**Introduction To Fraction Reducer Calculator:**

The Fraction Reducer Calculator is a web-based tool designed to simplify and reduce fractions to their simplest form. It provides users with a convenient way to input a numerator and denominator and then calculates and displays the reduced fraction.

**Working Of The Fraction Reducer Calculator:**

**Input:**

Users input the numerator and denominator into the designated fields.

**Validation:**

The calculator checks if the entered values are valid numbers and ensures the denominator is not zero.

If the inputs are invalid, an alert is displayed, prompting users to enter valid numbers.

**Reduction Process:**

The calculator uses the Greatest Common Divisor (GCD) algorithm to find the greatest common factor between the numerator and denominator.

The GCD is then used to divide both the numerator and denominator, reducing the fraction to its simplest form.

**Display:**

The reduced fraction is presented to the user in a clear and readable format.

**Formula For Fraction Reducer Calculator:**

The Fraction Reducer Calculator employs the Greatest Common Divisor (GCD) to reduce fractions. The GCD is calculated using the recursive Euclidean algorithm:=

{if ≡0(,mod )otherwise *GCD*(*a*,*b*)={ *bGCD* (*b*,*a*mod*b*)if *a*≡0otherwise

Once the GCD is determined, the reduced numerator and denominator are obtained by dividing the original values by the GCD:

Reduced Numerator=NumeratorGCDReduced Numerator=GCDNumerator Reduced Denominator=DenominatorGCDReduced Denominator=GCDDenominator

**Summary:**

The Fraction Reducer Calculator simplifies the process of reducing fractions by providing a user-friendly interface. It ensures that users input valid numerical values, applies the GCD algorithm to find the greatest common factor, and then displays the reduced fraction. This calculator is a handy tool for anyone working with fractions who wants a quick and accurate way to simplify them.