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Math

Compare Fractions Calculator

Compare two signed fractions exactly using reduced fractions and integer cross-products.

Exact method explained belowEditable inputs
Calculation notebook
Calculation notebook

The formula and worked example below explain the calculation.

See the method

Enter your values

Runs on your device

Your answer

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter first numerator, first denominator, second numerator, second denominator.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Normalize denominator signs and compare a×d with c×b. Integer cross-products avoid rounding a fraction to a decimal before comparing it.

A WORKED EXAMPLE

Using first numerator = 2, first denominator = 3, second numerator = 3, second denominator = 4, the result is 2/3 < 3/4. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Yes. Denominators are made positive before comparison, so a negative denominator and signed numerator are handled consistently.

What to keep in mind

Up to 200 digits per integer. Both denominators must be nonzero. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.

Common questions

Does this work with negative fractions?

Yes. Denominators are made positive before comparison, so a negative denominator and signed numerator are handled consistently.

How can I check the result?

Normalize denominator signs and compare a×d with c×b. Integer cross-products avoid rounding a fraction to a decimal before comparing it. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.

Methodology maintained by ClarityKit. How these tools are built and checked.