A unit rate is a comparison of two different quantities when they are combined together. Specifically, it expresses how many units of one quantity there are per one unit of another quantity. It's commonly used in various contexts like speed, price, and efficiency.

How to Calculate a Unit Rate

To find the unit rate, divide one quantity by the other and express it as a rate per 1 unit of the second quantity.

The formula for unit rate is:

$\text{Unit Rate} = \frac{\text{Quantity 1}}{\text{Quantity 2}}$

Example 1: Speed

If a car travels 120 miles in 3 hours, the unit rate would be: $\text{Unit Rate (speed)} = \frac{120 \text{ miles}}{3 \text{ hours}} = 40 \text{ miles per hour (mph)}$

Example 2: Price

If 5 apples cost $3, the unit rate is: $\text{Unit Rate (price)} = \frac{3 \text{ dollars}}{5 \text{ apples}} = 0.60 \text{ dollars per apple}$

Common Contexts for Unit Rates

1. Speed/Velocity: Miles per hour (mph) or kilometers per hour (km/h).
2. Price: Dollars per item, like $/pound or $/liter.
3. Fuel Efficiency: Miles per gallon (mpg).
4. Density: People per square mile or kilograms per cubic meter.

Let me know if you want to go over a specific unit rate example or if you have any other questions!

Related Questions:

1. How do unit rates relate to proportional relationships?
2. How can you convert between different units (e.g., mph to km/h)?
3. What’s the difference between a rate and a unit rate?
4. How do unit rates apply to real-world situations (like shopping or travel)?
5. How can unit rates help in comparing different options, like products or services?

Tip: Always ensure the second quantity is expressed as "per 1 unit" to identify the unit rate correctly.