How can a fraction be defined in mathematical terms?

A fraction is defined in mathematical terms as a ratio of two numbers. This means that it represents a division where the numerator (the top number) indicates how many parts are being considered, while the denominator (the bottom number) indicates how many equal parts make up a whole. For example, in the fraction 3/4, 3 represents the number of parts and 4 represents the total number of equal parts that make up the whole.

Defining a fraction this way emphasizes its fundamental relationship to division and ratios, which is critical in various mathematical applications, such as comparing quantities, performing arithmetic operations, and understanding proportional relationships. The clarity of this definition aligns with the concept that fractions describe a part of a whole in a very precise manner, making them essential in mathematics.