About

Reducing a fraction makes it easier to understand and use in further calculations. The process involves finding the largest number that divides evenly into both the top (numerator) and bottom (denominator) numbers. This number is called the Greatest Common Divisor (GCD). This tool automates the Euclidean algorithm to find the GCD and divides both parts of the fraction by it, guaranteeing the simplest form. It distinguishes between proper fractions (less than 1) and improper fractions (greater than 1), offering mixed number conversions for the latter.

Formulas

The logic relies on finding the GCD of numerator a and denominator b.

Simplified Numerator = a ÷ GCD(a, b)

Simplified Denominator = b ÷ GCD(a, b)

If the resulting numerator is greater than the denominator, it can be expressed as:

Mixed = q rd

Reference Data

Fraction	GCD	Simplified	Type
48	4	12	Proper
69	3	23	Proper
1215	3	45	Proper
1824	6	34	Proper
104	2	52	Improper
10010	10	10	Whole
12832	32	4	Whole
2114	7	32	Improper

Frequently Asked Questions

It is an efficient method for computing the GCD. It repeatedly replaces the larger number with the remainder of dividing the larger by the smaller, until the remainder is zero. The last non-zero remainder is the GCD.

Yes. If either the numerator or denominator is negative, the negative sign is typically moved to the front or the numerator in the simplified result. Two negatives make a positive.

You likely entered 0 as the denominator. Division by zero is undefined in mathematics because no number multiplied by 0 can equal a non-zero numerator.

Prime numbers are numbers divisible only by 1 and themselves (e.g., 2, 3, 5, 7, 11). Simplification often involves cancelling out common prime factors.