Comparing unit rates means determining and interpreting the amount of one quantity associated with one unit of another, then using equivalent rates to decide which relationship represents more or less per unit. Quantities may be represented as ratios, fractions, decimals, tables, or double number lines; the comparison requires attending to the order and units rather than comparing numbers alone, and supports proportional reasoning in measurement, pricing, and later algebra.
A unit rate tells how much of one quantity goes with 1 unit of another quantity. To compare unit rates, make sure both rates use the same units and put the quantities in the same order.
Example:
Store A sells 3 notebooks for $6.75. Store B sells 5 notebooks for $10.50. Which store has the lower price per notebook?
Find Store A’s unit rate.
Divide the total cost by the number of notebooks:
Store A charges $2.25 per notebook.
Find Store B’s unit rate.
Divide the total cost by the number of notebooks:
Store B charges $2.10 per notebook.
Compare the unit rates.
Since $2.10 per notebook is less than $2.25 per notebook, Store B has the lower price.
Always check that you are comparing the same kind of unit rate—in this case, dollars per notebook, not just the total prices.
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