Compare situations using unit rates

Unit-rate comparison means expressing each situation as an equivalent rate for one unit of a specified quantity—such as dollars per item, miles per hour, or liters per minute—and determining which represents more, less, or the same rate. The reasoning applies division and equivalent ratios to positive whole-number, decimal, and fraction quantities represented in contexts, tables, equations, or graphs, while distinguishing a rate from a total amount; generalized functions and compound rates are beyond this scope.

Detailed Explanation: Compare situations using unit rates

To compare two situations, first find the unit rate for each one. A unit rate tells how much happens for 1 unit of something.

For example:

Maya bikes $(18)$ miles in $2$ hours. Luis bikes $(25)$ miles in $3$ hours. Who bikes faster?

Step 1: Find Maya’s unit rate

Divide the distance by the time:

18 \div 2 = 9

Maya’s rate is $9$ miles per hour, or

9\text{ miles per hour}

Step 2: Find Luis’s unit rate

Divide his distance by his time:

25 \div 3 = 8\frac{1}{3}

Luis’s rate is $(8\frac{1}{3})$ miles per hour.

Step 3: Compare the unit rates

9 > 8\frac{1}{3}

Maya bikes faster because she travels more miles in 1 hour.

Remember to compare rates, not total amounts. Luis traveled farther altogether, but Maya traveled farther during each single hour.

Learn by doing: Compare situations using unit rates

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