A unit rate describes the amount of one quantity corresponding to one unit of another, found by dividing the quantities and labeling the resulting rate appropriately. Comparisons require expressing situations in compatible units, including rates involving fractions and decimals, and interpreting which rate is greater rather than comparing total amounts or denominators alone; this reasoning supports proportional relationships represented in tables, graphs, and equations.
A unit rate tells how much of one quantity corresponds to exactly unit of another quantity. To compare two situations, find both unit rates using the same units.
Example:
Store A sells pound of grapes for 5.25(1.2)$7.80$. Which store has the lower price per pound?
Step 1: Identify the units to compare.
We will compare the cost for pound, so each unit rate should be in dollars per pound.
Step 2: Find Store A’s unit rate.
Convert to a decimal:
Now divide:
Store A’s unit rate is 7.00$ per pound.
Step 3: Find Store B’s unit rate.
Store B’s unit rate is 6.50$ per pound.
Step 4: Compare the unit rates.
Store B has the lower price per pound, so Store B is the better buy.
Remember: Compare the unit rates, not the total prices or the amounts of grapes.
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