Compound measures

Objective. Calculate and compare speed, density and unit price.

1. Learn
2. Worked example
3. Practice
4. Feedback
5. Continue

Learn: the key idea

Compound measures combine two different quantities into a single rate, such as speed from distance and time, density from mass and volume, or unit price from cost and amount. Each compound unit is found by dividing one quantity by the other, and rearranging the formula lets you find any missing value. Speed equals distance divided by time, so travelling 150 km in 3 hours gives a speed of 150 ÷ 3 = 50 km/h. Always keep units consistent before dividing, converting minutes to hours or grams to kilograms if needed.

Worked example

A metal block has a mass of 540 g and a volume of 60 cm³. Calculate its density using compound units.

1 $Recall the formula: density = mass \div volume$
2 $Substitute the values: 540 \div 60$
3 $Divide: 540 \div 60 = 9$
4 $The density is 9 g/cm³$

Answer: 9 g/cm³

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. Pupils often divide the quantities the wrong way round, calculating time divided by distance instead of distance divided by time, giving a nonsensical speed like 0.02. Always check the formula and units match before dividing.

Your progress

Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.

0 of 5 steps complete

Your place saves automatically as you read.

My dashboard