Practice Solutions

1. It took Angie $\frac{1}{5}$ of an hour to walk $\frac{1}{2}$ miles. What is her speed in miles per hour?

$\frac{{\displaystyle \frac{1}{2} \mathrm{mi}}}{{\displaystyle \frac{1}{5} \mathrm{hr}}}=\frac{1}{2}÷\frac{1}{5}=\frac{1}{2}·\frac{5}{1}=\frac{5}{2} \raisebox{1ex}{$\mathrm{mi}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

$2.5 \raisebox{1ex}{$\mathrm{mi}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

Angie can walk 2.5 miles per hour.

2. A dozen eggs cost $3.79. What is the price per egg?

$\frac{\$3.79}{12 \mathrm{eggs}}=\raisebox{1ex}{$\$0.32$}\!\left/ \!\raisebox{-1ex}{$\mathrm{egg}$}\right.$

$\raisebox{1ex}{$\$0.32$}\!\left/ \!\raisebox{-1ex}{$\mathrm{egg}$}\right.$

The cost is $0.32 per egg.

3. A factory machine seals 450 bottles every 6 minutes. How many bottles are sealed each minute?

$\frac{450 \mathrm{bottles}}{6 \min }=75 \raisebox{1ex}{$\mathrm{bottles}$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$

$75 \raisebox{1ex}{$\mathrm{bottles}$}\!\left/ \!\raisebox{-1ex}{$\min $}\right.$

The factory seals 75 bottles per minute.

4. Ida painted $\frac{5}{6}$ of a wall  in $\frac{2}{3}$ of an hour. How many walls can Ida paint per hour?

$\frac{{\displaystyle \frac{5}{6}} \mathrm{walls}}{{\displaystyle \frac{2}{3}} \mathrm{hr}}=\frac{5}{6}÷\frac{2}{3}=\frac{5}{6}·\frac{3}{2}=\frac{15}{12}=\frac{5}{4}\raisebox{1ex}{$\mathrm{walls}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

$1.25 \raisebox{1ex}{$\mathrm{walls}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.$

Ida paints 1.25 walls per hour.

5. A car uses 8 gallons to travel 248 miles. What is the mileage of the car? Note: a car’s mileage is the miles it travels per gallon.

$\frac{248 \mathrm{mi}}{8 \mathrm{gal}}=31 \raisebox{1ex}{$\mathrm{mi}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{gal}$}\right.$

$31 \raisebox{1ex}{$\mathrm{mi}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{gal}$}\right.$

The car has a mileage of 31 miles per gallon.

6. 171 grams of a certain liquid has a volume of 18 milliliters. What is the density of this liquid? Note: density is the mass (grams) per volume (mL).

$\frac{171 \mathrm{grams}}{18 \mathrm{mL}}=9.5 \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mL}$}\right.$

$9.5 \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mL}$}\right.$

This liquid has a density of 9.5 grams per milliliter.

10. A liquid has a density of $8.4 \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mL}$}\right.$. Determine the mass of the liquid when the volume is $15 \mathrm{mL}$.

$\frac{8.4 \mathrm{g}}{1 \cancel{\mathrm{mL}}}·15 \cancel{\mathrm{mL} }=126 \mathrm{g}$

The mass is $126 \mathrm{g}$.

11. A car can drive 38.2 miles per gallon of gas. If the car drove 452 miles, determine how many gallons of gas were used and round your answer to the nearest gallon.

$\frac{452 \mathrm{mi}}{38.2 {\displaystyle \raisebox{1ex}{$\mathrm{mi}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{gal}$}\right.}}=452 \mathrm{mi} ·\frac{1 \mathrm{gal}}{38.2 \mathrm{mi}}=11.83 \mathrm{gal}$

The car used 12 gallons of gas to travel 452 miles.

12. Tyler walked for 1.5 hours at a rate of 2.8 miles per hour. Determine the distance walked.

$\frac{2.8 \mathrm{mi}}{1\cancel{ \mathrm{hr}}}·1.5 \cancel{\mathrm{hr}} =4.2 \mathrm{mi}$

Tyler walked 4.2 miles. 

13. A machine produces 140 parts per hour. Determine the time in hours to produce 520 parts.

$\frac{520 \mathrm{parts}}{140 {\displaystyle \raisebox{1ex}{$\mathrm{parts}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{hr}$}\right.}}=520 \cancel{\mathrm{parts}} ·\frac{1 \mathrm{hr}}{140 \cancel{\mathrm{parts}}}=3.71 \mathrm{hrs}$

It would take 3.71 hours to produce 520 parts.

14. Home Builders Inc. is able to build 3.2 homes per acre. Determine the number of homes Home Builders Inc. can build in 640 acres.

$\frac{3.2 \mathrm{homes}}{\cancel{\mathrm{acre}}}·640 \cancel{\mathrm{acres}}=2048 \mathrm{homes}$

Home Builders Inc. can build $2048$ homes in 640 acres.