What is a rate?
A rate compares two quantities of different kinds measured in different units. Unlike a ratio, a rate has a unit. Common examples are speed (km/h), price (RM per kg) and flow (litres per minute). A unit rate tells you the amount for exactly 1 unit of the other quantity, such as "RM3 per kg".
Key idea / Key idea
To find a unit rate, divide the first quantity by the second. Speed = distance ÷ time. Price per unit = total cost ÷ quantity.
Working out a rate
Worked example / Worked example
A car travels 240 km in 3 hours. Find its speed.
Speed = distance ÷ time = 240 km ÷ 3 h = 80 km/h.
This means the car covers 80 km in each hour.
Unit rates make it easy to compare value for money. If 2 kg of rice costs RM8 and 3 kg costs RM10.50, find each price per kg: RM8 ÷ 2 = RM4/kg and RM10.50 ÷ 3 = RM3.50/kg. The second pack is cheaper per kilogram, so it is better value. Rates can also be reversed: if a machine makes 30 items per minute, one item takes 1 ÷ 30 minute, or 2 seconds.
Rates work in both directions. From a speed you can find distance (distance = speed × time) or time (time = distance ÷ speed). For example, at 60 km/h a bus needs 120 ÷ 60 = 2 hours to travel 120 km. Always write the unit clearly, because "RM3 per kg" and "3 kg per RM" mean very different things.
Remember / Remember
- A rate compares different quantities and has a unit.
- "Per" means "for each 1", and it means divide.
- Speed = distance ÷ time.
- Compare deals by working out the unit rate.