Ratios, Rates, and Unit Rates

A ratio is a comparison of two quantities that shows the relative size of one quantity to another, often expressed as 'a:b'.

A rate is a specific kind of ratio that compares two different units, such as speed (miles per hour) or price (dollars per item).

A unit rate is a rate in which the second quantity is one unit. For example, if a car travels 60 miles in 1 hour, the unit rate is 60 miles per hour.

To calculate a unit rate, divide the first quantity by the second quantity. For example, if you have 15 hotdogs in 3 minutes, the unit rate is $$\frac{15 \text{ hotdogs}}{3 \text{ minutes}} = 5 \text{ hotdogs per minute}$$ .

The ratio of circles to squares is 5:3.

The price per gallon is $$\frac{46.80}{13} = 3.60$$ .

John's unit rate is 5 hotdogs per minute.

The unit cost per pizza is $$\frac{97.50}{15} = 6.50$$ .

You will travel 240 miles.

The formula for calculating a unit rate is: Unit Rate = Total Quantity / Number of Units.