Who is asking: Other
Level: All
Question:
I have a question regarding rates and ratios.
What is the difference between a ratio and a rate?
I thank you for your reply and answer.
Hi Kenneth,
Ratio, proportion, percent, quotient, fraction, rate -- there are dozens of ways of describing the same thing. The reason for this abundance of terminology is that rational numbers arise naturally in daily life, so special terminology arose that was convenient for each special purpose.
The choice of the terms rate or ratio in a statement has more to do with English usage than mathematical meaning. The term rate is usually used when something is changing. An ant might be crawling across my floor at the rate of one foot every two seconds. I wouldn't say that it is moving so that the ratio of its distance in feet to time in seconds is 1 to 2, although both statements have the same meaning. Similarly I might say that the ratio of the number of girls in my class to the number of boys is 5 to 3, but I wouldn't try to express this as a rate as nothing is changing.
When we use the term rate the "denominator" doesn't have to be time. If I am going on a trip of 250 miles and the change in elevation from my home to where I am going is 1000 feet then during the trip my elevation changes, on the average, at the rate of 4 feet per mile.
Penny