HesapHanem

Fraction Simplifier

How do I simplify a fraction?

Result

3/8
0.38
37.50%

How it is calculated

The numerator and denominator are reduced with the Euclidean algorithm. It finds the greatest common divisor g = gcd(|num|, |den|) by repeated remainders, then divides both numbers: simplified = (num ÷ g) / (den ÷ g). If the denominator is negative, both signs are flipped, so the minus sign always ends up in front of the numerator (6/-8 becomes -3/4, and -6/-8 becomes 3/4).

The decimal is num ÷ den rounded to two places, and the percent is that value times 100, also to two places. Only whole numbers are accepted: 2.5 as a numerator, a zero denominator or an empty field returns no result. A numerator of 0 gives 0/1. Improper fractions such as 22/7 stay improper, and no mixed number is produced.

Worked example

Simplify 18/48. The remainders go 48 mod 18 = 12, 18 mod 12 = 6, 12 mod 6 = 0, so the greatest common divisor is 6. Dividing both parts gives 18 ÷ 6 = 3 and 48 ÷ 6 = 8, so the simplified fraction is 3/8. As a decimal, 3 ÷ 8 = 0.375, which the tool shows rounded to 0.38. As a percentage the value is 37.5%, shown as 37.50%.

Try this example →

Common mistakes

  • Treating the decimal row as exact: 3/8 is exactly 0.375, but the tool rounds to two places and shows 0.38, and 1/3 shows 0.33. Use the percent row or divide by hand when you need more digits.
  • Entering a decimal in the numerator or denominator: 2.5/4 is rejected, so multiply both parts by 10 and enter 25/40 instead.
  • Typing a mixed number as one value: 2 1/2 cannot be entered, so convert it to 5/2 first. An improper result like 22/7 is not turned back into a mixed number.
  • Expecting a zero denominator to give infinity: division by zero is undefined, and the tool returns no result.
  • Looking for the minus sign in the denominator: negatives are always moved to the numerator, so 6/-8 is shown as -3/4.

About this calculator

This tool reduces a fraction to its lowest terms by dividing both the numerator and denominator by their greatest common divisor, and also converts the simplified fraction into its decimal and percentage equivalents. A fraction like 24/36 and its simplest form 2/3 represent exactly the same value, but the simplified version is easier to read, compare and work with.

Students use it constantly to check homework answers after simplifying fractions by hand, since a small arithmetic slip in finding the greatest common divisor produces a wrong "simplest form" that's easy to miss without a second check. It is also useful in cooking when scaling a recipe produces an awkward fraction, in construction and woodworking when converting measurements between fraction and decimal form, and any time two fractions need to be compared quickly by converting them to a common, simplified basis.

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Comments (1)

  • Editorial team

    Because the decimal is rounded to two places, 1/3 shows as 0.33 and 2/3 as 0.67, so keep the simplified fraction when you need an exact value for later steps. Zero over any non-zero number reduces to 0/1, and a minus sign always moves to the numerator. Improper fractions stay as they are, not turned into mixed numbers. Would a mixed-number view be useful in your work?

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