About the Simplify Fractions Calculator
This simplify fractions calculator reduces a fraction to its simplest form (lowest terms). Enter a numerator and denominator and it finds the greatest common factor (GCF), divides both parts by it, and shows the result as a proper or improper fraction, a mixed number and a decimal.
It is handy for checking homework, reducing recipe or measurement ratios, and cleaning up answers from fraction arithmetic. The table walks through the Euclidean algorithm so you can see exactly how the GCF was found rather than just trusting the answer.
Negative fractions are supported: the sign is always moved to the numerator, so 3/−4 is shown as −3/4. A denominator of zero is undefined and returns no result.
How to use the simplify fractions calculator
- 1Enter the numerator (top number).
- 2Enter the denominator (bottom number) — it cannot be zero.
- 3Read the fraction in simplest form and the GCF used to reduce it.
- 4Check the mixed number and decimal if you need another format.
- 5Follow the Euclidean steps in the table to see how the GCF was found.
Formula and method
A fraction is in lowest terms when the numerator and denominator have no common factor except 1. Dividing both by their greatest common factor (GCF) gets there in a single step, and the value of the fraction does not change because you are dividing by GCF/GCF = 1.
The GCF is found with the Euclidean algorithm: divide the larger number by the smaller, replace the larger with the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF. This is far faster than listing every factor, especially for big numbers.
- a
- Numerator
- b
- Denominator (non-zero)
- GCF
- Greatest common factor of a and b
Worked examples
Simplify 24/36
The greatest common factor of 24 and 36 is 12. Dividing both by 12 gives 2/3, which is about 0.6667 as a decimal.
Reduce an improper negative fraction 150/−45
The GCF of 150 and 45 is 15, so the fraction reduces to 10/3 with the negative sign moved to the numerator: −10/3. As a mixed number that is −3 1/3.
Simplify 84/98
Euclid: 98 = 1 × 84 + 14, then 84 = 6 × 14 + 0, so the GCF is 14. Dividing 84 and 98 by 14 gives 6/7.
Frequently asked questions
How do you simplify a fraction?+
Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For 18/24 the GCF is 6, so 18/24 = 3/4. You can also divide repeatedly by small common factors like 2, 3 and 5 until none remain.
How do I know if a fraction is in simplest form?+
A fraction is in simplest form when the GCF of its numerator and denominator is 1 — for example 5/8 or 7/12. If both numbers are even, or both end in 0 or 5, it can definitely be reduced further.
Can you simplify an improper fraction?+
Yes. Reduce it exactly the same way (22/8 becomes 11/4), then convert to a mixed number if you like by dividing: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.
What if the denominator is negative?+
By convention the negative sign is moved to the numerator or placed in front of the fraction, so 5/−10 simplifies to −1/2. A fraction with both parts negative is positive.
What is the simplest form of 0/5?+
Zero divided by any non-zero number is 0, so 0/5 simplifies to 0 (often written 0/1). A zero denominator, however, is undefined and cannot be simplified.