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Grades 6–8 · Everyday Life

How can different pack sizes be compared fairly?

A unit price expresses a price for a fixed amount of something. Using the same amount for both products makes a rate comparison possible even when the packs contain different quantities. A lower total price and a lower unit price are not the same thing.

J07 visual explanationFictional identical-content packs: A is 500 grams for 3 dollars; B is 1000 grams for 5 dollars. Using dollars per 100 grams, A is 0.60 and B is 0.50. B has the lower unit price. A common unit makes a price-rate comparison fair, but suitability also depends on needed quantity, storage and other constraints. No actual shopping or financial recommendation is made.Compare the same amountFictional packs · dollars per 100 gramsPack A500 g costs $3$3 ÷ 5$0.60 per 100 g5 groups of 100 gPack B1000 g costs $5$5 ÷ 10$0.50 per 100 g10 groups of 100 gB has the lower unit price, not every advantage.

In the diagramCompare the same amountFictional packs · dollars per 100 gramsPack A500 g costs $3$3 ÷ 5$0.60 per 100 g5 groups of 100 gPack B1000 g costs $5$5 ÷ 10$0.50 per 100 g10 groups of 100 gB has the lower unit price, not every advantage.

A costs $0.60 per 100 grams and B costs $0.50 per 100 grams. B has the lower unit price even though its whole pack costs more.

The fictional packs have identical contents. Pack A contains 500 grams for $3, while B contains 1,000 grams for $5. The comparison unit is 100 grams. A contains five of these groups, so its $3 price is divided by five, giving $0.60 per 100 grams.

B contains ten groups of 100 grams. Dividing $5 by ten gives $0.50 per 100 grams. B costs more in total but less for the same amount. If its stated price changes to $7, the unit price becomes $0.70 per 100 grams and the rate comparison reverses.

The common unit explains the arithmetic, but it does not decide what someone should buy. Needed quantity, available funds, storage and waste may matter alongside the price rate. These invented prices leave out taxes and discounts. They establish a comparison under stated conditions, not a recommendation about a real purchase.

About this explanation

Starting knowledge: Divide decimal prices by whole-number quantities and understand that rates must use matching units.

Sources

  • National Institute of Standards and Technology — Unit Pricing Guide, NIST SP 1181-2025
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