Fraction Calculator

Which calculator to use

1. Fraction Calculator — two fractions and one operation. Enter the numerator above each line and the denominator below it.
2. Mixed Numbers Calculator — the same four operations, but typed the way you would write them: 2 3/4, -2 3/4, 5 or 3/4.
3. Simplify Fractions Calculator — reduce one fraction, with an optional whole number in front, to its lowest terms.
4. Decimal to Fraction Calculator — turn 1.375 into 11/8, or 1 3/8.
5. Fraction to Decimal Calculator — divide a numerator by a denominator to fourteen significant figures.
6. Big Number Fraction Calculator — the same arithmetic for integers of any length.

What a fraction is

A fraction writes one quantity as parts of a whole: the numerator counts the parts you have and the denominator says how many equal parts make one whole. So 3/4 means three of the four pieces a unit is cut into. When the numerator is larger than the denominator — like 9/8 — the fraction is improper and represents more than one whole, and every result here is also shown as a mixed number when it has one.

The four operations, rule by rule

• Add / subtract: give both fractions a common denominator, then combine only the numerators. The calculator does this by cross-multiplying — a/b ± c/d becomes (ad ± cb) / bd.
• Multiply: numerator × numerator over denominator × denominator — no common denominator needed.
• Divide: flip the second fraction and multiply by that reciprocal.

Reading the calculation steps

Every answer is shown with its working, because the steps are usually what the question was really about. Adding 2/7 and 3/8, for instance, reads: expand each fraction to fifty-sixths, giving 16/56 and 21/56; add the numerators to get (16+21)/56; and that is 37/56, already in lowest terms. Where the combined fraction does reduce, the working shows the division by the greatest common divisor rather than jumping to the answer.

How the calculator simplifies

Every result is reduced to lowest terms by dividing the top and bottom by their greatest common divisor (GCD). For 6/12 the GCD is 6, so it collapses to 1/2. The sign is always carried on the numerator, so a negative result reads as −3/4 rather than 3/−4, and any improper fraction is also shown as a mixed number.

Worked examples

• Add: 2/7 + 3/8 → 16/56 + 21/56 = 37/56, or 0.66071428571429
• Mixed numbers: −2 3/4 + 3 5/7 → −11/4 + 26/7 = 27/28
• Simplify: 2 21/98 → 217/98 = 31/14 = 2 3/14
• Decimal to fraction: 1.375 → 1375/1000 = 11/8 = 1 3/8
• Fraction to decimal: 2/7 = 0.28571428571429

Fractions, decimals and mixed numbers

Every fraction is also a decimal and a percentage: 3/4 = 0.75 = 75%. Divide the numerator by the denominator to get the decimal, then multiply by 100 for the percentage. A mixed number splits an improper fraction into a whole part and a remainder — 9/8 becomes 1 1/8, because 8 goes into 9 once with 1 left over.

Common mistakes to avoid

• Adding across the top and bottom. 1/2 + 1/3 is not 2/5 — you must find a common denominator first.
• Flipping the wrong fraction when dividing. Take the reciprocal of the second fraction, not the first.
• Stopping before lowest terms. 6/12 is correct but not simplified; the calculator always reduces it to 1/2.
• Losing the sign in a mixed number. In −2 3/4 the minus applies to the whole value, so it is −11/4, not −2 + 3/4.

Working the other way, or with percentages instead? Try the percentage calculator, and for individual sums the scientific calculator evaluates full expressions.