Did you know that the packet with the lower price tag can cost more for every spoonful you use? Two bags of rice can look like a bargain and an expensive option until we account for their different sizes. This is an everyday mathematics question that asks children to compare quantities fairly, rather than simply choose the smaller number.
A unit price is the selling price divided by the quantity supplied, expressed on a common basis such as Singapore dollars per 100 grams or dollars per kilogram. When package sizes differ, convert the quantities into the same units and compare unit prices for genuinely comparable products. The cheapest per unit is not always the wisest purchase: the amount you need, waste, quality and actual promotion conditions also matter.
The hidden mathematics: what exactly is being compared?
A price label often shows the amount paid for a whole pack. That sticker price answers ‘How much cash must I spend on this pack?’ It does not directly answer ‘How much does the same quantity of product cost?’ A 500 g pack costing S$3.20 and a 1 kg pack costing S$5.80 are not comparable by the sticker prices alone. The packages contain different amounts, so we must choose a shared reference unit.
That shared unit acts like a common ruler. Mathematically, unit price is a rate: dollars for a stated mass, volume or count. A student who understands this relationship can use it with supermarket foods, school art materials, refill products and recipes. A student who only memorises ‘divide by 100’ may become confused when a label uses kilograms, millilitres or items.
Worked example: two fictional packets of rice
These prices and quantities are invented for classroom teaching; they are not a claim about current supermarket offers. Suppose rice Packet A contains 750 grams and costs S$4.20. Packet B contains 1.2 kilograms and costs S$6.12. Which is cheaper per 100 grams? We must first rewrite 1.2 kg as 1,200 g. Then we make a like-for-like comparison.
- Packet A: S$4.20 ÷ 750 g × 100 g = S$0.56 per 100 g.
- Packet B: S$6.12 ÷ 1,200 g × 100 g = S$0.51 per 100 g.
- Difference on the shared basis: S$0.56 − S$0.51 = S$0.05 per 100 g.
- Equivalent basis per kilogram: A costs S$5.60/kg and B costs S$5.10/kg.
- Conclusion for this example: B has the lower unit price, although its total sticker price is higher.
Check the arithmetic a second way. There are ten portions of 100 g in one kilogram, so S$0.51 per 100 g corresponds to S$5.10 per kilogram. B’s 1.2 kg pack would then cost 1.2 × S$5.10 = S$6.12, exactly the supplied packet price. This reverse check is more useful than trusting a calculator without understanding the units.
The conclusion has a clear boundary. Packet B is cheaper for the same mass of rice under the assumed prices and product comparability. That does not establish that B has better taste, nutrition, storage quality or overall suitability. Those are separate questions requiring separate information.
When the smaller pack is still the sensible purchase
Suppose a household needs only 700 g of this rice before moving house and cannot store the remainder. One 750 g A pack costs S$4.20. The 1.2 kg B pack costs S$6.12. If the household genuinely values only the amount it can use and cannot preserve or share the excess, paying S$1.92 extra for unused quantity might not make sense despite B’s lower unit price. This is an example of a trade-off, not a contradiction.
A good student should now be able to answer two questions independently: ‘Which packet costs less per 100 g?’ and ‘Which purchase better suits a household that needs approximately 700 g?’ The answers can differ because the decision criteria differ. Learning to state the question is part of learning the mathematics.
The three-unit conversion that prevents most errors
- Mass: 1 kilogram = 1,000 grams. Choose g, 100 g or kg and state which one you use.
- Volume: 1 litre = 1,000 millilitres. A liquid might be compared using S$/100 mL or S$/L.
- Count: eggs, batteries and pencils may be compared using S$ per item, provided the items are genuinely comparable.
- Keep the denominator consistent. S$0.51 per 100 g must not be compared numerically with S$5.60 per kg as though both were dollars for the same amount.
- Do not silently compare a pack’s nominal volume with another pack’s mass unless suitable density or conversion information is available.
