Enter the numerator and denominator of any number into the calculator. The calculator will simplify the fraction and display the lowest common integers.
How to Simplify a Fraction
A fraction is simplified when its numerator and denominator share no common factor greater than 1. The fastest method is to divide both parts by their greatest common divisor (GCD), also called the greatest common factor (GCF).
g = \gcd(x, y)
\frac{a}{b} = \frac{x \div g}{y \div g}Here, x/y is the original fraction, g is the greatest common divisor, and a/b is the fraction in simplest form.
Quick Method
- Find the greatest common divisor of the numerator and denominator.
- Divide both by that same value.
- Write the result with a positive denominator.
- If the denominator becomes 1, the fraction simplifies to a whole number.
Rules to Remember
| Situation | Result |
|---|---|
| Numerator and denominator have no common factor greater than 1 | The fraction is already simplified |
| Numerator is 0 and denominator is nonzero | The value is 0 |
| Numerator equals denominator and both are nonzero | The value is 1 |
| Denominator is 1 | The fraction equals a whole number |
| Denominator is 0 | The fraction is undefined |
| Fraction is negative | Keep the negative sign in front or in the numerator, not the denominator |
Examples
Example 1: Reduce to lowest terms
\gcd(18, 24) = 6
\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}Example 2: Negative fraction
\gcd(45, 60) = 15
\frac{-45}{60} = \frac{-45 \div 15}{60 \div 15} = \frac{-3}{4}Example 3: Simplifies to a whole number
\gcd(32, 8) = 8
\frac{32}{8} = \frac{32 \div 8}{8 \div 8} = \frac{4}{1} = 4Common Mistakes
- Reducing only the numerator or only the denominator.
- Using a common factor that is not the greatest one, then stopping too early.
- Leaving a negative sign in the denominator.
- Treating a denominator of 0 as valid.
- Canceling digits instead of canceling common factors.
Prime Factor Shortcut
If the GCD is not obvious, factor each number into primes and remove matching factors from both sides.
\frac{84}{126} = \frac{2^2 \cdot 3 \cdot 7}{2 \cdot 3^2 \cdot 7} = \frac{2}{3}When to Convert First
| Input Type | What to Do |
|---|---|
| Mixed number | Convert to an improper fraction first, then simplify |
| Decimal fraction | Rewrite with whole numbers by multiplying top and bottom by a power of 10, then reduce |
| Large numbers | Use the GCD directly for the fastest reduction |
FAQ
What does simplest form mean?
A fraction is in simplest form when the numerator and denominator have no common factor greater than 1.
Is simplifying a fraction changing its value?
No. It changes the appearance, not the value. Simplified fractions are equivalent fractions.
\frac{12}{16} = \frac{3}{4}Can every fraction be simplified?
Every valid fraction can be checked for simplification, but some are already in lowest terms.
What if the numerator is larger than the denominator?
The fraction can still be simplified normally. If needed, the final result can also be written as a mixed number.
Why simplify fractions?
Simplified fractions are easier to compare, calculate with, and communicate clearly in math, finance, measurement, and algebra.
