Simplify Fraction Calculator

The simplify fraction calculator reduces each fraction to its simplest form and shows the Greatest Common Factor (GCF) of the numerator and denominator. With the simplify fraction calculator you can practice simplifying fractions, also called reducing fractions. To reduce a fraction, you divide both numerator and denominator by the greatest common factor (GCF). This is also known as "writing a fraction in lowest terms". Writing a fraction in its simplest form means that both top and bottom numbers can no longer be divided by the same whole number other than 1. Make sure you have the simplest form of the fraction, with the numerator and denominator as small as possible, by using this simplify fraction calculator. Enter the numerator above the line and the denominator below the line and click the "Simplify Fraction" button to perform the calculation. The simplify fraction calculator reduces the fraction to its simplest form and shows you the GCF and the work and steps of the calculation.

Simplify Fraction Calculator (with steps)

Work and steps simplifying fraction

The simplify fraction calculator has not yet performed a calculation. Enter the numerator and denominator of the fraction you want to reduce. The complete work and steps of the reduction of the fraction will be shown here, including the Greatest Common Factor (GCF) of the numerator and denominator.

General explanation of simplifying fractions

To simplify a fraction, look for the greatest common factor (GCF) of the numerator and the denominator. In other words, what is the largest number by which both the numerator and denominator can be divided. Sometimes it is easy to see what the greatest common factor of the numerator and denominator is. If this is not the case, you can also do this step by step. You then divide the numerator and denominator by the same number until you are left with the simplest form of the fraction, also called irreducible fraction. The numerator and denominator can then no longer be divided by the same number (except 1).

Simplify fractions using Prime numbers

There are several methods available to find the GCF and simplify a fraction. We will now show you the method using prime numbers. A prime number is a number that is only divisible by itself and 1

The list of prime numbers is infinite: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 53, etc.

Let's simplify the fraction below:

Rewrite the numerator and denominator as a product of prime numbers

We will now rewrite both the numerator and the denominator as a product of only prime numbers (any number can be written as a product of only prime numbers).

Numerator:

2 x 12

2 x 2 x 6

2 x 2 x 2 x 3

Denominator:

2 x 30

2 x 2 x 15

2 x 2 x 3 x 5

2 x 2 x 2 x 3

2 x 2 x 3 x 5

Ignore the same factors

Now that both the numerator and denominator have been rewritten as a product of prime numbers, we can cancel out the numbers that appear in both the numerator and the denominator.

2 x 2 x 2 x 3

2 x 2 x 3 x 5

The fraction has now been reduced to its simplest form, leaving us with 2 as the numerator and 5 as the denominator. We can calculate the GCF by multiplying the numbers that we have just crossed out in both the numerator and the denominator:

GCF

2 x 2 x 3

Irreducible fraction

A fraction is the undivided result of dividing two numbers. The number above the fraction bar is called the numerator, and the number below the fraction bar is the denominator. A fraction is in its simplest form (irreducible, in its lowest terms) when the numerator and denominator have no common factors other than 1. In that case the greatest common factor (also called greatest common divisor or highest common factor) is 1.

On the other hand, a reducible fraction is a fraction that has some common factor and can be converted into its simplest (irreducible fraction) form by cancelling out that common factor (greatest common divisor). To reduce the fraction both the numerator and denominator have to be divided by that common factor.

Use the simplify fraction calculator to check if a fraction is irreducible or reduce the fraction and find the greatest common divisor.