Compare unit prices
Use a common amount and comparable products. P is the pack price, q is its quantity, b is the comparison amount and u is the price for that amount. Compare exact rates, then round the requested result
\[u=\frac{P}{q}\times b\]
- Quantities The pack quantity and comparison amount must use the same unit
- Decision Lower price per common amount means better value. Equal rates mean equal value
- Alternative rate When comparing quantity per dollar, choose the larger amount per dollar
Common mistakes
Comparing only pack prices
✕\(\displaystyle \begin{gathered}\text{Choose A because}\\3.28<10.92\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Choose B because}\\0.78<0.82\end{gathered}\)
A is 400 g for $3.28 and B is 1.4 kg for $10.92. Their prices per 100 g are $0.82 and $0.78, so B has the lower unit priceEarly rounding
✕\(\displaystyle \text{Price per 100 g}=\$1.00\)✓\(\displaystyle 4.62\div700\times100=0.66\)
For the 700 g pack costing $4.62, rounding the price per gram to $0.01 gives the incorrect price of $1 per hundred grams. Keep the original division to get $0.66Difficulty levels
introCompare two packs in matching units
standardCompare up to three packs or calculate a saving for a common amount
challengeConvert mixed units before comparing prices or savings
Questions about this topic
Is the largest pack always better value?+
No. Compare prices for the same amount
Does better unit value always mean I should buy that pack?+
No. Also consider the amount needed, whole-pack costs, quality and possible waste
Can I use a calculator?+
A calculator is allowed unless a question is marked no calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 1: Number and financial mathematics
In this chapter
Evaluate an integer expressionFactors, multiples, HCF, LCM and primesRound to decimal places or significant figuresEstimate an expression using rounded inputsConvert between fractions, mixed numbers and decimalsClassify real numbers and compare exact valuesAdd, subtract, multiply and divide fractions and mixed numbersWrite a ratio from countsWrite ratios in simplest formComplete equivalent ratiosUse a constant rateDivide a quantity in a given ratioDecide which option is the better valueConvert between fractions, decimals and percentagesFind a percentage of a quantityExpress one quantity as a percentage of another1F Percentages and money: Find the original amount from a percentageIncrease or decrease a quantity by a percentageFind percentage changePercentage error against a reference value1G Percentage change and percentage error: Find the original amount from a percentageProfit, mark-up and discountIncome and taxSimple interestCompound interest (optional extension)