The idea, step by step
Compare the same unit
A lower sticker price does not always mean better value. Convert quantities to one common unit, then divide price by quantity. You can compare dollars per kilogram, dollars per litre, or cents per item.
Do not compare dollars per kilogram with dollars per 100 g. They are different-sized units. State which unit you use and keep it the same for every offer.
Best value and best purchase
The lowest unit price answers a mathematical comparison. A sensible purchase also depends on how much is needed, the amount of money available, storage and possible waste. Explain any assumption that affects your recommendation.
If two offers have equal unit prices, either can be equally good value. Pack sizes may still lead to different total spending when the required quantity is not a multiple of both pack sizes.
A common trap
Choose the smallest price without looking at the quantity.
Instead: First compare a common unit price. Then check the number of packs needed and the total amount paid.
See the thinking
Compare different masses
Offer A is 750 g for AUD 6. Offer B is 1 kg for AUD 7.60. Which has the lower unit price?
- Convert 750 g to 0.75 kg.
- A costs dollars/kg.
- B costs AUD 7.60/kg, which is lower than AUD 8/kg.
Equal unit prices
Compare 700 mL for AUD 4.20 with 1 L for AUD 6.
- The first quantity is 0.7 L.
- Its unit price is dollars/L.
- The other offer also costs AUD 6/L.
Check your understanding
Which is cheaper per pen: 4 pens for AUD 6 or 6 pens for AUD 8.40?
Show answer
Six pens for AUD 8.40.
The prices per pen are AUD 1.50 and AUD 1.40.
Your turn
6 questions · 16 marks · Work at your own pace.
Read the questions online
- Compare 500 g for AUD 3.25 with 800 g for AUD 4.80. State the lower price per kilogram.3 marks
- Which is cheaper per pen: 3 pens for AUD 4.20 or 5 pens for AUD 6.50?2 marks
- Compare 2.5 kg for AUD 9 with 1.5 kg for AUD 5.70.2 marks
- Compare 250 mL for AUD 2.10 with 1.5 L for AUD 10.80.3 marks
- You need at least 600 g. A 400 g pack costs AUD 3; a 1 kg pack costs AUD 7. What is the cheapest purchase?3 marks
- A 500 mL bottle costs AUD 3 and a 750 mL bottle costs AUD 4.50. Find the cheapest way to buy exactly 1.5 L.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Compare 500 g for AUD 3.25 with 800 g for AUD 4.80. State the lower price per kilogram.3 marks
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800 g offer: AUD 6/kg, compared with AUD 6.50/kg. - Which is cheaper per pen: 3 pens for AUD 4.20 or 5 pens for AUD 6.50?2 marks
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Five-pen pack: AUD 1.30/pen. - Compare 2.5 kg for AUD 9 with 1.5 kg for AUD 5.70.2 marks
dollars/kg.
dollars/kg.
The 2.5 kg offer is cheaper per kilogram. - Compare 250 mL for AUD 2.10 with 1.5 L for AUD 10.80.3 marks
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The 1.5 L offer: AUD 7.20/L, compared with AUD 8.40/L. - You need at least 600 g. A 400 g pack costs AUD 3; a 1 kg pack costs AUD 7. What is the cheapest purchase?3 marks
Two small packs supply 800 g for AUD 6.
One large pack costs AUD 7.
Both meet the need; the small packs cost AUD 1 less.
Two 400 g packs, costing AUD 6. - A 500 mL bottle costs AUD 3 and a 750 mL bottle costs AUD 4.50. Find the cheapest way to buy exactly 1.5 L.3 marks
Both unit prices are AUD 6/L.
and .
Either three 500 mL bottles or two 750 mL bottles; both cost AUD 9.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Ratio scaling and division review; unit rates; comparing rates and best buys; speed, distance and time; converting compatible units; direct-proportion tables and graphs; modelling practical rate problems and checking assumptions.
Official curriculum source ↗