A quick sense check helps. A kilogram is ten times 100 grams. Therefore a per-kilogram price should be ten times the per-100-gram price for the same product and currency. If a pupil calculates S$0.51 per 100 g but S$0.051 per kilogram, the size relationship has gone in the wrong direction.
A discount can reverse the answer
Imagine Packet A alone is genuinely eligible for a simple 10% discount on its S$4.20 selling price, with no minimum spend or other conditions. Ten per cent of S$4.20 is S$0.42, so the new price is S$3.78. Its new rate is S$3.78 ÷ 750 × 100 = S$0.504 per 100 g, or S$5.04 per kg. B remains S$5.10 per kg. After the specified discount, A has the slightly lower unit price.
Notice the level of precision. A’s exact computed unit rate is S$0.504 per 100 g, which rounds to S$0.50 if prices are shown to two decimal places. B’s is S$0.51. When the difference is small, do not round away important information before comparing. Calculate first, then display the answer to a sensible number of decimal places.
Real promotions may involve loyalty accounts, coupon eligibility, minimum purchase amounts or bundle conditions. Children should learn to read those conditions, not treat a large percent sign as a universal price. The only reliable comparison uses prices the household could actually pay.
The denominator trap: net quantity, drained weight and serving size
Not all numbers on food packaging refer to the same material. A tin may display net contents including liquid and a separate drained weight for the solid food. A nutrition panel may give values per serving or per 100 g. These measurements answer different questions. If a family wants the solid food after draining, its effective price per usable mass may differ from the price per total package mass.
For example, in a second invented illustration, a can costs S$2.40 and states 400 g net contents but only 240 g drained food. The arithmetic is S$0.60 per 100 g of total stated contents but S$1.00 per 100 g of the stated drained portion. Both calculations are correct for their denominators, and neither should be mislabeled as the other. Check the actual label and food context; do not assume every can has a drained weight.
This distinction matters in life because arithmetic cannot correct a mistaken definition of the quantity. Teach pupils to write ‘S$ per 100 g of what?’ directly beside their calculation.
Why unit pricing matters in Singapore
On 15 March 2025, the Competition and Consumer Commission of Singapore (CCCS) and the Consumers Association of Singapore (CASE) announced a supermarket unit-pricing pilot. Their joint announcement explains unit price as a selling price per unit of measurement, such as dollars per litre or kilogram, intended to help compare different brands and pack sizes. That dated announcement is a useful real-world reference for this lesson. It should not be interpreted as proof that every shop or shelf currently displays unit prices.
Children do not have to know the details of a retail initiative to learn the skill. The transferable idea is that a number means little without its unit and its reference quantity. Whether a store already displays a unit rate or a student calculates one, the same relationship applies.
A diagnostic for the learner: two questions, not one
Give the learner these fictional price tags: juice carton A is 600 mL for S$2.70; carton B is 1 litre for S$4.20. Ask which costs less per 100 mL, then ask which has the lower total cost at the till. The correct unit calculations are A: S$2.70 ÷ 600 × 100 = S$0.45 per 100 mL; B: S$4.20 ÷ 1,000 × 100 = S$0.42 per 100 mL. B is cheaper per 100 mL; A has the smaller total purchase price.
If a child chooses A as cheaper on both measures, they may be confusing total with rate. If they say B without showing a shared unit, ask for reasoning rather than assuming real understanding. If the unit rate is correct but the conversion is wrong, diagnose the specific unit conversion instead of repeating every ratio method.
Guided practice that gradually removes support
- Stage 1: Put two labelled drawings beside the prices and underline the mass or volume in each.
- Stage 2: Convert both quantities to one unit with the tutor watching and checking the denominator.
- Stage 3: Divide price by quantity to find the cost per 1 g or 1 mL, then scale to 100 g or 100 mL.
- Stage 4: Hide the worked formula and ask the child to choose a sensible common comparison unit independently.
- Stage 5: Add a discount or a realistic need limit and ask the learner to explain why cheapest per unit may not mean best purchase.
