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General Calculators

Fraction Calculator

Add, subtract, multiply, and divide fractions with automated lowest-term simplification and mixed fraction conversion.

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Simplified Result
23 / 20
Mixed Fraction
1 3/20
Decimal Value:
1.15

Fraction Arithmetic & Lowest-Term Reduction

Executes addition, subtraction, multiplication, and division across proper, improper, and mixed fractions, simplifying results to lowest terms.

Add: (a/b) + (c/d) = (ad + bc) / bd | Multiply: (a/b) * (c/d) = ac / bd | Divide: (a/b) / (c/d) = ad / bc

Calculation Steps

  • 1For addition/subtraction: Find common denominator bd, cross-multiply numerators, and perform operation.
  • 2For multiplication: Multiply numerators together and denominators together.
  • 3For division: Multiply first fraction by the reciprocal (inverse) of the second fraction.
  • 4Reduce the resulting fraction to lowest terms by dividing by GCD.
  • 5Convert improper fractions to mixed numbers.

Practical Example

Scenario: Add two fractions: 3/4 + 2/5

Inputs: Fraction 1: 3/4 | Fraction 2: 2/5 | Operation: Addition

Calculation: (3 * 5 + 2 * 4) / (4 * 5) = (15 + 8) / 20 = 23 / 20 = 1 3/20

Result: Improper Fraction: 23/20 | Mixed Number: 1 3/20 | Decimal: 1.15

Assumptions & Disclaimers

Key Assumptions:

  • Denominators cannot be zero.
  • Input fractions can be proper (numerator < denominator) or improper.

Calculations maintain exact integer fraction representations without decimal rounding until explicitly requested.

Frequently Asked Questions

To divide fractions, flip the second fraction (find its reciprocal) and multiply it by the first fraction.

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