Rates

A ratio is considered a rate when it compares two \((2)\) different units, for example, miles per hour and cost per ounce.

A rate is a special type of ratio that’s used to describe the relationship between two different measurement units, for example, speed, wages, and prices.

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A car may be described like traveling, say, \(60\:\frac{miles}{hour}\) (per hour); a landscaper may earn \(\$35\) per mowed lawn, and gas might be sold at \(\frac{\$3}{gallon}\) (per gallon).

So rates are ratios that compare two \((2)\) different quantities which include different measurement units.

Rates are comparisons that provide information like, for example, feet per second, dollars per quart, dollars per hour, or miles per hour.

The word ‘per’ is generally indicating that we’re dealing with rates. A rate may be written by using words, or by using colons, and also as fractions. You should be aware of which type of quantities we compare when dealing with rates.

As an example: a business is looking to rent six \((6)\) autobuses for the transportation of \(300\) individuals during a company excursion.

The rate for describing that relationship may be written while using a colon, by using words, or by using a fraction. With rates, you need to include the respective units at all times!

So \(six \,(6)\, autobuses\, for\, 300\, individuals\).

Or: \(six \,(6)\, autobuses:\, 300 \,individuals\).

Or: \(six\, (6)\, \frac{autobuses}{300}\, individuals\).

 

Just as with a ratio, the rate may be also expressed in its simplest form. Just simplify the fraction (division by \(6\)):

\(\frac{6\, autobuses \,\div\,6}{300\,people\,\div\,6} = \frac{1\,autobus}{50\,people}\)

 

The fraction is indicating that our rate of ‘autobuses to individuals’ is \(6\) to \(300\). Or stated more simply, one \((1)\) autobus per (or: for) every \(50\) individuals.

Last Updated on August 10, 2024.