Fraction Calculator

Work with two fractions: choose an operation, enter numerators and denominators, and get a simplified result plus a decimal approximation.

Result

—

The formula

Addition and subtraction use a common denominator. Multiplication multiplies across. Division multiplies by the reciprocal. Results are reduced by the greatest common divisor (GCD).

Worked example

  1. Add 1/2 + 1/4
  2. Common denominator: (1×4 + 1×2) / (2×4) = 6/8
  3. Simplify by GCD 2 → 3/4

Result: 3/4 ≈ 0.75

How fraction arithmetic works

Fractions represent rational numbers as numerator ÷ denominator. Operations follow the usual field rules for rationals; we then cancel the GCD so the answer is in lowest terms.

Addition and subtraction

a/b ± c/d = (a×d ± c×b) / (b×d). Cross-multiplying builds a shared denominator so you combine like-sized pieces.

Multiplication and division

Multiply numerators and denominators: (a/b)×(c/d) = (a×c)/(b×d). Division by c/d multiplies by d/c, provided c ≠ 0.

Simplifying

We round intermediate values to integers for GCD reduction (inputs are expected to be integers). The display also shows a decimal approximation n/d.

Edge cases

Denominators must be non-zero. Dividing by a fraction with numerator 0 is undefined. Negative denominators are normalized so the sign sits on the numerator.

Interesting facts

  1. Ancient math

    Fractions appear in Egyptian papyri dating to around 1800 BCE, often as sums of unit fractions such as 1/2 + 1/4.

  2. Why invert and multiply

    Dividing by a/b is multiplying by b/a because a/b × b/a = 1 — you multiply by the reciprocal to undo the division.

  3. Improper vs mixed

    An improper fraction (7/4) and a mixed number (1¾) are equal values in different notation — choose what fits the problem.

  4. Common denominators

    Adding fractions needs a shared denominator so you are combining like-sized pieces of the same whole.

  5. Decimals are fractions

    0.75 is 75/100, which simplifies to 3/4. Percentages are fractions with denominator 100.

Frequently asked questions

Convert to a common denominator: (a/b) + (c/d) = (ad + bc)/(bd), then simplify. Select Add in the calculator and enter all four numbers.

Divide numerator and denominator by their greatest common divisor (GCD). The calculator reduces automatically after each operation.

Dividing by a fraction means multiplying by its reciprocal. (a/b) ÷ (c/d) = (a/b) × (d/c) = (ad)/(bc).

No — division by zero is undefined. The calculator hides the result if a denominator is 0.

Results are improper or proper fractions in lowest terms (or a whole number if the denominator reduces to 1), plus a decimal approximation.

References

  1. Fractions — Math is Fun (educational) — MathsIsFun Clear visual explanations of fraction operations for learners.
  2. NIST Handbook — mathematical constants and notation — National Institute of Standards and Technology (NIST) Authoritative style for expressing quantities and ratios.
  3. Khan Academy — Arithmetic with fractions — Khan Academy Free practice and instruction aligned with school curricula.