Three-Fraction Calculator

Combine three fractions with two operations and see each simplified calculation stage.

First fraction
Second fraction
Third fraction
Try an example:

Quick guide

How to calculate three fractions

  1. Enter the numerator and denominator for all three fractions.
  2. Choose the first and second operations.
  3. Select Calculate fractions.
  4. Check the first-stage and final-stage reductions.

The calculator intentionally evaluates from left to right so the workflow is predictable. Use parentheses and separate calculations if you need conventional multiplication-before-addition precedence.

Worked example: 1/2 + 2/3 + 3/4

First, 1/2 + 2/3 = 3/6 + 4/6 = 7/6.

Then, 7/6 + 3/4 = 14/12 + 9/12 = 23/12.

The final mixed number is 1 11/12.

Why reduce between stages?

Reducing an intermediate fraction keeps the next multiplication or common-denominator calculation smaller. It does not change the value, but it makes manual checking easier and reduces unnecessary factors.

Frequently Asked

Three-Fraction Calculator – Frequently Asked Questions

Common questions, edge-cases, and mathematical explanations.

How are the two operations evaluated?

This calculator works from left to right: it calculates the first two fractions, then applies the second operation to that result and the third fraction.

Can I mix addition, subtraction, multiplication, and division?

Yes. Each of the two operation menus can be set independently.

Are intermediate results simplified?

Yes. The first-stage result is reduced before it is used in the second stage.

Can I use negative fractions?

Yes. Enter a negative sign before any numerator.