Key takeaway: A unit rate is a rate that tells how much of one quantity matches exactly one unit of another quantity, such as 48 miles per 1 hour or \$0.35 per 1 ounce.
Grade 66.RP.A.2Ratios, Rates and Percents
Definition of Unit Rate
A unit rate compares two quantities measured in different units so that the second quantity equals 1. Instead of saying a printer makes 84 pages in 4 minutes, the rate for one minute is 21 pages in one minute.
Every rate \(a\) for \(b\) with \(b \neq 0\) can be scaled to one unit: \(\frac{a}{b}\) units of the first quantity for each single unit of the second. The word per usually signals it.
Formula and notation
Divide the first quantity by the second quantity:
\[\text{unit rate} = \frac{\text{first quantity}}{\text{second quantity}}\]
Write the answer with both units, using “per” or a slash: \(21\text{ pages/min}\), \(\$1.40\) per pound, \(62\) words per minute.
Key facts
- The denominator of a unit rate is always 1, so it is often left unwritten.
- Swapping the two quantities gives a second rate, such as minutes per page.
- Comparing unit prices shows which package is the better buy.
- On a double number line, the value for one unit sits directly above the 1.
Unit Rate example
A 12-ounce bag of trail mix costs \$4.20 at the school store. A 20-ounce bag costs \$6.60. Find the price per ounce of each bag and decide which one is the better buy.
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Small bag: \(\frac{\$4.20}{12\text{ oz}} = \$0.35\) per ounce.
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Large bag: \(\frac{\$6.60}{20\text{ oz}} = \$0.33\) per ounce.
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Compare: \(\$0.33 < \$0.35\), so each ounce costs less in the large bag.
The unit rates are \$0.35 and \$0.33 per ounce, so the 20-ounce bag is the better buy.
Common mistake
Watch out
Diego reads 150 pages in 6 days and writes the unit rate as \(6 : 150 = 0.04\) pages per day.
Why it is wrong
He divided in the wrong order. The quantity that should equal 1 (days) goes in the denominator: \(150 : 6 = 25\) pages per day. His 0.04 is actually days per page, the reciprocal rate. Read the units after “per” to choose the divisor.
Related terms and lessons
Browse the glossary: A–Z list · Grade 6 vocabulary · Ratios, Rates and Percents