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Hello:

A ratio usually has two units that are non-units of measure. As in, 3 blue squares to 2 red squares. And a rate usually compares two different units of measure. As in, 40 miles to 2 hours or 40 miles/2 hours.

1. If a ratio mixes a unit of measure with a non-unit of measure, as in 10 people to $5 or 10 people/$5, is this a rate or a ratio?

2. And likewise, if two of the same units of measure quantities are compared as in $5 to $10 or $5/$10, is this example a rate or ratio?

I thank you for your reply.

I am not sure what you mean by "non-units of measure," and cannot tell from your example. When you say "10 people to $5," which do you consider the non-unit of measure? The term "non-unit" is unclear, as both people and dollars are units.

A rate is a comparison of different units. For example, if the cost for 10 people is 5 dollars, the rate is (10 people)/(5 dollars) or (5 dollars)/(10 people)—and both equal 1.

A rate can also be expressed using a ratio: "The ratio of people to dollars is 10:5."

(5 dollars)/(10 dollars) is not a rate, because the units are the same. Note that the units cancel out, so the fraction can be reduced to the ratios 1:2

(5 dollars)/(10 dollars) = 5/10 = 1/2

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