# Online Fractions Simplifyer Calculator

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# Fractions Simplifyer

* gcd = greatest common divisor

## Fraction to simplified fraction table

Fraction | Simplifed Fraction |
---|---|

1/2 | 1/2 |

1/3 | 1/3 |

2/3 | 2/3 |

1/4 | 1/4 |

2/4 | 1/2 |

3/4 | 3/4 |

1/5 | 1/5 |

2/5 | 2/5 |

3/5 | 3/5 |

4/5 | 4/5 |

1/6 | 1/6 |

2/6 | 1/3 |

3/6 | 1/2 |

4/6 | 2/3 |

5/6 | 5/6 |

1/7 | 1/7 |

2/7 | 2/7 |

3/7 | 3/7 |

4/7 | 4/7 |

5/7 | 5/7 |

6/7 | 6/7 |

1/8 | 1/8 |

2/8 | 1/4 |

3/8 | 3/8 |

4/8 | 1/2 |

5/8 | 5/8 |

6/8 | 3/4 |

7/8 | 7/8 |

1/9 | 1/9 |

2/9 | 2/9 |

3/9 | 1/3 |

4/9 | 4/9 |

5/9 | 5/9 |

6/9 | 2/3 |

7/9 | 7/9 |

8/9 | 8/9 |

1/10 | 1/10 |

2/10 | 1/5 |

3/10 | 3/10 |

4/10 | 2/5 |

5/10 | 1/2 |

6/10 | 3/5 |

7/10 | 7/10 |

8/10 | 4/5 |

9/10 | 9/10 |

### Fractions Simplifier

This calculator simplifies or reduces a fraction to its simplest or lowest term. In other words, the numerator and denominator of the fraction cannot both be divided by any number to further reduce the fraction.

There are two steps in reducing the fraction:

1. The Greatest Common Divisor (GCD) is determined. The Greatest Common Divisor is the largest integer value which will divide the numerator and denominator without a remainder. This calculator uses Euclid's Algorithm to determine the Greatest Common Divisor.

2. The numerator and denominator are simply divided by the GCD.

** What is a fraction?**

A fraction is a ratio of two numbers, the numerator and the denominator. With this definition in mind, we can see that 1/2 is a fraction, 10/12 is a fraction, 3.3/6.2 is a fraction, and so on. Typically, we use whole numbers within fractions as it's more intuitive and simpler to use, especially when adding or subtracting fractions.

Additionally, you can turn any decimal value into a fraction.

Now, it's high time to ask yourself "How do you simplify fractions?" e.g., 4/8. The solution is to find a common factor of both numbers and divide them by this value. 2 is one of the common factors, so:

4 divided by 2 is 2.

8 divided by 2 is 4.

As a result, we continue by reducing the fraction 4/8 to 2/4.

In other words, we can say that 4/8 and 2/4 are equivalent fractions.

Although the outcome is correct, we usually want to reduce the fraction to its simplest form in these kinds of computations.

** Reducing fractions to lowest terms**

Reducing a fraction to its simplest form (or lowest term) is almost the same as the procedure explained in the previous section. The most significant difference is that we need to divide both the numerator and denominator by the greatest common factor (GCF). Let's take a look at the same example, 4/8:

1) Find the GCF of 4 and 8, which is 4.

2) 4 divided by 4 is 1.

3) 8 divided by 4 is 2.

4) 4/8 in simplest form is 1/2.

5) You can always convert a fraction to decimal, in this case 0.5.

And what is the simplest form of a fraction with negative numbers, e.g., -4/6? That isn't difficult at all! The only thing you need to know is that the negative number factors are the same as the positive ones multiplied by -1.

As a result, we can reduce the fraction -4/6 to -2/3.