What is the mathematical definition of a rational number?

A rational number is defined mathematically as a number that can be expressed as the quotient or fraction of two integers, where the numerator is an integer and the denominator is a non-zero integer. This definition encompasses a wide range of numbers, including integers, whole numbers, and finite and repeating decimals.

The ability to express a number as a fraction is what distinguishes rational numbers from irrational numbers, which cannot be represented in this way. For example, the number ( \frac{3}{4} ) is rational because it is the quotient of the integers 3 and 4. Additionally, the integer 5 can also be considered rational since it can be expressed as ( \frac{5}{1} ). Thus, any number that meets the criteria of being expressible as a fraction of two integers fits the definition of a rational number, confirming that the correct answer is the one stating that a rational number can be written as a fraction of two integers.