Answer:
A rate is a <em>ratio</em> between two related quantities.
Step-by-step explanation:
Often, the rate has associated units. Often, the word "per" is used to separate the quantities of the ratio, as in "miles per hour" or "dollars per gallon". In this context, "per" means "divided by."
If the units of the quantities are the same, they cancel, and the rate is a "pure number" (a number with no units). A tax rate, for example, is some number of dollars per dollar, a pure number, often expressed as a percentage.
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<em>Unit rates</em>
A "unit rate" is a rate in which one of the quantities is 1 unit. Usually, that is the denominator quantity. A rate that is not a unit rate can be made to be a unit rate by carrying out the division of the numbers.
For example, 3 dollars for 2 pounds ($3/(2#)) is expressed as the unit rate $1.50 per pound.
Some years ago, grocery stores began putting unit rates on price tags so that prices could be compared more easily (at least some of the time). Sometimes the comparison is complicated by different units being used for similar products.
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<em>Percentages</em>
A percentage is the ratio of similar measurements, expressed with a denominator of 100. ("Cent" means "hundred" in "per cent.") The "/100" in the ratio is generally abbreviated as the symbol "%". Since the ratio is of quantities with similar units, it is a pure number.
Occasionally, you will find the idea of "percent" used to relate quantities that are measured <em>differently</em>. For example, a drug that has a concentration of x mg/(100 mL) may be specified as an x% solution.
The proportion of items of significantly different density may be specified either by weight or by volume. That is a mixture that is x% "by weight" may be y% "by volume" (x≠y). The choice of weight or volume will generally depend on the typical way an amount of the mixture is measured.
