Simplify Fractions Calculator
Free fraction simplifier: reduce any fraction to its lowest terms with the greatest common divisor, and see it as a mixed number and a decimal.
Step by step
What it does
A fraction is in its simplest form, or lowest terms, when the numerator and the denominator have no common divisor other than 1. To get there, divide both by their greatest common divisor (GCD): 84/126 has a GCD of 42, so it simplifies to 2/3. The value does not change, only the way it is written.
How to use it
- Type the fraction, for example 84/126.
- Read the greatest common divisor of the numerator and the denominator.
- Read the simplified fraction, the mixed number and the decimal.
The arithmetic runs in your browser. Nothing you type is sent anywhere and nothing is stored, so you can use these with real numbers.
Frequently asked questions
How do I find the greatest common divisor?
With Euclid's algorithm: divide the larger number by the smaller and keep the remainder, then repeat with the smaller number and the remainder until the remainder is 0. For 126 and 84: 126 = 84 + 42, then 84 = 2 × 42 + 0, so the GCD is 42.
Can I simplify a fraction step by step instead?
Yes. Dividing by any common factor, such as 2, then 3, then 7, reaches the same result. Dividing by the GCD gets there in one step.
Should an improper fraction be turned into a mixed number?
Both are correct. 7/4 is simplified already; 1 3/4 is the same value written as a mixed number. Many teachers prefer improper fractions in algebra and mixed numbers in everyday measures.
What about negative fractions?
The sign goes in front of the fraction: −10/4, 10/−4 and −(10/4) are all the same number, and all simplify to −5/2.
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Wikipedia — Fraction
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