What is the definition of a rate?

A rate is best defined as a ratio that compares two different units. This definition is fundamental in mathematics, as rates provide a way to express how one quantity changes in relation to another. Common examples include speed (miles per hour), price (cost per item), and density (mass per volume). Each of these examples involves comparing quantities that have different units, which is the essence of what makes a rate distinct from simply a ratio that compares the same units.

While other concepts such as a measure of speed may involve rates, they do not encompass the broader definition, as they focus on specific scenarios rather than the general idea of comparing different units. Therefore, understanding rates as a comparison of different units is critical in various applications, including real-world situations such as determining travel time or calculating costs.