Rates and Unit Rates: Practice

"Pages per minute" means pages for a single minute, so divide the pages by the minutes.

$36 \div 4 = 9$

The printer prints $9$ pages per minute.

"Dollars per pound" means dollars for a single pound, so divide the dollars by the pounds.

$10 \div 5 = 2$

The rice costs $2$ dollars per pound.

"Eggs per cake" means eggs for a single cake, so divide the eggs by the cakes.

$12 \div 6 = 2$

The recipe uses $2$ eggs per cake.

The word "per" means "for each" and marks the quantity in the denominator.

$\text{miles } \textbf{per} \text{ hour} = \frac{\text{miles}}{\text{hour}}$

So "per" points to the denominator quantity.

"Dollars per hour" means dollars for a single hour, so divide the dollars by the hours.

$90 \div 6 = 15$

The worker earns $15$ dollars per hour.

"Buckets per minute" means buckets for a single minute, so divide the buckets by the minutes.

$20 \div 5 = 4$

The hose fills $4$ buckets per minute.

The bar is read as "per," and the top quantity is named first.

$\frac{8 \text{ apples}}{2 \text{ dollars}} = 8 \text{ apples per } 2 \text{ dollars}$

So it reads "$8$ apples per $2$ dollars."

Speed in miles per hour is miles for a single hour, so divide the miles by the hours.

$300 \div 5 = 60$

The train's speed is $60$ miles per hour.

A unit rate is the amount for a single unit, so its denominator is $1$.

$\frac{60 \text{ miles}}{1 \text{ hour}} = 60 \text{ miles per hour}$

The denominator of a unit rate is $1$.

A unit rate has a count of $1$ for the second quantity. "$30$ miles per hour" means per one hour, while the others compare against $3$ hours, $2$ pounds, or $5$ minutes.

$\frac{30 \text{ miles}}{1 \text{ hour}}$

So "$30$ miles per hour" is the unit rate.

"Laps per hour" means laps for a single hour, so divide the laps by the hours.

$32 \div 4 = 8$

The swimmer does $8$ laps per hour.

"Dollars per notebook" means dollars for a single notebook, so divide the dollars by the notebooks.

$8 \div 4 = 2$

Each notebook costs $2$ dollars.