Unit Rates and Unit Pricing
Learn to calculate and interpret unit rates, find the best buy between products, and apply unit rates in everyday decisions.
Every time you comparison-shop at the grocery store, evaluate a job offer by the hour, or calculate how far you can drive on a tank of gas, you're using unit rates. The 48-oz bottle for $4.32 versus the 32-oz bottle for $3.20 — which is cheaper? Without unit pricing, you're just guessing. With it, you know in 10 seconds.
- Calculate a unit rate by dividing so the denominator equals 1
- Use unit pricing to identify the best buy between two or more products
- Project totals from a known unit rate (earnings, distance, consumption)
A unit rate expresses a ratio with denominator 1 — you divide the numerator by the denominator until you get "per 1 unit":
\[ \text{Unit Rate} = \frac{\text{quantity A}}{1 \text{ unit of B}} \]To find a unit rate from any ratio \(\frac{a}{b}\): divide both terms by \(b\), giving \(\frac{a/b}{1}\). The result \(a/b\) is the unit rate. Once you have it, multiply by any quantity of B to find the corresponding A.
Best Buy Comparison
Unit Price Comparison — Which is Cheaper Per Ounce?
Brand A saves $0.01 per oz — on a year's supply that adds up.
A cyclist rides 78 miles in 3 hours. What is the unit rate (speed)?
\[ \frac{78 \text{ miles}}{3 \text{ hours}} = \frac{78 \div 3}{3 \div 3} = \frac{26}{1} = 26 \text{ mph} \]Using this unit rate: in 4.5 hours the cyclist covers \(26 \times 4.5 = 117\) miles.
Shampoo: Brand A — 32 oz for $3.84. Brand B — 20 oz for $2.60. Which is the better deal?
\[ \text{Brand A: } \frac{\$3.84}{32\text{ oz}} = \$0.12\text{/oz} \qquad \text{Brand B: } \frac{\$2.60}{20\text{ oz}} = \$0.13\text{/oz} \]Brand A costs $0.12/oz vs Brand B at $0.13/oz. Brand A is the better deal by $0.01 per ounce.
A part-time worker earns $247.50 for 22.5 hours of work this week. If they worked full-time (2,080 hours/year) at the same rate, what would their annual salary be?
- Find the unit rate (hourly): \(\$247.50 \div 22.5 = \$11.00\text{/hr}\).
- Project annually: \(\$11.00 \times 2{,}080 = \$22{,}880\text{/year}\).
At this hourly rate, the full-time equivalent salary is $22,880 per year.
Test yourself before moving on:
- A car travels 312 miles on 12 gallons. What is the unit rate (mpg)?
- Cereal: Box A is 18 oz for $3.96; Box B is 24 oz for $4.56. Which is the better deal?
- At $15.50 per hour, how much does an employee earn in a 37.5-hour work week?
▶ Show Answers
- \(312 \div 12 =\) 26 mpg.
- Box A: \(3.96/18 = \$0.22\text{/oz}\). Box B: \(4.56/24 = \$0.19\text{/oz}\). Box B is the better deal.
- \(15.50 \times 37.5 =\) $581.25.
- Comparing totals instead of per-unit: Brand B costs less in total ($2.60 vs $3.84), but costs more per ounce. Total price tells you what you pay today; unit price tells you what you're actually getting for your money.
- Rounding too early: Round only the final answer. Mid-calculation rounding compounds errors — $0.12 vs $0.125 can flip your best-buy decision.
- Inverting the rate: Speed is miles per hour (miles on top), not hours per mile. Keep the "per 1 unit" quantity in the denominator.
- A unit rate has 1 in the denominator — divide numerator by denominator to get there.
- Unit price is cost ÷ quantity — the universal comparison metric for shopping decisions.
- Multiply a unit rate by any quantity to scale up: 26 mpg × 14 gallons = 364 miles.
- The unit rate is the constant of proportionality k in any proportional relationship y = kx.
Procurement managers evaluate supplier bids using unit pricing every day. A contract offering 5,000 units for $62,500 versus 8,000 units for $96,000 — which supplier offers the better rate? ($12.50/unit vs $12.00/unit — the larger order wins.) At enterprise scale, a $0.50/unit difference across 50,000 units/year is $25,000 in annual savings. Supply chain professionals who master unit rates save their companies real money on every purchasing decision.
Calculator Connection
Use the Ratio Solver to quickly find unit rates — enter your ratio and set the denominator to 1 to see the unit rate instantly.
Try it with the Calculator
Apply what you've learned with this tool.
Unit Rates and Unit Pricing — Quiz
5 questions per attempt · Beginner · Pass at 70%
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