn by doing: Convert rates with compatible units

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