Why is my negative sign on top?

Because the convention puts it there. A negative denominator is rewritten with the sign on the numerator, which is the same number in a form everyone reads the same way.

Math & Statisticsfractions

Simplify Fraction Calculator

A fraction reduced to lowest terms, with the mixed number, the decimal and the percentage, and an optional second fraction to add. Dividing by the greatest common divisor reaches the answer in one step, where cancelling common factors by eye usually takes several and often stops early.

Also called: reduce fraction, fraction simplifier.

Simplified fraction

2/3

2/3, reached by dividing both parts by their greatest common divisor of 42. The fraction is already less than one, so there is no mixed form. As a decimal it is 0.6667. Enter a second fraction to add it to this one.

Numerator

Denominator

Greatest common divisor

As a decimal

0.67

As a percentage

66.67

As a mixed number

2/3

Sum of the two fractions

No second fraction entered

On the mixed form

The fraction is already less than one, so there is no mixed form. As a decimal it is 0.6667.

On the sum

Enter a second fraction to add it to this one.

How this is calculated

Equivalent fractions

Fraction	Decimal
2/3	0.67
4/6	0.67
6/9	0.67
8/12	0.67
10/15	0.67

Method and background

How this is calculated

The greatest common divisor is found by the Euclidean algorithm, repeatedly replacing the larger number by the remainder of dividing it by the smaller until nothing is left over. Dividing both parts by that divisor gives the irreducible form immediately. The sign convention matters and is worth stating: a negative sign belongs on the numerator, so a fraction with a negative denominator is rewritten rather than left as it was typed. Adding a second fraction uses the product of the denominators as a common denominator and then reduces, which reaches the same answer as the lowest common denominator would with less bookkeeping.

dividing both parts by their greatest common divisor is what makes the result irreducible in one step rather than several

g: Greatest common divisor

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

84 over 126

Numerator: 84
Denominator: 126
Add this numerator: 0
Add this denominator: 0

Simplified fraction2/3

gcd(84, 126) = 42

Open this example

a negative denominator moves its sign up

Numerator: 3
Denominator: -9
Add this numerator: 0
Add this denominator: 0

Simplified fraction-1/3

boundary: the sign convention puts the minus on the numerator

Open this example

Method and limits

What it assumes

Integer inputs, since a fraction of two decimals is a division rather than a fraction.

What it deliberately does not model

A denominator of zero has no value, and this page declines rather than returning infinity.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why is my negative sign on top?: Because the convention puts it there. A negative denominator is rewritten with the sign on the numerator, which is the same number in a form everyone reads the same way.