Unit Rate
In short: A unit rate is the amount of one quantity for exactly 1 unit of another, found by dividing, as in 48 miles in 6 hours giving 8 miles per hour.
6th GradeRatios and Percents6.RP.A.2
What is Unit Rate?
A unit rate boils a comparison down to a single step: how much for one. Saying a hiker covers 2.5 miles for every 1 hour is easier to use than saying 15 miles in 6 hours.
Precisely, if a quantity \(a\) goes with \(b\) units of another quantity and \(b \neq 0\), the unit rate is \(\frac{a}{b}\) per 1 unit. The denominator of the simplified comparison is always 1.
How to spot it
- A question asks “how much for one”, “per minute”, “each” or “per person”.
- Two offers or two speeds must be compared fairly, and their totals cover different amounts.
- A table or graph shows a total for several units, and you need the amount at 1.
- A word problem lists a total cost, distance or work and the number of items or hours.
The method
- Write the comparison as a fraction with the quantity you want per unit on top.
- Divide the top number by the bottom number to get the amount for 1.
- Attach the unit phrase, such as miles per hour or dollars per ounce.
- Multiply the unit rate by any new amount to find a new total, or compare two unit rates directly.
Unit Rate: solved example
Problem
A 12-pack of sparkling water costs $7.20 and a 20-pack costs $11.80. Which pack has the lower price per bottle?
Solution
First pack: \(7.20 \div 12 = 0.60\), so \$0.60 per bottle.
Second pack: \(11.80 \div 20 = 0.59\), so \$0.59 per bottle. The 20-pack costs a cent less for each bottle.
Try it
Question 1
A printer outputs 266 pages in 14 minutes. Find the pages per minute.
Show the answer
\(266 \div 14 = 19\), so the printer outputs 19 pages per minute.
Question 2
A recipe uses \(\frac{3}{4}\) cup of oil for 6 muffins. How much oil goes into one muffin?
Show the answer
\(\frac{3}{4} \div 6 = \frac{3}{24} = \frac{1}{8}\), so each muffin uses \(\frac{1}{8}\) cup.
Unit Rate vs. Unit Price
A unit rate is the general idea of an amount per one unit, and it can be about speed, work, water use or money. A unit price is the special case where the amount is a cost, so it always reads dollars (or cents) per item, ounce or pound.
Keep going
Lessons
Worksheets and quizzes
- Unit Rates and Rate Language – Worksheet
- Unit Rates and Rate Language – Quiz
- Unit Rates with Fractions – Worksheet
- Unit Rates with Fractions – Quiz
Related words
Whole dictionary: A–Z · 6th Grade · Ratios and Percents