Fraction Calculator

Add, subtract, multiply or divide fractions — or simplify one — with exact reduced answers in mixed, decimal and percent forms, plus every step.

All fraction arithmetic happens locally in your browser. Nothing ever leaves your device.

Fraction A
+
Fraction B
Fraction
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Mixed number
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Decimal
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Percent
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History
Your calculations from this session will appear here (up to 8).

The history lives only in this page — reloading clears it.

How It Works

Every operation is done in exact fraction arithmetic — no floats are used until the final decimal display — so 1/3 + 1/6 returns 1/2, never 0.49999999. The calculator keeps numerators and denominators as integers, applies the operation, then reduces the answer once with the greatest common divisor. Addition and subtraction first build a common denominator; multiplication and division cancel factors before they ever let numbers grow large.

Reducing with the Euclidean algorithm
The gcd of the numerator and denominator is found by repeated remainders: gcd(84, 360) → 360 = 4×84 + 24, 84 = 3×24 + 12, 24 = 2×12 + 0, so gcd = 12. Dividing top and bottom by 12 gives 7/60, the lowest terms in one step. The Steps panel prints exactly these lines for your numbers.
Why ÷ flips the second fraction
Dividing by b/c means multiplying by its reciprocal c/b, because (b/c) × (c/b) = 1. So 5/6 ÷ 2/3 becomes 5/6 × 3/2, cancel 3 against 6, and lands on 5/4. Keep the first fraction, change ÷ to ×, flip the second — the panel shows the keep-change-flip line explicitly.
Common denominators for + and −
You can only add what is counted in the same units, so both fractions are rewritten over the least common denominator, LCM(d1, d2) = d1 ÷ gcd(d1, d2) × d2. For 3/4 + 1/6 the LCD is 12: the lines become 9/12 + 2/12, then 11/12. The result is then reduced as usual.

Frequently Asked Questions

How does the calculator handle negative fractions?

By the usual sign rules. A minus in front of a fraction applies to the whole value, so it is stored on the numerator; a negative denominator is folded onto the numerator too, because -a/-b = a/b and -a/b = a/-b. Multiplying or dividing two negatives gives a positive, and adding negatives works like walking further left on the number line. You can type the minus sign in any of the four boxes.

How do I convert a mixed number back to an improper fraction?

Multiply the whole part by the denominator, add the numerator, and keep the same denominator: 3 1/4 becomes (3 × 4 + 1)/4 = 13/4. The calculator does the reverse automatically — whenever a result is improper it also prints the mixed-number form — and the Steps panel shows the division line behind it.

Why does the decimal sometimes show an ≈ sign?

A fraction has an exact terminating decimal only when its reduced denominator is built from 2s and 5s (halves, quarters, fifths, eighths, twentieths...). Denominators like 3, 6, 7, 9, 11 produce repeating decimals, so 1/3 is shown as ≈ 0.3333333333 — ten decimal places, rounded. The fraction result stays exact; that is the point of keeping the numerator/denominator form on screen.

Why is dividing by a fraction the same as multiplying by its flip?

Because division asks 'how many of these fit in that', and multiplying by the reciprocal answers exactly that: a ÷ (b/c) = a × (c/b), since (b/c) × (c/b) = 1 — the flipped fraction is the multiplicative inverse. The Steps panel shows this keep-change-flip line before doing the multiplication so the flip never feels like a magic rule.

Is anything uploaded to a server?

No. All numerator and denominator arithmetic runs in your browser with plain JavaScript, and the calculation history lives only in memory until you reload the page. Nothing is stored on a server, and there is no account or network request attached to a computation.