Unit Rate Formula

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

The Formula

unit rate=total quantitynumber of units\text{unit rate} = \frac{\text{total quantity}}{\text{number of units}}

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

Quick Example

\$15 for 3 pounds gives \$5 per pound (unit rate). 240 miles in 4 hours gives 60 mph.

Notation

Written as 'per' with a slash or fraction: 6060 mph =60 miles1 hour= \frac{60 \text{ miles}}{1 \text{ hour}}

What This Formula Means

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.

Formal View

r=Qn where Q is total quantity and n is the number of units, giving rate per 1 unitr = \frac{Q}{n} \text{ where } Q \text{ is total quantity and } n \text{ is the number of units, giving rate per 1 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?

Common Mistakes

  • Dividing the smaller number by the larger to keep it 'simple' - divide so the chosen unit lands on 11 (totalunits\frac{\text{total}}{\text{units}}).
  • Comparing two deals by total price instead of per-one - reduce each to cost per one item first.
  • Dropping the unit label - 2020 alone is meaningless; it must be 2020 miles per hour or $20 per ticket.

Why This Formula Matters

Unit rates are how a third-grader decides which package is the better buy and the seed of slope and constant speed later; without reducing to per-one, students compare $3 for 44 against $5 for 77 and pick wrong. Recognizing it by "Am I scaling the comparison so the bottom quantity is exactly one unit?" — rather than by familiar numbers — is what lets a student tell it apart from ratio and total / whole amount and ratio that isn't yet a unit rate in a mixed problem set.

Frequently Asked Questions

What is the Unit Rate formula?

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

How do you use the Unit Rate formula?

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

What do the symbols mean in the Unit Rate formula?

Written as 'per' with a slash or fraction: 6060 mph =60 miles1 hour= \frac{60 \text{ miles}}{1 \text{ hour}}

Why is the Unit Rate formula important in Math?

Unit rates are how a third-grader decides which package is the better buy and the seed of slope and constant speed later; without reducing to per-one, students compare $3 for 44 against $5 for 77 and pick wrong. Recognizing it by "Am I scaling the comparison so the bottom quantity is exactly one unit?" — rather than by familiar numbers — is what lets a student tell it apart from ratio and total / whole amount and ratio that isn't yet a unit rate in a mixed problem set.

What do students get wrong about Unit Rate?

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.

What should I learn before the Unit Rate formula?

Before studying the Unit Rate formula, you should understand: division, ratios.

← Back to Unit Rate See All Examples Practice Problems