What is one common misconception students have about fractions?

Students often hold the misconception regarding the numerator or denominator being able to be larger without fully understanding what that means. This stems from a lack of comprehension about the roles that the numerator and denominator play in defining a fraction.

When students understand that the numerator represents parts of a whole while the denominator represents the whole itself, they can then grasp the concept that fractions can represent values greater than one when the numerator exceeds the denominator. For instance, in the fraction 5/3, the numerator is larger than the denominator, indicating that the value is greater than one whole.

Recognizing this allows students to explore fractions beyond just simple representations and leads them to understand operations involving fractions more deeply, such as comparing and simplifying them. This comprehension is crucial for advancing in their mathematical abilities and effectively applying fractions in various contexts.