This online Simplify Fraction Calculator is a free online tool that offers the possibility to simplify a fraction. It allows simplifying proper and improper fractions, as well as mixed numbers (mixed fractions), both positive and negative. The numerator and denominator in a fraction are separated by the slash symbol (/). It is important to leave space between the whole number and the fraction part of a mixed number. In case of a negative number, the minus sign (-) precedes the fraction or the whole number in a mixed fraction without space between them.
Fraction Simplification
Fraction simplification (or reducing fractions) is a process of presenting a fraction in the form of an irreducible proper fraction. A fraction is irreducible when the greatest common factor of their numerator and denominator equals to 1. Our reduce fraction calculator also converts an improper fraction into a mixed number (mixed fraction).
How to Simplify Fractions
When working with fractions it is always more convenient to deal with fractions reduced to their simplest form. 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.
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. As a result of this division, we get the simplified fraction 3/7.
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. So, 3/7 is said to be an irreducible fraction. In this example, 13 was the greatest common factor for the numerator and the denominator of 39/91.
As a result, we come to the following simple algorithm for simplifying fractions.
Step 1. Find the greatest common divisor of the numerator and the denominator of a given fraction.
Step 2. Divide the numerator and the denominator by this greatest common divisor.
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.
As another example, let’s consider the fraction 42/231.
1. The greatest common divisor of 42 and 231 is the number 21.
2. 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 above algorithm can be reformulated as follows:
Step 1. Find all the factors of the numerator and the denominator of a given fraction.
Step 2. Determine the common factors of the numerator and the denominator.
Step 3. Sequentially divide the numerator and the denominator by the common factors until they have no common factor other than 1.
In the above example of the fraction 42/231, you can then proceed as follows.
1. The factors of the numerator 42 are 1, 2, 3, 6, 7, 14, 21, 42, and the factors of the denominator 231 are 1, 3, 7, 11, 21, 33, 77, 231.
2. The common factors of the numerator and the denominator are: 1, 3, 7, 21.
3. Let’s start dividing the numerator and denominator by 3: (42 ÷ 3) / (231 ÷ 3) = 14/77. We can not divide by 3 any further. So, we will continue to divide by 7 and will have (14 ÷ 7) / (77 ÷ 7) = 2/11. Obviously, we cannot further divide by 7 or 21. Therefore, the reduced form of 42/231 is 2/11.
Our Simplify Fraction Calculator can perform these tedious operations in no time. It also deals with improper fractions and performs mixed fraction simplification.
Related calculators
If you need to perform basic math operations with fractions please check out our Mixed Fractions Calculator. To compare two fractions you can use our Comparing Fractions Calculator.