Fraction Calculator
By Talcart · Last updated July 10, 2026
Fraction Calculator
A fraction calculator adds, subtracts, multiplies, and divides fractions and returns the answer in lowest terms - for example, 1/4 + 2/3 = 11/12. It finds the common denominator for you, shows each intermediate step, and simplifies the result by dividing out the greatest common factor, so the final fraction is always in its cleanest form.
Key facts
- The Rhind Mathematical Papyrus (c. 1650 BC) shows Egyptian scribes computing almost entirely with unit fractions such as 1/2, 1/3, and 1/15.
- A fraction in lowest terms has a terminating decimal expansion if and only if its denominator has no prime factors other than 2 and 5 - so 3/8 terminates (0.375) but 1/3 never does.
- The horizontal fraction bar was used by Arab mathematicians in the 12th century and spread to Europe through Fibonacci's Liber Abaci (1202).
What is the Fraction Calculator?
A fraction expresses a part of a whole as a ratio of two integers: a numerator (top) counting the parts, and a denominator (bottom) stating how many parts make one whole. So 3/4 means three of four equal parts. Fractions where the numerator is smaller than the denominator are proper (3/4); larger ones are improper (7/4) and can be written as mixed numbers (1 3/4). Unlike decimals, fractions represent values like 1/3 exactly, with no repeating-digit truncation - which is why exact arithmetic uses them.
How does the Fraction Calculator work?
Addition and subtraction require a common denominator: the calculator finds the LCD of the two denominators, scales each fraction, then combines numerators - the general formula is a/b +/- c/d = (ad +/- bc) / bd. Multiplication is direct: a/b x c/d = ac/bd. Division multiplies by the reciprocal: a/b / (c/d) = ad/bc. After every operation the result is reduced by dividing numerator and denominator by their GCF, computed with the Euclidean algorithm, and improper results can be expressed as mixed numbers.
What is the Fraction Calculator formula?
- Always simplify the final fraction by dividing by GCF
Fraction, decimal, and percent equivalents
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1667 (approx.) | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 2/3 | 0.6667 (approx.) | 66.67% |
| 3/4 | 0.75 | 75% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
How do you use the Fraction Calculator?
- Enter both fractions.
- Pick the operation.
- Read result and step-by-step.
Worked example
| Scenario | 1/4 + 2/3 |
| Calculation | (1×3 + 2×4) / (4×3) = 11/12 |
| Result | 11/12. |
Common use cases
Tips & best practices
Always simplify the final fraction.
Frequently asked questions
Rewrite both fractions over a common denominator, then add the numerators. For 1/4 + 2/3, the least common denominator of 4 and 3 is 12, so convert to 3/12 + 8/12 = 11/12. In general, a/b + c/d = (ad + bc) / bd; simplify the result if the top and bottom share a factor.
1/2 + 1/3 = 5/6. The least common denominator of 2 and 3 is 6, so 1/2 becomes 3/6 and 1/3 becomes 2/6; adding numerators gives 5/6. As a decimal that is approximately 0.8333. The answer is already in lowest terms because 5 and 6 share no common factor greater than 1.
Multiply by the reciprocal of the divisor - flip the second fraction, then multiply across. For 3/4 divided by 2/5: flip 2/5 to 5/2, then 3/4 x 5/2 = 15/8, which equals 1 7/8. This works because dividing by a number is the same as multiplying by its multiplicative inverse.
Multiply the numerators together and the denominators together: a/b x c/d = ac/bd. For example, 2/3 x 3/4 = 6/12, which simplifies to 1/2. No common denominator is needed. A shortcut is cross-cancelling before multiplying: the 3s cancel in 2/3 x 3/4, leaving 2/4 = 1/2 directly.
Multiply the whole number by the denominator, add the numerator, and keep the same denominator. For 2 3/4: 2 x 4 + 3 = 11, so the improper form is 11/4. Convert mixed numbers before doing any fraction arithmetic - operations like subtraction and division are far less error-prone on improper fractions.
Addition combines quantities, so the pieces must be the same size: you cannot directly add fourths to thirds any more than metres to feet. Converting to twelfths makes the units match. Multiplication instead scales one quantity by another - taking 2/3 of 3/4 - so the denominators simply multiply and no conversion is needed.