A cyclist travels 42 km in 2.5 h. Find the average speed.
- Rate = distance ÷ time.
- 42 ÷ 2.5 = 16.8 km/h.
- At that constant rate, 1 hour corresponds to 16.8 km.
Rates & unit rates
Describe how much for one.
A rate keeps both quantities and their units
A rate compares quantities with different units, such as 180 km in 3 h or $12 for 4 notebooks. A unit rate expresses one quantity per 1 unit of the other.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
Choose the direction before dividing
180 km ÷ 3 h = 60 km/h. The reverse rate is 3 h ÷ 180 km = 1/60 h/km, or 1 min/km. Both can be meaningful, but they answer different questions.
An average rate is a model
Travelling 180 km in 3 hours gives an average speed of 60 km/h. It does not mean the vehicle travelled at exactly that speed at every moment. Use constant-rate assumptions only when justified.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
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Finding unit rates
Name the quantity that becomes one before dividing.
Open on YouTube →Worked examples
Four notebooks cost $10. Find the cost per notebook and notebooks per dollar.
- $10 ÷ 4 = $2.50 per notebook.
- 4 ÷ $10 = 0.4 notebooks per dollar.
- Name the direction and unit of each rate.
Try it before checking.
A printer makes 90 pages in 3 minutes. How many pages per minute?
A first hint
Divide pages by minutes.
Compare your reasoning
90 ÷ 3 = 30 pages/min.
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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Explain a little more.
How could two trips have the same average speed but very different journeys?
Use this thinking in the If… project →