Explanation:
"Unit rate" means the denominator of the rate is 1 unit.
When we talk about unit rates, we're usually interested in the ratio of one thing to another. Sometimes, the values of interest are something other than 1, so the rate must be computed by dividing one by the other.
"Rate" is another way to say "ratio". "Per" can be taken to mean "divided by."
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So, for example, to find the rate "dollars per pound", we divide the number of dollars by the number of pounds. (dollars divided by pounds)
$6/(2 lb) = (6/2) $/lb= $3/lb
The denominator of $3/lb is 1 lb, so we call this the unit rate.
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The unit rate in the above example can also be expressed in terms of pounds per dollar. That form would help answer the question, "how many pounds can we buy with $6?" In that form, the unit rate is calculated as ...
(2 pounds)/(6 dollars) = (1/3) pound/dollar
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This should help you see that when you are given two values and asked, "what is the unit rate?", you need to make a judgment as to the unit rate of interest. <em>The denominator unit is the independent variable</em>, which depends on the problem and the intended use of the unit rate.
When problems involve time, quite often, the time unit is the one that is wanted in the denominator: feet per second, kilometers per hour, liters per minute, that sort of thing.
Sometimes, the problem may require the unit rate to have time in the numerator: days per house (for construction time, for example). "Rate of completion" problems are often described using time per job, but work rates need to be added using jobs per time, so you have to make sure you're using the unit rate appropriate for the problem at hand.
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In most problems that involve units, I find it useful to keep the units with the numbers: 3 $/lb, not just 3. That way, I can tell if the math I'm doing results in appropriate units. Units get multiplied, divided, canceled, added just like any other variables. If you find you're trying to add feet to minutes, you know you're doing something wrong.
