GCSE · Maths · AQA · Spec 8300 · Foundation
Compound units — speed, rates of pay, unit pricing
Kilometres per hour, pounds per hour, pence per gram: a car, a pay slip and a supermarket shelf look like three problems — the word 'per' makes them one.
Compound units · Rate of pay
A 3-hour shift in 15-minute blocks. Drag along it and watch which readouts move with the time — and which two never move at all.
WHAT YOU'VE LEARNED
A quick recap of today's lesson.
Read 'per' as 'for each one' — and three different problems become one skill.
What you need to know
- A compound unit joins two quantities with 'per': km/h is kilometres for each 1 hour, £/h is pounds for each 1 hour, p/g is pence for each 1 gram.
- The unit tells you the calculation. A rate is the total divided by the amount — speed = distance ÷ time, rate of pay = pay ÷ hours, unit price = cost ÷ amount — and multiplying the rate by an amount scales it back up to a total.
- To change a compound unit into related units, convert BOTH of its parts: for m/s to km/h the time part goes from seconds to hours (× 3600) and the distance part from metres to kilometres (÷ 1000).
- Time is not counted in tens. Minutes ÷ 60 gives hours (15 minutes = 0.25 hours, 90 minutes = 1.5 hours), and the decimal part of an hour × 60 gives the minutes back.
- To compare rates, write them all in the same unit in both parts — for example pence per millilitre — and only then compare the numbers. For prices, the lowest cost per unit is the best value.
The big picture
A compound unit such as km/h, £ per hour or pence per gram tells you how much of one quantity goes with ONE of another. Use it to scale up or down, convert both of its parts when the units change, and bring rates to the same unit before you compare them.
Key points
Worked example
Problem
A café worker is paid £93.60 for a 7.5-hour shift. (a) Work out the rate of pay in pounds per hour. (b) At the same rate, how much is the worker paid for a 32-hour week?
⚠ Watch out
Converting only one part of a unit. To change 0.45p per gram into pounds per kilogram, multiplying by 1000 for the grams gives 450 — but that is 450p per kg. The pence must become pounds too (÷ 100): the answer is £4.50 per kg, not £450.
Memory hook
'Per' = 'for each ONE'. Say the unit out loud — kilometres PER hour — and it tells you the division: kilometres ÷ hours.
Check yourself
Without looking back: a runner covers 400 m in 1 minute 20 seconds. Work out the speed in metres per second, then change it into kilometres per hour.
Flashcards
(7)What does 'per' mean in a compound unit such as £ per hour?
How do you find a rate from a total?
A car travels at 60 km/h for 2.5 hours. How far does it go?
How do you change a speed in m/s into km/h?
How do you write a time given in minutes as hours?
What must you do before comparing two prices for value?
Change £4.20 per kilogram into pence per gram.
Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.
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