Sequentially divide the numerator and the denominator by the common factors until they have no common factor other than 1. Determine the common factors of the numerator and the denominator. Find all the factors of the numerator and the denominator of a given fraction. The above algorithm can be reformulated as follows: So, this fraction can be reduced to the lowest terms by dividing the numerator and the denominator by 21 giving as a result the fraction 2/11. The greatest common divisor of 42 and 231 is the number 21.Ģ. If the found greatest common divisor is not equal to 1 then after the division you will get a simplified form if the initial fraction.Īs another example, let’s consider the fraction 42/231.ġ. ![]() Divide the numerator and the denominator by this greatest common divisor. ![]() Find the greatest common divisor of the numerator and the denominator of a given fraction. In this example, 13 was the greatest common factor for the numerator and the denominator of 39/91.Īs a result, we come to the following simple algorithm for simplifying fractions. So, 3/7 is said to be an irreducible fraction. It is important to note that the fraction 3/7 cannot be simplified further because the numerator and the denominator of this fraction do not have a common divisor other than 1. As a result of this division, we get the simplified fraction 3/7. To make sure that both of these fractions are equivalent, just notice that the numerator and the denominator of the fraction 39/91 are simultaneously divisible by 13: 39/13 = 3 and 91/13 = 7. For example, it is much easier to carry out calculations with the fraction 3/7 than with the fraction 39/91, although both fractions are equivalent in a sense that they express the same part of the whole. When working with fractions it is always more convenient to deal with fractions reduced to their simplest form. ![]() ![]() Our reduce fraction calculator also converts an improper fraction into a mixed number (mixed fraction). A fraction is irreducible when the greatest common factor of their numerator and denominator equals to 1. Fraction simplification (or reducing fractions) is a process of presenting a fraction in the form of an irreducible proper fraction.
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