Difference Between Numerator and Denominator

Numerator vs Denominator

A number which can be represented in the form of a/b, where a and b (≠0) are integers, is known as a fraction. a is called the numerator and b is known as the denominator. Fractions represent parts of whole numbers and belong to the set of rational numbers.

The numerator of a common fraction can take any integer value; a∈ Z, while the denominator can only take integer values other than zero; b∈ Z – {0}. The case in which denominator is zero is not defined in modern mathematical theory and considered invalid. This idea has an interesting implication in the study of calculus.

It is commonly misinterpreted that when the denominator is zero the value of the fraction is infinite. This is not mathematically correct. In every situation, this case is excluded from the possible set of values. For example take a tangent function, which approaches infinity when the angle approaches π/2 . But the tangent function is not defined when the angle is π/2 (It is not in the domain of the variable). Therefore, it is not reasonable to say that tan π/2 = ∞. (But in early ages, any value divided by zero was considered zero)

The fractions are often used to denote ratios. In such cases, the numerator and the denominator represent the numbers in the ratio. For example consider the following 1/3 →1:3

The term numerator and denominator can be used for both surds with fractional form (like 1/√2, which is not a fraction but an irrational number) and to rational functions such as f(x)=P(x)/Q(x) . The denominator here is also a non-zero function.

Numerator vs Denominator

• The numerator is the top (the part above the stroke or the line) component of a fraction.

• The denominator is the bottom (the part below the stroke or the line) component of the fraction.

• The numerator can take any integer value while the denominator can take any integer value other than zero.

• The term numerator and denominator can also be used for surds in the form of fractions and to rational functions.