What is a rate? What is a ratio? Are all rates ratios, and are all ratios rates?

Answer 1

Rates and ratios essentially the same thing.

The usage in English is slightly different, but if you peel back the cover, it turns out they are talking about the same underlying things, so they are the same things.

A ratio is a fraction, so usage-wise it refers more to the arithmetic.

A rate expresses the relationship between two things (rate of money per item, rate of change of distance per time, etc.) But, rates are expressed as fractions, so rates are always ratios. And ratio fractions in turn indicate rates.

Some people might say that the ratio of boys to girls in a room would not be a rate. But, it is a rate, it is the average rate at which boys and girls entered the room. And by a concept called the Mean Value Theorem, if it is the average rate, then it is provable there was some point in time when it was the actual rate.

Is the ratio of two pure dimensionless numbers a rate? The ratio of 3 to 4? Sure. Just like the pure number 6 is also a count (of six things), a pure ratio of two numbers expresses some rate somewhere.

It is useful to talk about the nuances in order to understand, but with the understanding comes the realization that they are the same things.

Answer 2

A rate tells a value per a different value

m/h (mph) miles per hour

A ratio is when you compare two numbers to each other

11 boys 13 girls
ratio of boys to girls
11:13 11 to 13 11/13

all rates are ratios because you're comparing two different things to eachother like the m/h
you're going so many miles per hour.

say 10 miles/hour the ratio of miles to hours is
10:1 10 to 1 or 10/1

not all ratios are rates because you may not be trying to find the percent or fraction of one thing to another but simply comparing the boys to girls...

11 boys 13 girls

you don't have 11boys for every 13 girls because the rate may change at no constant value the next day there can be 15 boys and 13 girls.

Answer 3

A rate is something per fixed measure. 20 per thousand is a rate. ratio is a comparison - like 15:20 . rates can be ratios. all ratios aren't rates.

Answer 4

Rate and ratio are two different concepts but they are same as far as calculations are concerned. Rate expresses the measure of one quatity for a standard measure of a reference quantity. Ratio is comparison of two similar quantities.
Some people are not following the strict meaning of ratio and using the term for two different quantities. But the term ratio should be used for dissimilar quantities. It should be used for similar quantities only.