How to simplify a fraction
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). This keeps the fraction's value the same while reducing it to lowest terms.
Divide the numerator and denominator by their GCD Example: 6/8 GCD of 6 and 8 = 2 6 ÷ 2 / 8 ÷ 2 = 3/4 A fraction is fully simplified when the numerator and denominator have no common factor other than 1. Finding the GCD first is a direct way to reach lowest terms without repeatedly testing smaller factors. If you need to find the greatest common divisor itself, use the GCF and LCM Calculator.
What does simplest form mean?
Simplest form, also called lowest terms, means that a fraction cannot be reduced any further. For example, 12/18 is not in simplest form because both numbers are divisible by 6:
12/18 GCD = 6 12 ÷ 6 / 18 ÷ 6 = 2/3 The fractions 12/18 and 2/3 have the same value, but 2/3 is the simplified form because its numerator and denominator have no common factor greater than 1.
Negative fractions
A negative fraction can be simplified in the same way as a positive fraction. The negative sign can be written before the fraction or on either the numerator or denominator:
-8/12 = -2/3 8/-12 = -2/3 The calculator reduces the numerical parts of the fraction while preserving its value and sign.
Simplifying vs. calculating with fractions
Simplifying a fraction only reduces it to lowest terms. If you need to add, subtract, multiply, or divide fractions, including calculations involving multiple fractions, use the Fraction Calculator.
Fractions, decimals, and ratios
A simplified fraction can also be useful when converting between different ways of representing the same value. For example, 1/2 is equal to 0.5. If you need to convert a fraction directly to a decimal, use the Fraction to Decimal Calculator.
You can also convert a decimal into a fraction with the Decimal to Fraction Calculator. Ratios are another way to compare quantities; for ratio calculations, use the Ratio Calculator.
Frequently asked questions
How do I simplify a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 6/8 simplifies to 3/4 because the GCD of 6 and 8 is 2.
How do I know when a fraction is fully simplified?
A fraction is fully simplified when its numerator and denominator have no common factor other than 1. In other words, their greatest common divisor is exactly 1.
What if the simplified fraction is a whole number?
Then it can be written as the whole number. For example, 100/25 simplifies to 4 because 100 divided by 25 is 4.
Can you simplify an improper fraction?
Yes. An improper fraction can be reduced just like any other fraction. For example, 8/12 simplifies to 2/3. If you want to express an improper fraction as a mixed number, use the Mixed Number Calculator.
Does simplifying a fraction change its value?
No. Dividing the numerator and denominator by the same nonzero number produces an equivalent fraction with the same value. For example, 6/8 and 3/4 are equal.