Fraction Calculator

The four operations follow predictable rules. To add or subtract, find a common denominator first, then add or subtract the numerators. To multiply, multiply the numerators and denominators straight across. To divide, flip the second fraction (its reciprocal) and multiply. The calculator shows each step so you can see where the working comes from rather than just the answer.

Common denominators are the bit students get stuck on. The quick method: multiply the two denominators together (1/4 + 1/6 → use 24). The cleaner method: find the lowest common multiple. For 4 and 6, the LCM is 12, so 1/4 + 1/6 = 3/12 + 2/12 = 5/12. The lowest common multiple keeps the numbers smaller and saves simplifying at the end.

Every fraction has three valid forms. The improper fraction (7/4), the mixed number (1 3/4), and the lowest-terms version (already done in this case, since 7 and 4 share no common factors). Exam mark schemes usually want the answer in lowest terms, often as a mixed number unless an improper fraction is specifically asked for.

To simplify, divide top and bottom by their greatest common divisor. For 18/24, the GCD is 6, so 18/24 = 3/4. For more on factors, the [Greatest Common Factor Calculator](/greatest-common-factor-calculator) explains the underlying maths. The calculator on this page automatically returns the simplified form, the improper version, the mixed number, and the decimal equivalent so you can pick whichever the question wants.