Simplify fractions calculator
This simplify fractions calculator reduces any fraction to lowest terms, showing the greatest common divisor as its own step rather than skipping straight to the answer. Typing 6/8 returns 3/4 — the same value, written with the smallest numbers that still name it exactly.
- Find the greatest common divisorgcd(6, 8) = 2
- Divide numerator and denominator by it6÷2 / 8÷2
- Reduced fraction3/4
How to simplify a fraction
6/8 and 3/4 are equivalent fractions — the same value, written two different ways. Simplifying finds the version with the smallest possible numerator and denominator.
- Find the greatest common divisor of the numerator and denominator:
gcd(6, 8). - Divide both the numerator and the denominator by it:
6÷2 / 8÷2. - The result is the fraction in lowest terms:
3/4. Its own greatest common divisor is 1 — nothing left to cancel.
Worked examples
A fraction with one shared prime
10/15 has exactly one common divisor bigger than 1: 5. Dividing both by it gives 2/3 in a single step.
A fraction with more than one common divisor
12/18 shares more than one common divisor bigger than 1. Dividing by the greatest one, 6, reaches 2/3 directly. Dividing by a smaller common divisor first only gets partway there — the mistake covered below.
An already-reduced fraction
3/4 shares no common divisor bigger than 1, so it is already in lowest terms — the calculator returns it unchanged rather than claiming a reduction that didn't happen.
Common values
Click a fraction to load it into the calculator above.
| Fraction | Simplified |
|---|---|
| 3/4 | |
| 2/3 | |
| 2/3 | |
| 2/3 | |
| 3/4 | |
| 2/5 | |
| 3/4 | |
| 5/9 |
Where people get it wrong
Dividing by a common divisor that isn't the greatest one leaves the fraction only partly reduced. 12/18 divided by 2 gives 6/9 — smaller numbers, but 6 and 9 still share a common divisor of 3. Dividing by the greatest common divisor instead — 6 — reaches the fully reduced 2/3 in one step instead of two.
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Frequently asked questions
How do you simplify a fraction?
Find the greatest common divisor of the numerator and denominator, then divide both by it. What's left is the fraction in lowest terms — no further common divisor left to cancel.
What is the greatest common divisor?
The largest whole number that divides both the numerator and the denominator evenly. 6 and 8 share the common divisors 1 and 2 — 2 is the greatest of those, so it's the one to divide by.
How can you tell a fraction is already fully reduced?
Its greatest common divisor is 1 — no whole number bigger than 1 divides both the numerator and the denominator evenly. 3/4 is one example: nothing but 1 divides both 3 and 4.
Is dividing by any common divisor enough, or does it have to be the greatest one?
It has to be the greatest one, or the fraction stops short of fully reduced. Dividing 12/18 by 2 gives 6/9, which looks simpler but still shares a common divisor of 3 — dividing by 6, the actual greatest common divisor, reaches 2/3 in one step instead of two.
Does simplifying change the value of the fraction?
No — a fraction and its simplified form name the exact same value, just with smaller numbers. That is what makes them equivalent fractions, not two different amounts.