Which of the following best defines 'ratios' in mathematics?

Ratios in mathematics are fundamentally understood as a comparison between two quantities. They express how much of one thing there is when compared to another, providing a way to compare sizes, amounts, or magnitudes. For example, if a recipe calls for 2 cups of flour to 3 cups of sugar, the ratio of flour to sugar is 2:3. This reflects not just the individual quantities but also their relative proportions.

Other definitions, such as methods of averaging, statistical variance measurements, or algebraic equations, do not capture the essence of what a ratio represents. Ratios focus specifically on the relationship and comparative size between two quantities, making option A the best definition in this context.