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Reduce any fraction to lowest terms instantly.
Enter a fraction like 8/12 and get its simplest form right away, plus the decimal value. The simplifier divides both numbers by their greatest common divisor, which is exactly how your math teacher wants it done. A handy checker for homework and quick classroom answers.
Simplifying a fraction means reducing it to lowest terms — dividing the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. The fraction 24/36 and the fraction 2/3 represent exactly the same value, but 2/3 is the form you want for answers, comparisons, and further arithmetic. Simplified fractions are easier to compare (is 4/6 or 5/8 bigger? reduce to 2/3 vs 5/8 and the answer is clearer), easier to add (common denominators come from reduced forms), and are what teachers and textbooks expect as final answers.
The workhorse for finding the GCD is the Euclidean algorithm: divide the larger number by the smaller, take the remainder, and repeat with the divisor and remainder until the remainder is zero — the last nonzero divisor is the GCD. For 48 and 18: 48 / 18 = 2 remainder 12; 18 / 12 = 1 remainder 6; 12 / 6 = 2 remainder 0, so the GCD is 6. For small numbers, listing factors works fine too: the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24, and of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36 — the greatest shared factor is 12.
Two finishing details. First, the sign convention: keep any negative sign in the numerator (write -3/4, not 3/-4). Second, improper fractions simplify the same way — 45/12 reduces by GCD 3 to 15/4, which you may then write as the mixed number 3 3/4. Simplifying does not change a fraction's value; it only changes its clothes.
Both the numerator and denominator are divided by their greatest common divisor (GCD), which leaves the fraction in lowest terms.
Find the GCD of 24 and 36. Using factors: 24 = 2 x 2 x 2 x 3, and 36 = 2 x 2 x 3 x 3. The shared prime factors are 2 x 2 x 3 = 12, so the GCD is 12. Divide top and bottom: 24 / 12 = 2, 36 / 12 = 3, giving 2/3. Check: 2 and 3 share no common factor besides 1, so the fraction is fully reduced. As a decimal, 2/3 = 0.666..., exactly equal to 24/36 = 0.666... — same value, simplest form.
Find the GCD with the Euclidean algorithm: 120 / 45 = 2 remainder 30; 45 / 30 = 1 remainder 15; 30 / 15 = 2 remainder 0, so the GCD is 15. Divide: 45 / 15 = 3, 120 / 15 = 8, giving 3/8. Verify there is nothing left to reduce: 3 is prime and does not divide 8, so 3/8 is final. As a percentage this is 3/8 = 0.375 = 37.5 percent — and now you see why simplified fractions convert so cleanly: 45/120 would have been an awkward division by hand.
Find the greatest number that divides both the top and bottom evenly, then divide both by it. For 8/12 the GCD is 4, so 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2/3.
A fraction is in lowest terms when no number except 1 divides both the numerator and denominator. For example, 2/3 is in lowest terms but 8/12 is not.
Yes — it reduces the fraction to lowest terms first. An improper fraction like 10/4 becomes 5/2, which you can also read as 2½.