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What Is a Unit Rate?
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A unit rate is a rate with a denominator of 1 — it tells you how much of one quantity there is for exactly one unit of another. "60 miles per hour" and "$3 per pound" are unit rates: one hour, one pound.
Rate vs. unit rate:
- A rate compares two quantities with different units: 150 miles in 3 hours.
- A unit rate reduces that to a single unit: 50 miles per hour.
Every unit rate is a rate, but only rates "per one" are unit rates. The giveaway word is usually per — per hour, per item, per gallon, per person.
How to find a unit rate: divide the first quantity by the second.
Unit rate = quantity ÷ number of units
Worked examples:
1. Speed. A car travels 150 miles in 3 hours.
150 ÷ 3 = 50 miles per hour
2. Price. 5 pounds of apples cost $12.50.
12.50 ÷ 5 = $2.50 per pound
3. Rate of work. A printer prints 240 pages in 8 minutes.
240 ÷ 8 = 30 pages per minute
4. Fuel economy. A car uses 12 gallons to travel 384 miles.
384 ÷ 12 = 32 miles per gallon
Unit price — where this matters in real life. A unit price is a unit rate for cost, and it's how you compare products of different sizes:
| Option | Price | Size | Unit price |
|---|---|---|---|
| Small box | $4.50 | 15 oz | 4.50 ÷ 15 = $0.30/oz |
| Large box | $7.20 | 30 oz | 7.20 ÷ 30 = $0.24/oz |
The large box is cheaper per ounce, so it's the better value. This is exactly what supermarket shelf labels show in small print, and it's the most practical use of the concept.
Note that bigger isn't automatically cheaper per unit — comparing unit prices sometimes reveals that the family size costs more per ounce.
Unit rates with fractions. If a recipe uses ⅔ cup of flour for ¼ of a batch:
⅔ ÷ ¼ = ⅔ × 4 = 8/3 = 2⅔ cups per batch
Dividing by a fraction means multiplying by its reciprocal.
Common unit rates you already use:
- Miles per hour (mph) — speed
- Dollars per hour — wages
- Miles per gallon (mpg) — fuel economy
- Beats per minute (bpm) — heart rate
- Words per minute (wpm) — typing speed
- Cost per person — splitting a bill
- Calories per serving
Unit rate vs. ratio vs. proportion — often confused:
| Term | What it is | Example |
|---|---|---|
| Ratio | Compares two quantities, often the same unit | 3 girls to 4 boys (3:4) |
| Rate | A ratio comparing different units | 150 miles in 3 hours |
| Unit rate | A rate where the second quantity is 1 | 50 miles per hour |
| Proportion | An equation stating two ratios are equal | 3/4 = 6/8 |
Using a unit rate to solve problems. Once you have it, scaling is simple multiplication. If apples are $2.50 per pound, then 7 pounds cost 2.50 × 7 = $17.50. This is why converting to a unit rate first makes most rate problems easier — you find the "per one" figure, then multiply.
A tip for word problems: the unit you want to end up with tells you which way to divide. For "miles per gallon", miles goes on top and gallons on the bottom — the word per means divided by, and whatever follows it becomes the denominator.