The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". The cookie is used to store the user consent for the cookies in the category "Analytics". This cookie is set by GDPR Cookie Consent plugin. These cookies ensure basic functionalities and security features of the website, anonymously. Necessary cookies are absolutely essential for the website to function properly. It also deals with improper fractions and performs mixed fraction simplification. Our Simplify Fraction Calculator can perform these tedious operations in no time. Therefore, the reduced form of 42/231 is 2/11. Obviously, we cannot further divide by 7 or 21. So, we will continue to divide by 7 and will have (14 ÷ 7) / (77 ÷ 7) = 2/11. Let’s start dividing the numerator and denominator by 3: (42 ÷ 3) / (231 ÷ 3) = 14/77. The common factors of the numerator and the denominator are: 1, 3, 7, 21.ģ. In the above example of the fraction 42/231, you can then proceed as follows.ġ. 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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