Unit rates, prices and constant speed
Find an amount per one unit and use it to compare or predict.
Before you begin
- Division
- Equivalent ratios and units
Choose which quantity becomes one
A unit rate compares one quantity with one unit of another. If six identical notebooks cost $15, cost per notebook is 15 ÷ 6 = $2.50. Reversing the division gives notebooks per dollar, a different but valid rate. Write the units with the result to show which rate you found. Comparisons are meaningful only when they use the same unit and comparable items.
Use a rate under a stated assumption
For constant speed, distance per hour remains the same, so distance equals speed times time. A journey's average speed is total distance divided by total time, but this does not mean its speed was constant at every moment. In price models, check for fixed fees or different pack sizes before assuming a proportional relationship.
Worked example
Pack A has 8 identical pens for $6; pack B has 12 for $8.40. Which has the lower unit price?
Show the worked solution
- Pack A costs 6 ÷ 8 = $0.75 per pen.
- Pack B costs 8.40 ÷ 12 = $0.70 per pen.
- Compare the same unit: $0.70 is lower than $0.75.
Pack B, at $0.70 per pen.
Try it yourself
At a constant 18 km/h, how far does a cyclist travel in 2.5 hours?
Common mistakes
- A lower total price is not necessarily a lower unit price.
- Keep time units consistent with the speed or flow rate.
What can you explain now?
A tap fills 21 litres in 3 minutes at a constant rate. How long will 35 litres take?
Compare with the explanation
5 minutes.
The unit rate is 21 ÷ 3 = 7 L/min. Time is 35 L ÷ 7 L/min = 5 min.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