Which of the following describes the relationship between two quantities showing how many times one value contains another?

The choice that describes the relationship between two quantities, indicating how many times one value contains another, is the ratio. A ratio is a mathematical expression that compares two values by division, effectively showing the relative size of one quantity to another. It communicates how many times one value can be found within the other, such as in the context of comparing ingredients in a recipe or speeds of different vehicles.

In scenarios involving ratios, we typically express it in the form 'a to b,' indicating how much of one quantity relates to another. This concept is widely used in various fields including engineering, mathematics, and science to represent comparative relationships in a clear and concise manner.

While proportions, fractions, and percentages are related mathematical concepts, they do not specifically indicate how many times one value contains another in the same direct way that a ratio does. Proportions deal with the equality of two ratios, fractions represent parts of a whole, and percentages describe a quantity out of 100, which is a different form of relationship.