Unit Rates | Open Textbooks

What is a Unit Rate?

A Unit Rate Compares to ONE

A unit rate tells you how much of something you get for every 1 of something else.

You've probably seen unit rates everywhere without even realizing it! When you see a price tag that says "$2.50 per pound" or a speed limit sign showing "55 miles per hour," those are unit rates.

How to Find a Unit Rate

Unit Rate = Total Amount ÷ Number of Units

Divide to get the amount "per 1" or "per unit"

Rate vs. Unit Rate

$12

for 4 pounds

→

$3

per 1 pound

The rate is "$12 for 4 pounds." The unit rate is "$3 per pound" because we divided to find the cost for just 1 pound.

Key Things to Know About Unit Rates

The word "per" means "for each one" - miles per hour, dollars per item, etc.
Unit rates make comparing easy - which is cheaper: $8 for 4 or $15 for 6?
Always divide by the second quantity - to find "per pound," divide by the number of pounds
Include the units! - "$3" is incomplete; "$3 per pound" is a unit rate

Common Unit Rates in Daily Life

🚗

Speed

60 mph

Miles per hour

💵

Price

$3.49/lb

Dollars per pound

💧

Flow

5 gal/min

Gallons per minute

❤️

Heart Rate

72 bpm

Beats per minute

Using Unit Rates to Compare

Unit rates are powerful because they let you compare different quantities fairly. Let's see an example:

🏪 Store A

6 bottles of water for $4.50

$4.50 ÷ 6 = $0.75 per bottle

🏪 Store B

8 bottles of water for $5.60

$5.60 ÷ 8 = $0.70 per bottle

Store B is cheaper at $0.70 per bottle vs. $0.75 per bottle!

Pro Tip: When comparing unit rates, make sure you're comparing the same units. "Miles per hour" and "feet per second" can't be directly compared without converting first!

Worked Examples

Let's work through several unit rate problems step by step.

Example 1: Finding a Unit Price

A 12-pack of juice boxes costs $6.00. What is the cost per juice box?

1

Identify what you're finding:
Cost "per" juice box means cost for 1 juice box.

2

Set up the division:
Divide total cost by number of juice boxes.

$6.00 ÷ 12 boxes = ?

3

Calculate:

$6.00 ÷ 12 = $0.50

Unit Rate: $0.50 per juice box (or 50 cents each)

Example 2: Finding Speed

A car travels 240 miles in 4 hours. What is the car's speed in miles per hour?

1

Identify what you're finding:
Speed is distance "per" time (miles per hour).

2

Set up the division:
Divide distance by time.

240 miles ÷ 4 hours = ?

3

Calculate:

240 ÷ 4 = 60

Speed: 60 miles per hour (60 mph)

Example 3: Comparing Unit Rates

Brand A cereal: 15 oz for $4.50
Brand B cereal: 20 oz for $5.40
Which brand is the better buy?

1

Find Unit Rate for Brand A:

$4.50 ÷ 15 oz = $0.30 per oz

2

Find Unit Rate for Brand B:

$5.40 ÷ 20 oz = $0.27 per oz

3

Compare:
$0.27/oz < $0.30/oz
Lower price per ounce = better deal!

Brand B is the better buy at $0.27 per ounce vs. $0.30 per ounce.

Example 4: Using Unit Rate to Find Total

Apples cost $1.25 per pound. How much do 8 pounds cost?

1

We already have the unit rate:
$1.25 per pound

2

Multiply to find total:

$1.25 × 8 pounds = ?

3

Calculate:

$1.25 × 8 = $10.00

8 pounds of apples cost $10.00

Practice Problems

Try these problems on your own!

Problem 1: Unit Price

A 5-pound bag of potatoes costs $3.75. What is the cost per pound?

Problem 2: Speed

A runner completes a 10-mile race in 2 hours. What is the runner's speed in miles per hour?

Problem 3: Better Deal

Which is the better deal?
Option A: 3 notebooks for $5.25
Option B: 5 notebooks for $8.00

Problem 4: Finding Total

Gas costs $3.50 per gallon. How much does 12 gallons cost?

Check Your Understanding: Unit Rate Challenge

Test your unit rate skills with this 6-question challenge!

Unit Rate Challenge

Score: 0 / 6

Question 1 of 6

Challenge Complete!

0/6

Next Steps

Key Takeaways:

A unit rate tells you the amount "per 1" (per unit)
Find a unit rate by dividing the total by the number of units
Unit rates make it easy to compare different quantities
Common unit rates include price per item, miles per hour, and cost per pound

Look for unit rates when shopping - compare prices per ounce or per item
Practice calculating speeds when you travel
Move on to the next unit to explore integers!