Fraction Calculator

Step by step

1. On Fraction maths, fill in the top and bottom of each fraction. Leave the “whole” box at 0 unless you are entering a mixed number like 2 ¾.
2. Choose + − × ÷ or ^ in the middle. The answer appears instantly in simplest form.
3. Read the mixed number, improper fraction, decimal and percent underneath — the same value written four ways.
4. Open The working to see the common denominator, the reciprocal flip, or whatever step the question needed. It is the method a teacher wants written down.
5. Use Simplify one to reduce a single fraction, and Decimal ↔ fraction to go the other way — write repeating digits in brackets, like 0.1(6).

Good to know

• Every answer is computed with whole numbers only, never decimals, so 1/3 + 1/6 comes back as exactly 1/2 — no rounding creeps in.
• A negative mixed number carries the sign across the whole thing: entering −2 and 1/2 means −2½, which is −5/2.
• Improper fractions are fine to type. 7/4 needs no whole-number part.
• For adding and subtracting, the calculator uses the lowest common denominator rather than just multiplying the two — that is why the numbers in the working stay small.
• The decimal converter is exact for repeating decimals typed with brackets. Without brackets, an endless decimal gets the closest fraction under your denominator cap.

The maths behind it

• Add or subtract a/b ± c/d = (a·(L/b) ± c·(L/d)) / L where L = lcm(b, d) Same denominator first, then the numerators only.
• Multiply a/b × c/d = (a·c) / (b·d) Straight across. No common denominator required.
• Divide a/b ÷ c/d = (a·d) / (b·c) Flip the second fraction and multiply — “keep, change, flip”.
• Simplify a/b → (a÷g) / (b÷g), g = gcd(a, b) Dividing both parts by their greatest common factor gives simplest form in one move.
• Repeating decimal 0.f(c) = (fc − f) / (99…9 00…0) One 9 per repeating digit, one 0 per fixed decimal place. So 0.1(6) = (16 − 1)/90 = 1/6.