Maths · Ratio & Proportion
Best buy & unit rate
Compare prices via unit-rate reasoning.
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What is a unit rate?
A unit rate tells you the price for one item or one unit of measure. For example, if 4 apples cost £2, the unit rate is 50p per apple. Finding the unit rate helps you compare different deals quickly and fairly.
How to find a unit rate
Divide the total cost by the quantity. If 6 pencils cost £1.80, divide 1.80 by 6 to get £0.30 per pencil. You can also find the cost per gram, per litre, or per metre.
Using unit rates to find the best buy
Calculate the unit rate for each option. The option with the lowest unit rate is the best value. A large pack might look expensive, but its unit rate could be cheaper than a small pack.
Working with different units
Sometimes you need to compare 500 g at one price and 2 kg at another. Convert to the same unit first. Remember 1 kg equals 1000 g, so you can compare fairly.
Worked examples
1. Shop A sells 3 bars of soap for £2.40. Shop B sells 5 bars for £3.50. Which is better value?
- Shop A: divide £2.40 by 3 to get £0.80 per bar.
- Shop B: divide £3.50 by 5 to get £0.70 per bar.
- £0.70 is less than £0.80, so Shop B offers better value.
2. A 250 ml bottle of juice costs £1.20. A 400 ml bottle costs £1.80. Which has the lower unit rate?
- 250 ml bottle: divide £1.20 by 250 to get £0.0048 per ml or 0.48p per ml.
- 400 ml bottle: divide £1.80 by 400 to get £0.0045 per ml or 0.45p per ml.
- The 400 ml bottle is cheaper per ml, so it is better value.
3. Rice costs £4.80 for 1.5 kg. What is the price per kilogram?
- Divide £4.80 by 1.5 to find the unit rate.
- 4.80 ÷ 1.5 = 3.20.
- The rice costs £3.20 per kilogram.
Try it yourself
Pack A: 8 batteries for £3.60. Pack B: 12 batteries for £5.04. Which pack offers better value?
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