Fraction Calculator
Perform arithmetic with fractions. Enter two fractions, choose an operation, and get a simplified result shown as both a fraction and a decimal, with step-by-step working.
How Fraction Calculator works
Adding and subtracting fractions
To add or subtract fractions, you must first find a common denominator. The simplest approach is to multiply the denominators together (cross-multiplication): (a/b) + (c/d) = (a×d + b×c) / (b×d). Then simplify by dividing numerator and denominator by their greatest common divisor (GCD). For example, 1/4 + 1/6 = (1×6 + 1×4) / (4×6) = 10/24 = 5/12.
Multiplying fractions
Multiplication is the simplest operation on fractions: multiply the numerators together and the denominators together. (a/b) × (c/d) = (a×c) / (b×d). For example, 2/3 × 3/4 = 6/12 = 1/2. You can simplify before multiplying (cross-cancelling) to keep numbers smaller, but the result is the same either way.
Dividing fractions
To divide by a fraction, multiply by its reciprocal (flip the second fraction). (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d) / (b×c). For example, 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 and 7/8. This rule — "keep, change, flip" — is the standard approach taught in schools.
Simplifying fractions using GCD
A fraction is in its simplest form when the numerator and denominator share no common factors other than 1. To simplify, find the GCD (greatest common divisor) of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example, 12/18: GCD(12, 18) = 6, so simplified = 2/3.
Mixed numbers and improper fractions
When the result is an improper fraction (numerator larger than denominator), it can also be expressed as a mixed number: divide to get the whole part and keep the remainder as the fractional part. For example, 7/4 = 1 and 3/4. The decimal equivalent is always 7 ÷ 4 = 1.75. This calculator returns the improper fraction form, which is more convenient for further calculation.
Frequently asked questions
How do I add fractions with different denominators?
Find a common denominator, convert both fractions, then add the numerators. The simplest method is to multiply the two denominators together: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. If both denominators share common factors, using the lowest common multiple keeps the numbers smaller, but cross-multiplication always works.
How do I simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD). For 24/36: GCD(24, 36) = 12, so 24/36 = 2/3. If you're unsure of the GCD, try dividing both by small primes (2, 3, 5, 7) repeatedly until no further division is possible.
What is a reciprocal?
The reciprocal of a fraction is obtained by flipping it: the reciprocal of a/b is b/a. For example, the reciprocal of 3/4 is 4/3. Reciprocals are used when dividing fractions. Every non-zero number has a reciprocal: the reciprocal of 5 (which is 5/1) is 1/5.
Can this calculator handle negative fractions?
Yes — enter a negative number for either the numerator or denominator. A negative numerator with a positive denominator gives a negative fraction (e.g., -1/4 = -0.25). If both are negative, the result is positive. The calculator normalises the sign to the numerator.
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