Adding Fractions Calculator

Adding Fractions Calculator

Add two fractions, reduce the exact result to lowest terms, and see its decimal value.

Last updated: August 2026 | By Summa Calculator

Fraction Addition Calculator
Enter integer numerators and non-zero integer denominators. Proper, improper, and negative fractions are supported; mixed-number input is not.
Sum
5/6
0.83333333

The Addition Rule

For fractions a/b and c/d, with b and d non-zero, the sum can be found directly by cross-multiplying:

a/b + c/d = (ad + bc) / bd

This formula always gives a common denominator. The result can then be reduced by dividing the numerator and denominator by their greatest common divisor.

Same Denominator vs Different Denominators

If the denominators already match, add the numerators and keep that denominator before simplifying.

1/8 + 3/8 = 4/8 = 1/2

If the denominators differ, rewrite the fractions using equivalent fractions with a shared denominator.

1/2 + 1/3 = 3/6 + 2/6 = 5/6

The least common denominator is often convenient by hand, but any valid common denominator produces the same final reduced fraction.

Adding Negative Fractions

A fraction is negative when exactly one of its numerator or denominator is negative. If both are negative, the fraction is positive.

-3/4 + -5/8 = -6/8 + -5/8
= -11/8

This calculator normalizes the final sign so the denominator of the displayed result is positive.

Improper Results and Decimals

A sum can be greater than one, so an improper fraction is a perfectly valid result. For example, -11/8 is already in lowest terms.

This calculator keeps the exact reduced fraction and also displays a decimal rounded to at most eight decimal places. It does not convert the result to mixed-number notation.

Questions About Adding Fractions

Do I always need the least common denominator?

No. You need a common denominator, but it does not have to be the least one. The final reduced sum is the same.

Can I enter a whole number?

Yes, by writing it as a fraction such as 5/1. The inputs themselves are numerator and denominator fields.

Can I enter mixed numbers directly?

No. Convert a mixed number to an improper fraction before entering it.

Why is a zero denominator rejected?

A fraction with denominator zero is undefined, so it cannot be used in fraction arithmetic.

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