CalculatorFly

Simplify Fractions & Mixed Numbers Online

The Simplify Fractions Calculator is a handy tool for students, teachers, and anyone needing to reduce fractions or mixed numbers to their simplest form. Simplifying a fraction means expressing it using the smallest possible whole numbers for the numerator and denominator, without changing its value.

📝 How to Use This Calculator

To simplify a fraction or mixed number:

1. Enter the Whole Number (Optional): If you're simplifying a mixed number (e.g., 2 ¾), enter the whole part here. If it's just a fraction (e.g., ¾), you can leave this blank or enter 0.
2. Enter the Numerator: This is the top number of the fractional part.
3. Enter the Denominator: This is the bottom number of the fractional part. It cannot be zero.
4. Click "Simplify Fraction": The calculator will show the step-by-step simplification.

The calculator will display the original input, its conversion to an improper fraction, the simplification process by dividing by the Greatest Common Divisor (GCD), and the final result as both a simplified improper fraction and a mixed number (if applicable), along with its decimal equivalent.

🔢 The Mathematics of Simplifying Fractions

The process involves a few key steps:

1. Convert to an Improper Fraction (if a mixed number):A mixed number like W n/d (where W is whole, n is numerator, d is denominator) is converted to an improper fraction using the formula: ((W × d) + n) / d. For example, 2 ¾ becomes ((2 × 4) + 3) / 4 = 11/4.
2. Find the Greatest Common Divisor (GCD):The GCD (also known as Greatest Common Factor or GCF) is the largest positive integer that divides both the numerator and the denominator of the improper fraction without leaving a remainder.
3. Divide by the GCD:Both the numerator and the denominator of the improper fraction are divided by their GCD. This step reduces the fraction to its lowest terms. For example, if the fraction is 10/15, the GCD is 5. So, (10 ÷ 5) / (15 ÷ 5) = 2/3.
4. Convert Back to a Mixed Number (if the simplified fraction is improper):If the simplified fraction's numerator is still larger than its denominator (e.g., 7/3), it's converted back to a mixed number. The whole part is floor(numerator / denominator), the new numerator is numerator mod denominator, and the denominator remains the same. For example, 7/3 becomes 2 ⅓.

💡 Frequently Asked Questions (FAQ)

Why do we simplify fractions?

Simplifying fractions makes them easier to understand, compare, and use in further calculations. It is the standard way to present a fractional answer in mathematics.

What is the Greatest Common Divisor (GCD)?

The GCD is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6. Finding the GCD is the key to simplifying a fraction.