Ratio, Proportion & Rates of Change
Grade 5-7Compound Measures
A compound measure combines two other quantities into a single rate, such as speed, density or pressure, and each one uses the same kind of formula triangle to move between the three linked values. This lesson covers calculating speed, density and pressure, converting between units of speed, and finding the average speed for a journey made up of multiple stages.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Speed, distance and time
Speed is distance divided by time. Rearranging gives distance = speed × time, and time = distance ÷ speed.
A car travels 150 km in 3 hours. Its average speed is 150 ÷ 3 = 50 km/h.
Density, mass and volume
Density is mass divided by volume. Rearranging gives mass = density × volume, and volume = mass ÷ density.
A metal block has a mass of 540 g and a volume of 60 cm³. Its density is 540 ÷ 60 = 9 g/cm³.
Pressure, force and area
Pressure is force divided by area. Rearranging gives force = pressure × area, and area = force ÷ pressure.
A force of 200 N acts on an area of 4 m². The pressure is 200 ÷ 4 = 50 Pa.
Converting units and finding average speed over multiple stages
To convert between km/h and m/s, convert kilometres to metres and hours to seconds, remembering that there are 3600 seconds in an hour.
For a journey with more than one stage, find the total distance travelled and the total time taken separately, then divide total distance by total time. Do not average the individual speeds directly, since this ignores how long was spent at each speed.
Worked Examples
Three exam-style questions, fully solved.
A metal block has a mass of 540 g and a volume of 60 cm³. Find its density.
Easy- 1.Divide the mass by the volume: 540 ÷ 60
Answer: 9 g/cm³
A car travels at 25 m/s. Convert this speed to km/h.
Medium- 1.Find the distance travelled in 1 hour: 25 × 3600 = 90000 m
- 2.Convert metres to kilometres: 90000 m = 90 km
Answer: 90 km/h
A car travels for 3 hours at 60 km/h, then for 2 hours at 45 km/h. Find the average speed for the whole journey.
Hard- 1.Find the distance for the first stage: 3 × 60 = 180 km
- 2.Find the distance for the second stage: 2 × 45 = 90 km
- 3.Divide the total distance by the total time: (180 + 90) ÷ (3 + 2)
Answer: 54 km/h
Avoid These
The most common mistakes students make.
Using the wrong rearrangement of the formula, such as dividing distance by time when time is actually the missing value.
Mixing units when calculating average speed, such as combining km/h and m/s without converting them to match first.
When converting between km/h and m/s, forgetting to also convert kilometres to metres, or forgetting to divide or multiply by 3600 to convert hours to seconds.
Finding the average speed for a multi-stage journey by averaging the two speeds directly, instead of dividing total distance by total time.
Leaving out or misstating the units in the final answer, such as writing a density value with no units, or the wrong units for pressure.
FAQ
Questions parents and students ask.
Before this topic, make sure you know
What to learn next
Want a plan built around your child specifically?
Get our free 8-video course, or book a free Roadmap Call for a personalised plan.