Compound Units
Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
What a learner can do afterwards
- Calculate average speed given distance and time, converting between km/h and m/s if needed
- Compare unit prices of two products sold in different quantities to find the better deal
- Use the density formula to find mass, volume, or density given the other two values
1 · Read
Some units come from dividing one measurement by another. Speed is distance ÷ time. Unit price is cost ÷ quantity. Density is mass ÷ volume. These are called compound units.
A cyclist rides 30 km in 2 hours. Speed = distance ÷ time = 30 ÷ 2 = 15 km/h. To change km/h into metres per second, turn the distance into metres and the time into seconds: 18 km/h is 18,000 m in 3,600 s, and 18,000 ÷ 3,600 = 5 m/s.
A rock has a mass of 150 g and a volume of 50 cm³. Density = mass ÷ volume = 150 ÷ 50 = 3 g/cm³. Turn it round to find a mass: a 40 cm³ piece of the same rock has mass 3 × 40 = 120 g.
Check the units before you divide. If time is in minutes but you want km/h, convert it to hours first. The answer's units come from the division too, like km/h or g/cm³.
Compound units come from dividing one measurement by another: speed, unit price, and density all follow amount ÷ amount, matched to the right units.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
15 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.