Fraction Calculator
Add, subtract, multiply or divide two fractions or mixed numbers. Get the simplified answer, its decimal and percent, and the working step by step.
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The formula
Addition and subtraction use a common denominator. Multiplication multiplies across. Division multiplies by the reciprocal. Results are reduced by the greatest common divisor (GCD).
Worked example
- Add 1/2 + 1/4.
- Common denominator: LCM of 2 and 4 is 4.
- Rewrite: 1/2 = 2/4 and 1/4 = 1/4.
- Add: 2 + 1 = 3 → 3/4 (already simplified).
Result: 3/4 ≈ 0.75
How fraction arithmetic works
Fractions represent rational numbers as numerator ÷ denominator. Operations follow the usual field rules for rationals; we then cancel the GCD so the answer is in lowest terms.
Addition and subtraction
a/b ± c/d = (a×d ± c×b) / (b×d). A shared denominator lets you combine like-sized pieces.
Multiplication and division
Multiply numerators and denominators: (a/b)×(c/d) = (a×c)/(b×d). Division by c/d multiplies by d/c, provided c ≠ 0.
Simplifying
Divide numerator and denominator by their GCD. Mixed numbers convert to improper fractions before computing, then can be shown as whole + proper fraction again.
Edge cases
Denominators must be non-zero. Dividing by a fraction with numerator 0 is undefined. Put negatives on the numerator or the whole part — not the denominator.
Interesting facts
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Ancient math
Fractions appear in Egyptian papyri dating to around 1800 BCE, often as sums of unit fractions such as 1/2 + 1/4.
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Why invert and multiply
Dividing by a/b is multiplying by b/a because a/b × b/a = 1 — you multiply by the reciprocal to undo the division.
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Improper vs mixed
An improper fraction (7/4) and a mixed number (1¾) are equal values in different notation — choose what fits the problem.
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Common denominators
Adding fractions needs a shared denominator so you are combining like-sized pieces of the same whole.
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Decimals are fractions
0.75 is 75/100, which simplifies to 3/4. Percentages are fractions with denominator 100.
Frequently asked questions
Convert to a common denominator: (a/b) + (c/d) = (ad + bc)/(bd), then simplify. Select + and enter both fractions.
Divide numerator and denominator by their greatest common divisor (GCD). The calculator reduces automatically after each operation.
Dividing by a fraction means multiplying by its reciprocal. (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc).
No — division by zero is undefined. The calculator hides the result if a denominator is 0.
Yes. Turn on Mixed numbers to enter a whole part with each fraction (for example 1 1/2).
References
- Fractions — Math is Fun (educational) Clear visual explanations of fraction operations for learners.
- Khan Academy — Arithmetic with fractions Free practice and instruction aligned with school curricula.