Each stage has a different objective. At the start, accuracy matters more than speed. Later the student should make the decisions without copying the previous worked example. A good tutor checks whether the learner can transfer the reasoning to a different type of product.
A fresh transfer exercise with full answers
Consider fictional sketchbooks for a class project. Pack C has six identical notebooks for S$9.90. Pack D has ten for S$15.00. A student needs seven notebooks and may buy whole packs only, with no leftover resale. Cost per notebook is C: S$9.90 ÷ 6 = S$1.65; D: S$15.00 ÷ 10 = S$1.50. D has a lower unit price. But the cheapest way to buy at least seven notebooks from only these pack types is one D pack for S$15.00, rather than two C packs for S$19.80.
Now change the requirement to six notebooks. One C pack costs S$9.90 and meets the need, while one D costs S$15.00. The best purchase for that stated requirement is C despite D’s lower cost per notebook. The student should keep their explanation tied to the number of units needed and the whole-pack restriction.
Common mistakes and what each one reveals
- Choosing the lower sticker price: a comparison-definition problem; ask what each price covers.
- Converting 1.2 kg to 120 g: a place-value and metric-unit problem; rebuild that conversion separately.
- Mixing S$/kg with S$/100 g: a common-unit problem; put both rates on the same scale.
- Using a guessed promotion price: a conditions-and-evidence problem; refer to actual eligibility.
- Declaring the cheapest unit price the best purchase in every situation: a decision-making problem; include quantities needed, waste and quality.
These are different errors. Calling them all ‘careless’ loses useful information. An effective repair lesson selects the unstable step and verifies it with a new problem before increasing speed or complexity.
How parents and teachers can see real progress
Ask pupils to compare two new products verbally: they should name the unit, show one correct conversion, calculate a rate and explain the purchase context. Record whether they can do those four things unaided. Later give a changed scenario—different discount, pack size or number needed—and watch whether the learner revises their decision for a defensible reason.
The improvement measure is not merely a higher score on a repeated worksheet. It is whether the child can choose a valid reference unit and justify the comparison in an unfamiliar example. No lesson can guarantee examination results or the cheapest possible household outcome every time, but these habits support better reasoning.
Limits and safety
Unit price alone does not measure product quality, durability, suitability, food allergies or nutrition. Do not invite a child to make unsupervised purchases, use unfamiliar dietary products or ignore family needs. In everyday shopping, adults make the final purchasing decision while students practise observing quantities and asking sensible questions.
Some products are sold by count and others by weight or volume. Some labels describe concentrated products intended for dilution, while others describe ready-to-use products. Comparisons are only as meaningful as the assumptions that define equivalent use. A simple arithmetic lesson should teach learners to notice when products are not genuinely comparable.
Frequently asked questions
Does the bigger package always have the lower unit price?
No. Calculate the actual rate from the price and amount. Promotions, pricing strategies and package design can make a smaller pack cheaper per unit.
Can we compare rice by grams and cooking oil by millilitres?
Not directly on one numerical unit-price scale. Compare like products with consistent quantities, or use a justified conversion appropriate to the decision.
Why does the unit price change after a discount?
The amount of product stays the same while the amount paid falls, so price divided by quantity decreases.
How should we handle rounding?
Keep enough precision to compare, then round for presentation. For close prices, rounding too early can hide a small difference.
Is unit price the same as value for money?
It contributes to value, but value also depends on usefulness, quality, waste and the buyer’s constraints.
Continue with eduKate learning
For the underlying ordered comparison, see how to keep the order of a ratio correct. The Mathematics Learning Hub connects everyday quantities to wider problem solving. The eduKate Education learning hub explains improvement through output and corrective feedback, while our Clementi Mathematics teaching reference models careful diagnosis followed by independent checking.
The practical lesson is simple: find the price for the same amount first. Then ask whether the amount you actually need makes that lower unit rate the right choice.