A rate is a ratio that compares two different kinds of things, like miles and hours. A unit rate tells how much for one: miles for one hour, dollars for one pound. Unit rates are equivalent ratios whose second number is 1.
Key idea
To find a unit rate, divide. The quantity you are counting goes on top, and the "per" thing goes underneath: $\frac{120 \text{ miles}}{3 \text{ hours}} = 40$ miles per hour.
Why it works
To get from 3 hours down to 1 hour, divide by 3. To keep the ratio the same, divide the miles by 3 as well: $120 : 3 = 40 : 1$. Writing it as a fraction says the same thing, because a fraction is a division: $\frac{120}{3} = 120 \div 3 = 40$.
Worked example: A price per item
4 notebooks cost \$7. What is the price of one notebook?
- Price per notebook means dollars for 1 notebook: dollars ÷ notebooks.
- $7 \div 4 = 1.75$.
Answer: \$1.75 per notebook.
Worked example: Two unit rates from one ratio
A printer prints 90 pages in 6 minutes. Find pages per minute and minutes per page.
- Pages per minute: $90 \div 6 = 15$.
- Minutes per page: $6 \div 90 = \frac{1}{15}$ of a minute (4 seconds).
- The two rates are reciprocals: $15 \times \frac{1}{15} = 1$.
Answer: 15 pages per minute, or $\frac{1}{15}$ minute per page.
Common mistake
Dividing in the wrong order gives the other unit rate. For 120 miles in 3 hours, $3 \div 120 = \frac{1}{40}$ is hours per mile, not miles per hour. Quick check: say the units out loud. The word after "per" is the one you divide by. Then ask if the size makes sense: a car covers many miles in an hour, so miles per hour should be a big number.