Understanding Rates and Unit Rates

In math, a ratio compares two numbers. A rate is a special type of ratio that compares two quantities measured in different units.

For example, if you drive a car, you might measure your speed in "miles per hour." If you buy apples at the store, you might look at the "dollars per pound." Both of these are rates.

What is a Unit Rate?

A unit rate is a rate where the second quantity (the denominator) is exactly $1$. It tells you how much of something you get for just one unit of another thing.

Examples of unit rates include:

• $60$ miles per $1$ hour ($60$ mph)
• $2$ dollars per $1$ pound (\2$/lb)
• $15$ words per $1$ minute

How to Calculate a Unit Rate

To find a unit rate, write the rate as a fraction and divide both the top and bottom numbers by the bottom number.

Example: Find the unit rate if you travel $240$ miles in $4$ hours.

1. Write the rate as a fraction: $\frac{240 \text{ miles}}{4 \text{ hours}}$
2. Divide the numerator by the denominator to make the bottom number $1$: $240 \div 4 = 60$
3. The unit rate is: $\frac{60 \text{ miles}}{1 \text{ hour}} \text{ or } 60 \text{ miles per hour}$

Using Unit Rates to Find the Better Deal

Unit rates are incredibly useful for shopping. By calculating the "unit price" (the cost for just one item), you can easily compare deals.

Example: Which is the better deal: $6$ apples for \3.00$or$10$apples for$$4.50$?

• Deal 1: Find the cost of $1$ apple. $\frac{\$3.00}{6 \text{ apples}} = \$0.50 \text{ per apple}$

• Deal 2: Find the cost of $1$ apple. $\frac{\$4.50}{10 \text{ apples}} = \$0.45 \text{ per apple}$

Because \0.45$is less than$$0.50$, **$10$apples for$$4.50$ is the better deal**.

Using Unit Rates to Solve Problems

Once you know a unit rate, you can multiply it to find the answer for any amount.

Example: At a unit rate of $55$ miles per hour (mph), how far can you travel in $3.5$ hours?

Since you travel $55$ miles in $1$ hour, multiply $55$ by the number of hours: $55 \times 3.5 = 192.5$

You can travel $192.5$ miles in $3.5$ hours.