Fraction Calculator

Add, subtract, multiply and divide fractions and mixed numbers. Results are automatically simplified to lowest terms, and each answer is shown as an improper fraction, a mixed number, a decimal and a percentage — plus the full step-by-step working so you can trace exactly how the result was produced.

Enter two fractions

Leave the Whole fields at 0 (or blank) for proper fractions. Enter a non-zero whole part for mixed numbers, e.g. 2 whole, numerator 1, denominator 2 = "2 ½".

Enter two fractions, choose an operator, and press Calculate.

How fraction arithmetic works

Adding and subtracting

Fractions must share a common denominator before they can be added or subtracted. The simplest approach is to cross-multiply the denominators:

a/b + c/d = (a·d + c·b) / (b·d)

The calculator uses this cross-multiplication method because it works for every pair of fractions without needing to compute the least common denominator first. The result is then simplified by dividing the numerator and denominator by their greatest common divisor.

Multiplying

a/b × c/d = (a·c) / (b·d)

Multiply numerators together and denominators together. Simplify the result.

Dividing

a/b ÷ c/d = (a·d) / (b·c)

Dividing by a fraction is the same as multiplying by its reciprocal — flip the second fraction and multiply.

Mixed numbers

A mixed number such as 2 ½ is first converted to an improper fraction: 2 ½ = (2 × 2 + 1) / 2 = 5 / 2. The rest of the calculation then proceeds normally.

Worked examples

Example 1 — Adding fractions with different denominators

Calculate 1/3 + 1/4

Common denominator: 3 × 4 = 12. Rewrite: 4/12 + 3/12 = 7/12.

Result: 7/12 ≈ 0.5833

Example 2 — Subtracting fractions

Calculate 5/6 − 1/3

Common denominator: 6. Rewrite: 5/6 − 2/6 = 3/6 = 1/2.

Result: 1/2 = 0.5

Example 3 — Multiplying fractions

Calculate 2/3 × 3/4

Multiply across: (2 × 3) / (3 × 4) = 6/12 = 1/2.

Result: 1/2 = 0.5

Example 4 — Dividing fractions

Calculate 2/3 ÷ 4/5

Multiply by the reciprocal: 2/3 × 5/4 = 10/12 = 5/6.

Result: 5/6 ≈ 0.8333

Example 5 — Mixed numbers

Calculate 2 ½ + 1 ¾

Convert to improper fractions: 5/2 + 7/4. Common denominator: 10/4 + 7/4 = 17/4 = 4 ¼.

Result: 17/4 = 4 ¼ = 4.25

Simplifying fractions

A fraction is in its simplest form when the numerator and denominator have no common factors other than 1. To simplify, divide both by their greatest common divisor (GCD):

12 / 18 → gcd(12, 18) = 6 → 2 / 3

The calculator always simplifies the final answer automatically. If you want to explore the GCD calculation separately, use the GCF calculator.

Common mistakes

  • Adding numerators and denominators separately. 1/2 + 1/3 is not 2/5. It is 5/6. You must first find a common denominator.
  • Forgetting to simplify. The result is more useful as 1/2 than as 4/8. The calculator simplifies automatically, but if you are working by hand, always check.
  • Mixing up mixed numbers and improper fractions. 2 ½ is 5/2, not 2/2 + 1/2 (which would be 3/2). The whole part multiplies the denominator before adding the numerator.
  • Dividing by zero. A fraction with a zero denominator is undefined. The calculator will catch this and show a clear error.
  • Not flipping the right fraction when dividing. a/b ÷ c/d becomes a/b × d/c — the second fraction is flipped, not the first.

Decimal to Fraction Converter

Convert any decimal into a simplified fraction.

Fraction to Decimal Converter

Convert a fraction into its decimal form.

Mixed Number Calculator

Work with mixed numbers and improper fractions.

Greatest Common Factor Calculator

The divisor used to simplify fractions.

Frequently asked questions

Find a common denominator (usually the least common multiple of the denominators), rewrite both fractions with that denominator, then add the numerators. For example, 1/3 + 1/4 = 4/12 + 3/12 = 7/12.

Multiply the first fraction by the reciprocal of the second. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Yes. Enter the whole-number part in the "Whole" field and the fractional part in the numerator and denominator fields. For example, to enter 2 ½, type 2 in Whole, 1 in Numerator, 2 in Denominator.

The result is displayed both as an improper fraction (numerator larger than the denominator) and as a mixed number, so you can use whichever form is more appropriate. For example, 17/4 is also shown as 4 ¼.

Yes. Put the minus sign in the numerator field (for example, −3/4) rather than in the denominator. The calculator will handle the sign correctly through all operations.

A denominator of zero makes the fraction undefined, so the calculator returns a clear error message rather than producing Infinity or NaN.