How it works
Each number is entered as a whole part (optional), a numerator (top) and a denominator (bottom). For 2⅔ type 2, 2 and 3; for ¾ leave the whole part empty and type 3 and 4. The calculator works with whole numbers only, so the answer is exact — no rounding until the decimal at the end.
The four rules
a/b + c/d = (a×d + c×b) ÷ (b×d) a/b − c/d = (a×d − c×b) ÷ (b×d) a/b × c/d = (a×c) ÷ (b×d) a/b ÷ c/d = (a×d) ÷ (b×c)The result is then simplified by dividing the top and bottom by their greatest common divisor (GCD). Mixed numbers are first turned into improper fractions: 2⅔ = (2×3 + 2)/3 = 8/3.
Worked example. 1½ + 2⅔: convert to improper fractions, 3/2 + 8/3. Cross-multiply: (3×3 + 8×2) ÷ (2×3) = (9 + 16) ÷ 6 = 25/6. The GCD of 25 and 6 is 1, so it is already simplified. As a mixed number: 25 ÷ 6 = 4 remainder 1, so 4⅙; as a decimal, 4.1666666667.
Common questions solved by hand
- Simplify a fraction: enter it and add 0 (for example 18/24 + 0/1 = 3/4).
- Dividing by a fraction is multiplying by its reciprocal: ÷ 2/5 is the same as × 5/2.
- Negative fractions: put the minus sign on the whole part, or on the numerator when there is no whole part.
- Dividing by zero is impossible, so 1/2 ÷ 0/5 shows a clear message instead of a number.
To turn a decimal into a percentage or work with percentages, use the percentage calculator. For longer expressions such as (1/2 + 1/3) × 6, the scientific calculator accepts fractions typed with /.