A fraction represents a numerical value, which defines the parts of a whole. Suppose a number “a” has to be divided into 8 parts, then it is represented as a/8. Here, the fraction a/8 represents 1/8th part of a. The general form of a fraction is a/b such that a ≠ 0 and a, b are positive integers. The different types of fractions are defined based on the numerical value of the numerator and denominator. Also, various arithmetic operations such as addition, subtraction, multiplication and division can be performed on fractions. When coming to the inverse of a fraction, the inverse exists in two ways, i.e. under addition and multiplication.
Additive Inverse of a Fraction: When two fractions add up to zero, then the two fractions are called additive inverse of one another. For example, ¼ and -¼ are two fractions such that (¼) + (-¼) = 0. Where -¼ is the additive inverse of a fraction ¼.
General form: -a/b is the additive inverse of a/b since (a/b) + (-a/b) = (a/b) – (a/b) = 0.
Multiplicative Inverse of a Fraction: When the product of two fractions is 1, then the two fractions are called multiplicative inverse of one another. For example, 3/5 and 5/3 are two fractions such that (3/5) × (5/3) = 1. Here, 5/3 is the multiplicative inverse of 3/5. In other words, the multiplicative inverse of a fraction obtained by interchanging the numerator and denominator.
General form: b/a is the multiplicative inverse of a/b since (a/b) × (b/a) = 1
Inverse fractions are fractions that when added together equal 0 in case of additive inverse or when multiplied together equal 1, in case of multiplicative inverse.