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Fraction Calculator

Add, subtract, multiply and divide fractions with step-by-step results.

Inputs

Results

1/2 + 3/4 =
5/4
Decimal ≈ 1.25
Unreduced
10/8
Reduced
5/4
Decimal
1.25
Step-by-step working
  1. 1
    Find a common denominator
    LCD of 2 and 4 is 8.
  2. 2
    Rewrite fractions
    1/2 = (1×4)/2×4 = 4/8 and 3/4 = (3×2)/4×2 = 6/8.
  3. 3
    + the numerators
    4 + 6 = 10 over 8.
  4. 4
    Reduce to lowest terms
    GCD of 10 and 8 is 2. Divide both by 2 → 5/4.

What is the Fraction Calculator?

A fraction calculator is a free online tool that adds, subtracts, multiplies and divides fractions — including mixed numbers and improper fractions — and shows step-by-step results so you can follow the work. It's ideal for homework, recipes, carpentry, and any problem involving ratios.

Fraction Calculator formula

Operations on a/b and c/d: addition/subtraction use the lowest common denominator LCD = lcm(b, d), giving (a·d ± c·b)/(b·d), then reduce by gcd. Multiplication: (a/b)·(c/d) = (a·c)/(b·d). Division: (a/b) ÷ (c/d) = (a·d)/(b·c), provided c ≠ 0. The final fraction is reduced by gcd(numerator, denominator) and the sign is normalized to the numerator.

How to use the Fraction calculator

  1. 1Enter the first fraction's numerator and denominator (use a negative numerator for negative fractions).
  2. 2Pick an operation: add (+), subtract (−), multiply (×), or divide (÷).
  3. 3Enter the second fraction's numerator and denominator.
  4. 4Read the reduced fraction, its decimal equivalent, and the step-by-step breakdown showing the LCD and cross-multiplication.
  5. 5If you divide by a fraction whose numerator is 0, the calculator shows a clear 'Cannot divide by zero' message.

Example calculation

Compute 1/2 × 2/3. Multiplication gives (1×2)/(2×3) = 2/6. Reduce by gcd(2,6) = 2 → 1/3. Decimal: 1 ÷ 3 ≈ 0.333333. The steps panel shows each multiplication and the reduction.

Frequently asked questions

How do I add fractions with unlike denominators?
Find the lowest common denominator (LCD) — the least common multiple of the two denominators — then rewrite each fraction with that denominator and add the numerators. For 1/4 + 1/6 the LCD is 12, so 3/12 + 2/12 = 5/12. The calculator does this automatically and shows the LCD in the steps.
How are fractions reduced to lowest terms?
After computing the result, the calculator divides both the numerator and denominator by their greatest common divisor (gcd). For example, 6/8 → gcd(6,8) = 2 → 3/4. The sign is moved to the numerator so the denominator is always positive.
Can I use improper fractions and mixed numbers?
Yes. Enter any integer numerator and a non-zero denominator — improper fractions like 7/4 are accepted directly and reduce normally. For mixed numbers, convert first (e.g., 2 1/3 = 7/3) or compute the whole and fractional parts separately and add them.
What happens when I divide by zero?
Division by a fraction whose numerator is 0 is mathematically undefined, so the calculator displays 'Cannot divide by a zero numerator (the second fraction is 0)' instead of producing Infinity or NaN. A zero denominator in either input is rejected with 'Denominators must be non-zero'.
How does the fraction calculator handle negative fractions?
The sign is normalized to the numerator — so 1/(−2) is treated internally as −1/2 before any operation. The result is similarly normalized so the denominator is always positive and the sign sits on the numerator.

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