What is the definition of an improper fraction?

An improper fraction is defined as a fraction in which the numerator is greater than the denominator. This means that the value of the fraction is equal to or greater than one. For example, the fraction 7/4 is improper because 7 (the numerator) is greater than 4 (the denominator), indicating that the quantity represented is more than a whole.

In contrast, a proper fraction features a numerator that is less than the denominator, making its value less than one. Additionally, a fraction that equals one has a numerator and denominator that are equal, which falls outside the definition of an improper fraction. Lastly, the ability to simplify a fraction does not determine whether it is proper or improper; simplification is based on the common factors of the numerator and denominator rather than their relative sizes. Hence, the correct description of an improper fraction is one where the numerator exceeds the denominator.