Ratio, Proportion & Rates of Change
Grade 3-5Best Buy Problems
Every "which is better value" question comes down to converting each option into the same unit, usually a price per single item or per 100 g, so they can be compared directly instead of guessed at. This lesson covers finding a unit price, comparing prices for different-sized quantities, comparing single items to multipacks, and finding the cheapest way to buy an exact quantity.
Written by Asad, Co-Founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Finding a unit price
Divide the total price by the quantity to find the price of a single unit, such as one item, one kilogram or one litre.
A pack of 6 yoghurts costs £2.40. The price per yoghurt is £2.40 ÷ 6 = £0.40.
Comparing prices for different-sized quantities
When two products come in different sized quantities, find the price per common unit, such as price per 100 g or price per litre, for each one, then compare these values directly. The smaller price per unit is the better value.
Rice is sold as 500 g for £1.50, or 800 g for £2.24. The 500 g bag costs £1.50 ÷ 500 × 100 = £0.30 per 100 g, and the 800 g bag costs £2.24 ÷ 800 × 100 = £0.28 per 100 g. The 800 g bag is better value, since its price per 100 g is lower.
Comparing a single item to a multipack
Find the price of a single item within the multipack by dividing the multipack price by the number of items, then compare this to the price of buying one item on its own.
A single can costs £0.65, and a multipack of 6 cans costs £3.30. The price per can in the multipack is £3.30 ÷ 6 = £0.55, which is £0.10 cheaper per can than buying single cans.
Finding the cheapest way to buy an exact quantity
When an exact number of items is needed and they only come in fixed pack sizes, work out how many packs of each size are needed, calculate the total cost for each option, then compare the totals directly, rather than just comparing the price per item.
Notebooks come in packs of 5 for £3.75, or packs of 8 for £5.60, and exactly 40 are needed. Buying packs of 5: 40 ÷ 5 = 8 packs, costing 8 × £3.75 = £30. Buying packs of 8: 40 ÷ 8 = 5 packs, costing 5 × £5.60 = £28. Packs of 8 are cheaper overall.
Worked Examples
Three exam-style questions, fully solved.
A pack of 6 yoghurts costs £2.40. Find the price per yoghurt.
Easy- 1.Divide the total price by the number of yoghurts: £2.40 ÷ 6
Answer: £0.40
Rice is sold in two sizes: 500 g for £1.50, or 800 g for £2.24. Which is the better buy?
Medium- 1.Find the price per 100 g for the 500 g bag: £1.50 ÷ 500 × 100 = £0.30
- 2.Find the price per 100 g for the 800 g bag: £2.24 ÷ 800 × 100 = £0.28
- 3.Compare the two prices per 100 g: £0.28 is lower than £0.30
Answer: The 800 g bag is better value
A shop sells notebooks in packs of 5 for £3.75, or packs of 8 for £5.60. Sara needs exactly 40 notebooks. Find the cheapest way for her to buy them, and the total cost.
Hard- 1.Find the cost buying packs of 5: 40 ÷ 5 = 8 packs, costing 8 × £3.75 = £30
- 2.Find the cost buying packs of 8: 40 ÷ 8 = 5 packs, costing 5 × £5.60 = £28
- 3.Compare the two totals: £28 is less than £30
Answer: Buy packs of 8, total cost £28
Avoid These
The most common mistakes students make.
Comparing prices per pack directly, instead of converting each option to a common unit, such as price per 100 g or price per item.
Making an arithmetic slip when finding a unit price, especially when working with decimals.
Concluding the wrong option is better value by misreading which price per unit is actually smaller.
Assuming the option with the lowest price per unit is always the cheapest for buying an exact quantity, instead of comparing the total cost of each combination of packs.
Rounding a unit price too early, which can lead to the wrong final comparison or total cost.
FAQ
Questions parents and students ask.
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