Finding Unit Rates
Calculate unit rates by dividing the numerator quantity by the denominator quantity to express ratios as a single unit, solving proportional relationships in Grade 7 math.
Key Concepts
Property A unit rate is a rate whose denominator is 1. A unit price is the cost per unit.
Examples Which is cheaper: 4 candy bars for 3.20 dollars or 5 for 3.50 dollars? $\frac{3.20 \text{ dollars}}{4} = 0.80$ dollars per bar vs $\frac{3.50 \text{ dollars}}{5} = 0.70$ dollars per bar. The 5 pack is the better buy! A car travels 120 miles on 4 gallons of gas. The unit rate is $\frac{120 \text{ miles}}{4 \text{ gallons}} = 30$ miles per gallon. You earn 45 dollars for 5 hours of work. Your unit rate is $\frac{45 \text{ dollars}}{5 \text{ hours}} = 9$ dollars per hour.
Explanation Ever wondered which deal is truly better? Unit rates are your secret weapon! By finding the cost for just one item, like a can of soda, you can easily compare prices. This makes you a super savvy shopper because you always know the cost 'per one,' which helps you spot the best value every single time.
Common Questions
What is a unit rate?
A unit rate expresses a ratio as the quantity per single unit of another quantity. For example, miles per hour, price per pound, or words per minute are unit rates. To find a unit rate, divide the numerator quantity by the denominator quantity so the denominator equals 1.
How do unit rates help compare quantities?
Unit rates allow direct comparison between different-sized quantities. For example, if Store A sells 3 apples for $1.50 and Store B sells 5 apples for $2.25, you calculate unit rates: $0.50/apple vs. $0.45/apple. Store B is cheaper per apple, which the unit rate makes immediately clear.
How is a unit rate different from a ratio?
A ratio compares two quantities and may have any denominator, like 60 miles per 2 hours. A unit rate always has a denominator of 1, like 30 miles per 1 hour. Unit rates are a specific type of ratio that simplifies comparison and real-world problem-solving.