Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure

Q: How do I revise Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure for GCSE?

Read the notes on Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure, then test yourself without looking. Answering questions and checking what you missed builds recall faster than re-reading.

Q: Is this Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure guide aligned to the Pearson Edexcel specification?

Yes. This guide is linked to the Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure topic in the Pearson Edexcel GCSE specification.

A compound unit is built from two other measures, and the unit itself tells you which division to do.

Study notes

From the checked teaching notes for this specification point.

The idea

A compound unit is built from two other measures, and the unit itself tells you which division to do. Speed is distance divided by time, in units such as km/h. Density is mass divided by volume, in units such as g/cm³. Pressure is force divided by area, in units such as N/m². A unit price follows the same shape, total cost divided by the number of items, and a rate of pay is total pay divided by the time worked. Rearrange the relationship when the missing quantity is on top, so distance = speed × time. Make the units agree before you start. A metal block of mass 240 g and volume 30 cm³ has a density of 8 g/cm³. A journey of 90 km taking one and a half hours gives an average speed of 60 km/h, which is the same as one kilometre every minute.

What earns the marks

Choosing the correct relationship, for example writing density = mass ÷ volume before any numbers go in.
A correct conversion so that the two measures agree, such as changing minutes into hours.
The calculation carried out correctly, even if the unit is then left off or written wrongly.
The final answer stated with its compound unit.

Common mistakes and how to put them right

Dividing the wrong way round, for example working out volume ÷ mass and calling the result a density.
Mixing units inside one calculation, such as a distance in metres with a time in hours, without converting first.
Reading a decimal time wrongly, treating 1.5 hours as one hour and fifty minutes.
Averaging two speeds by adding them and halving, instead of using total distance ÷ total time.

Exam tips

Write the relationship out in words first, then put the numbers in; the division you need becomes obvious and the method is on the page.
Convert everything into the units named on the answer line before you calculate, not afterwards.
When a rate is per hour and the time is in minutes, turn the minutes into a fraction of an hour, so 24 minutes becomes 0.4 of an hour.

Try the lesson

The start of the Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing, density and pressure lesson, made from checked teaching notes for this specification point.

Have a go first

A car travels 180 kilometres in 4 hours at a constant speed. Work out the speed of the car in kilometres per hour.

Tip: press 1 to 4 to choose

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