Fraction Calculator

Add, subtract, multiply, and divide fractions. Get simplified results and decimal coversions.

Methodology, assumptions, and limitations

Fractions are converted to a common denominator for addition or subtraction, multiplied directly for multiplication, and multiplied by the reciprocal for division. The final numerator and denominator are reduced by their greatest common divisor.

Assumptions
  • Denominators must be nonzero integers.
  • Mixed numbers are interpreted as a whole number plus a proper fraction.
  • A negative sign applies to the entire fraction.
Limitations
  • Division by a zero-valued fraction is undefined.
  • Decimal display is an approximation when the fraction has a repeating expansion.
  • The simplified fraction remains the exact result.

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Analysis
Interpretation of the current calculator output

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How to Use

Step-by-step instructions
  1. 1Enter the numerator and denominator for both fractions.
  2. 2Select the operation (+, -, *, /).
  3. 3View the simplified result and its mixed/decimal counterparts.

Fraction Arithmetic

Calculating with fractions requires finding a common denominator for addition and subtraction, or multiplying across for multiplication.
a/b + c/d = (ad + bc) / bd

Variables:

Frequently Asked Questions

How do you multiply fractions?

Multiply the top numbers (numerators) together, and then multiply the bottom numbers (denominators) together.

Why do you need a common denominator?

To add or subtract fractions, they must represent the same size parts of a whole, which means their denominators must be identical.