AQA · GCSE · Mathematics
Course version: 8300 · Version from Sept 2015
Use compound units such as speed, rates of pay, unit pricing
Full specification wording
Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing
A compound unit combines two measures, such as miles per hour (speed), pounds per hour (rate of pay) or pounds per kilogram (unit pricing).
Checked against the AQA 8300 specification (opens in a new tab) on .
- Point 12 of 21
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
A compound unit combines two measures, such as miles per hour (speed), pounds per hour (rate of pay) or pounds per kilogram (unit pricing). To use them, divide the first quantity by the second, keeping the units consistent. For speed, use speed = distance ÷ time; for pay, pay rate = total pay ÷ hours worked; for unit pricing, price per unit = total price ÷ number of units. If units differ, convert first: for example, 30 minutes is 0.5 hours, so 20 miles in 30 minutes is 20 ÷ 0.5 = 40 miles per hour. Always write the compound unit in the answer, such as £8.50 per hour or 40 mph.
What earns the marks
- Identify the two quantities being compared and the compound unit required, such as miles per hour, pounds per hour or pounds per kilogram.
- Divide the first quantity by the second to find the rate, for example speed = distance ÷ time.
- Convert units where necessary so both quantities use compatible measures before dividing.
- Write the answer with the correct compound unit and check that the size of the answer is reasonable.
- Use a given rate to find a total, for example multiply an hourly rate by the number of hours worked.
Common mistakes and how to put them right
Dividing the wrong way round.
Put it right: Speed is distance divided by time, not time divided by distance. For example, 100 miles in 2 hours is 50 mph; dividing 2 hours by 100 miles gives 0.02 hours per mile, which is not the speed in mph.
Mixing units without converting.
Put it right: 45 minutes must be changed to 0.75 hours before dividing distance by time, otherwise the speed will be wrong.
Forgetting the compound unit in the answer.
Put it right: A speed answer of 50 is incomplete; write 50 mph or 50 miles per hour.
Confusing unit pricing with total price.
Put it right: Unit price is total price divided by quantity, so a 2 kg bag costing £6 has a unit price of £3 per kg, not £6 per kg.
Exam tips
- Write down the formula or division you are using before substituting numbers, so the method is clear.
- Convert all units to the same measure first, especially minutes to hours or grams to kilograms.
- Check the reasonableness of your answer: a car speed of 500 mph or a pay rate of £0.05 per hour should prompt you to recheck the calculation.
Try the lesson
The start of the Ratio, proportion and rates of change: use compound units such as speed, rates of pay, unit pricing lesson, made from checked teaching notes for this specification point.
Have a go first
A cyclist travels 45 kilometres in 3 hours at a steady speed. Work out the cyclist's average speed in kilometres per hour.
Listen
A compound unit combines two measures, such as miles per hour (speed), pounds per hour (rate of pay) or pounds per kilogram (unit pricing). To use them, divide the first quantity by the second, keeping the units consistent. For speed, use speed = distance ÷ time; for pay, pay rate = total pay ÷ hours worked; for unit pricing, price per unit = total price ÷ number of units. If units differ, convert first: for example, 30 minutes is 0.5 hours, so 20 miles in 30 minutes is 20 ÷ 0.5 = 40 miles per hour. Always write the compound unit in the answer, such as £8.50 per hour or 40 mph. A strong answer earns marks for these points. Identify the two quantities being compared and the compound unit required, such as miles per hour, pounds per hour or pounds per kilogram. Divide the first quantity by the second to find the rate, for example speed = distance ÷ time. Convert units where necessary so both quantities use compatible measures before dividing. Write the answer with the correct compound unit and check that the size of the answer is reasonable. Exam tip: Write down the formula or division you are using before substituting numbers, so the method is clear.
Watch it explained
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Read the described scene instead
Compound units compare two different measures in one rate. Common examples are miles per hour for speed, pounds per hour for rate of pay, and pounds per kilogram for unit pricing. Each one tells you how much of the first quantity matches one unit of the second. To use a compound unit, first identify the two quantities being compared and the compound unit you need. Then divide the first quantity by the second, keeping the units consistent. The result is a rate, such as distance per hour or cost per kilogram. The main formulas follow the same pattern. For speed, use speed equals distance divided by time. For pay, use pay rate equals total pay divided by hours worked. For unit pricing, use price per unit equals total price divided by number of units. Write the compound unit in the answer. Consider a journey of 20 miles in 30 minutes. Pause here: what must you convert before dividing? Because 30 minutes is 0.5 hours, the speed is 20 divided by 0.5, which equals 40 miles per hour. The compound unit is written as 40 mph, and you can check that the size is reasonable. Watch for four common mistakes. Speed is distance divided by time, not time divided by distance. Convert units first, so 45 minutes becomes 0.75 hours. Always write the compound unit, such as 50 mph. And unit price is total price divided by quantity, so a 2 kilogram bag costing 6 pounds has unit price 3 pounds per kilogram, not 6 pounds per kilogram. Remember the pattern: identify the two measures, convert to compatible units, divide the first by the second, and write the compound unit. Use multiplication when a rate is given and you need a total, such as an hourly rate multiplied by hours worked. Check that the answer's size is reasonable.
Key words
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compound unit
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speed
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rates of pay
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unit pricing
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See every definition
- compound unit
- A unit that combines two measures, such as miles per hour, pounds per hour or pounds per kilogram.
- speed
- Distance per unit time, found using speed = distance ÷ time.
- rates of pay
- Money per unit time, found using pay rate = total pay ÷ hours worked.
- unit pricing
- Cost per unit quantity, found using price per unit = total price ÷ number of units.
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