Enter numerator and denominator to reduce the fraction to its simplest form
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Denominator =
Result
Original Fraction
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Simplest Form
Step-by-Step Derivation
Fraction Simplification Formula
a/b = (a÷GCD(a,b)) / (b÷GCD(a,b)), where GCD is the Greatest Common Divisor
Divide both numerator and denominator by their GCD to get the simplest form. In a reduced fraction, the numerator and denominator are coprime (GCD = 1).
⚠Note: The denominator cannot be 0. If the numerator is 0, the simplified fraction is 0. If the numerator and denominator are already coprime (GCD = 1), no simplification is needed.
What Is Fraction Simplification?
Fraction simplification (reducing fractions) is the process of converting a fraction into its simplest form where the numerator and denominator are coprime. It is one of the most fundamental and commonly used skills in algebra.
Greatest Common Divisor (GCD)
GCD(a, b) is the largest number dividing both a and b. For 36 and 48, GCD = 12, so 36/48 = (36÷12)/(48÷12) = 3/4.
Euclidean Algorithm
GCD(a, b) = GCD(b, a mod b). For example, GCD(48,36) → GCD(36,12) → GCD(12,0) → 12.
Coprime
Two numbers are coprime if their GCD is 1. The numerator and denominator of a reduced fraction are always coprime, e.g., 3/7, 5/9, 1/2.
Negative Fractions
The negative sign is conventionally placed on the numerator. For example, -3/6 = -(3/6) = -1/2, and -4/-8 = 1/2 (negative × negative = positive).
A fraction is in simplest form when its numerator and denominator have a GCD of 1. For example, 3/4, 2/5, 5/7 are all simplest-form fractions that cannot be reduced further.
How do you find the Greatest Common Divisor (GCD)?▼
Using the Euclidean algorithm: GCD(a,b) = GCD(b, a mod b), iterating until the remainder is 0. The last non-zero remainder is the GCD. For example, GCD(48,36) → GCD(36,12) → GCD(12,0) → 12.
Is a fraction with denominator 0 meaningful?▼
No, a fraction with denominator 0 is mathematically undefined. The divisor (denominator) cannot be zero.
How to simplify a negative fraction?▼
For negative fractions, keep the negative sign on the numerator. For example, -3/6 = -(3/6) = -1/2. For -4/-8, the two negatives cancel to give 1/2. First compute GCD using absolute values, then handle the sign.
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