Fraction Calculator

Add, subtract, multiply, or divide any two fractions. The calculator automatically simplifies the answer to its lowest terms and shows you the step-by-step working so you understand how the result was reached.

Numerator
Denominator
Numerator
Denominator
= ?

Result

How to Calculate Fractions

Adding and Subtracting Fractions

Fractions can only be directly added or subtracted when they share the same denominator. If the denominators differ, first find the Least Common Denominator (LCD), convert each fraction, then add or subtract the numerators.

a/b + c/d = (a×d + c×b) / (b×d) → then simplify

Example: 1/3 + 1/4 = (4 + 3) / 12 = 7/12

Multiplying Fractions

Multiply the numerators together and the denominators together, then simplify the result.

a/b × c/d = (a×c) / (b×d)

Example: 2/3 × 3/5 = 6/15 = 2/5 (simplified)

Dividing Fractions

Dividing by a fraction is the same as multiplying by its reciprocal. Flip the second fraction, then multiply.

a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)

Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6 (simplified)

Simplifying Fractions

Find the GCD of the numerator and denominator, then divide both by it.

Simplified = (Numerator ÷ GCD) / (Denominator ÷ GCD)

Example: 8/12 — GCD is 4 → 8÷4 / 12÷4 = 2/3

Common Fraction Equivalents

FractionSimplifiedDecimalPercentage
1/21/20.550%
1/31/30.333…33.33%
1/41/40.2525%
2/41/20.550%
3/43/40.7575%
2/32/30.66766.67%
4/81/20.550%
5/101/20.550%

Frequently Asked Questions

What does the calculator do when denominators are zero?

A fraction with a denominator of zero is undefined in mathematics. If you enter zero as a denominator, the calculator will alert you and ask for a valid entry. Division by zero has no meaningful result.

Can I enter negative fractions?

Yes. You can enter negative values in the numerator or denominator fields. The calculator will handle the signs correctly and return a properly simplified result, including negative fractions where applicable.

What is the LCD and why is it needed?

The Least Common Denominator is the smallest number that both denominators divide into evenly. It is required for addition and subtraction so both fractions can be expressed in compatible terms before combining their numerators.

What is a mixed number?

A mixed number combines a whole number with a fraction, such as 2½. To use this calculator with mixed numbers, first convert them to improper fractions. For example, 2½ becomes 5/2 (multiply 2 × 2, then add 1).

Why does the calculator always simplify the answer?

Simplified fractions are the standard mathematical convention and are easier to read and compare. Simplification divides both the numerator and denominator by their Greatest Common Divisor, reducing the fraction to its smallest equivalent form.