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Reduce fractions to lowest terms instantly using the greatest common divisor (GCD) method
GCD: 4
Find the GCD of numerator and denominator, then divide both by the GCD to get the simplified fraction.
Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 12/16 simplifies to 3/4 by dividing both by 4. The simplified fraction represents the same value but uses smaller, easier-to-work-with numbers.
The GCD (Greatest Common Divisor) is the largest number that divides evenly into both the numerator and denominator. You can find it using the Euclidean algorithm, prime factorization, or listing factors. For 12 and 16: factors of 12 are 1,2,3,4,6,12 and factors of 16 are 1,2,4,8,16, so GCD is 4.
Not all fractions can be simplified further. A fraction is already in simplest form when the numerator and denominator share no common factors other than 1 (they are coprime). For example, 3/7 cannot be simplified because 3 and 7 share no common factors except 1.
Simplifying and reducing fractions mean the same thing—converting a fraction to its lowest terms by dividing both numerator and denominator by their GCD. Both terms are used interchangeably in mathematics. The process and result are identical regardless of which term you use.
Simplify improper fractions (where numerator ≥ denominator) the same way as proper fractions: find the GCD and divide both parts by it. For example, 24/18 becomes 4/3 by dividing both by 6. You can also convert to a mixed number after simplifying: 4/3 = 1⅓.
Simplified fractions are easier to understand, compare, and use in calculations. 3/4 is clearer than 75/100. Simplified fractions make addition, subtraction, and comparison easier. They're also the standard form for final answers in mathematics—teachers and textbooks expect fractions in lowest terms.
Yes, algebraic fractions can be simplified by factoring and canceling common factors. For example, (6x²)/(9x) simplifies to (2x)/3 by canceling the common factor of 3x. The process is the same: find common factors in numerator and denominator, then divide both by those factors.
If a fraction is already in simplest form (GCD = 1), the simplified result equals the original fraction. For example, 5/7 is already simplified because 5 and 7 share no common factors. The calculator will show the same fraction, confirming it cannot be reduced further.