Unit Rate Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Unit Rate.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

A rate expressed as a quantity per single unit of another quantity, such as miles per hour or cost per item.

'60 miles per hour' tells you the distance in one hour—easy to compare.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: A unit rate rewrites a comparison so the second quantity equals a single unit.

Common stuck point: The procedure for unit rate is the easy part; the trap is dividing the smaller number by the larger to keep it 'simple'. Asking "Am I scaling the comparison so the bottom quantity is exactly one unit?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I scaling the comparison so the bottom quantity is exactly one unit?

Worked Examples

Example 1

easy
A car travels 240 miles using 8 gallons of gas. What is the unit rate in miles per gallon?

Answer

30 miles per gallon30 \text{ miles per gallon}

First step

1
A unit rate means the amount for exactly 1 gallon.

Full solution

  1. 2
    Set up the rate: 240 miles8 gallons\frac{240 \text{ miles}}{8 \text{ gallons}}.
  2. 3
    Divide: 240÷8=30240 \div 8 = 30.
A unit rate expresses a quantity per one unit of another. Divide the total quantity by the total number of units to find the rate per single unit.

Example 2

medium
A 12-pack of juice costs \$5.40. A 20-pack costs \$8.00. Which is the better deal?

Example 3

medium
A 5-pound bag of rice costs \$8.50. What is the price per pound?

Example 4

medium
An athlete burns 600 calories in 45 minutes. What is the burn rate in calories per minute?

Example 5

hard
If 4 workers paint 360 ft of fence in 6 hours, what is the unit rate per worker per hour?

Example 6

medium
A car travels 270 miles using 9 gallons. If gas costs \$3.60/gal, what is the cost per mile?

Example 7

medium
A 24-oz bottle of shampoo costs \$6.00. What is the cost per ounce, and how much would a 36-oz bottle cost at the same rate?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A runner completes 15 laps in 45 minutes. What is the unit rate in minutes per lap?

Example 2

medium
Brand A sells 12 oz of cereal for \$3.60. Brand B sells 18 oz for \$4.50. Which is the better deal?

Example 3

easy
A car travels 120 miles in 2 hours. What is its speed in miles per hour?

Example 4

easy
8 apples cost $4\$4. What is the cost per apple?

Example 5

easy
A printer prints 90 pages in 3 minutes. Find pages per minute.

Example 6

easy
A faucet fills 15 liters in 5 minutes. Find liters per minute.

Example 7

easy
A runner covers 400 meters in 50 seconds. Find meters per second.

Example 8

easy
12 identical pencils weigh 60 grams. Find the weight per pencil.

Example 9

easy
A store sells 3 notebooks for $6\$6. What is the price per notebook?

Example 10

easy
A heart beats 140 times in 2 minutes. Find beats per minute.

Example 11

medium
Brand A: 12 oz for $3.00\$3.00. Brand B: 20 oz for $4.40\$4.40. Which has the lower cost per ounce?

Example 12

medium
A car uses 6 gallons to travel 150 miles. Find the fuel efficiency in miles per gallon.

Example 13

medium
If 4 workers build a wall in the same time, and together they lay 96 bricks per hour, what is each worker's rate in bricks per hour?

Example 14

medium
A recipe needs 3 cups of flour for 24 cookies. How many cups are needed per cookie, and for 40 cookies?

Example 15

medium
A train travels at 75 miles per hour. How far does it go in 40 minutes?

Example 16

medium
Typing speed: 270 words in 6 minutes. At this rate, how many words in 10 minutes?

Example 17

medium
A 5-pound bag of rice costs $8\$8. A 2-pound bag costs $3.50\$3.50. Which is the better deal per pound?

Example 18

medium
A 12-ounce bottle of juice costs $1.80\$1.80. What is the cost per ounce in cents?

Example 19

medium
A factory makes 1,800 parts in an 8-hour shift. What is the production rate per hour?

Example 20

challenge
Pump A fills a tank at 12 liters per minute; Pump B at 8 liters per minute. Working together, how long to fill a 200-liter tank?

Example 21

challenge
Runner A: 100 m in 12 s. Runner B: 200 m in 25 s. Who is faster, and by how many m/s?

Example 22

challenge
A worker is paid $54\$54 for 4.5 hours. If the rate stays the same, how much for a 7-hour shift?

Example 23

easy
A bike rider travels 36 miles in 3 hours. What is the unit rate in miles per hour?

Example 24

easy
5 lemons cost \$2.50. What is the cost per lemon?

Example 25

easy
A garden hose fills a bucket of 8 liters in 4 minutes. What is the rate in liters per minute?

Example 26

medium
Brand X: 16 oz of yogurt for \$3.20. Brand Y: 24 oz for \$4.32. Which has the lower price per ounce?

Example 27

medium
A printer prints 240 pages in 8 minutes. How many pages does it print in 1 minute?

Example 28

medium
A train travels 350 km in 5 hours. At this rate, how far does it travel in 1 hour? In 9 hours?

Example 29

medium
A baker uses 9 cups of flour for 36 cookies. How many cups per cookie?

Example 30

easy
A factory produces 600 widgets in 5 hours. How many widgets per hour?

Example 31

hard
A 6-pack of soda costs \$3.00. A 12-pack costs \$5.40. Which is the better deal per can?

Example 32

medium
A juice carton holds 64 oz and serves 8 people. How many ounces per person?

Example 33

easy
A backpack costs \$24 and weighs 3 lb empty. What is the cost per pound of empty backpack?

Example 34

medium
A printer uses 20 ml of ink for 100 pages. What is the rate in ml per page?

Example 35

easy
A bird flaps its wings 240 times in 2 minutes. Find flaps per minute.

Example 36

medium
It takes 5 hours to fly 2000 miles. What's the unit rate in miles per hour, and how long to fly 3200 miles at the same rate?

Example 37

easy
A class of 25 students raised \$200. What is the average amount per student?

Example 38

medium
A pump moves 480 gallons in 12 minutes. How long to pump 1 gallon?

Example 39

hard
Sam earns \$54 for 6 hours of work. Maya earns \$72 for 9 hours. Who has the higher hourly rate?

Example 40

challenge
A bakery uses 10 lbs of flour for 80 muffins and 15 lbs for 100 cookies. Which uses more flour per item?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

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