These tools start where the two-fraction calculator falls short: expressions with several operators, powers, roots, unknowns or other ways of writing a number. Choose by what you have in front of you and what you want to get. Each row of the table shows an input and its result.
| I have | I want | Tool | Input and output |
|---|---|---|---|
| An expression in x | To simplify it | Algebraic fractions | (x²−1)/(x−1) → x + 1, with x ≠ 1 |
| A fraction and an exponent | Its power | Powers of fractions | (2/5)² → 4/25 |
| A fraction under a root | To know if it is rational | Roots of fractions | √(9/16) → 3/4 |
| Any fraction | Its continued fraction coefficients | Continued fractions | 5/8 → [0; 1, 1, 1, 2] |
| Any fraction | A sum of unit fractions | Egyptian fractions | 2/3 → 1/2 + 1/6 |
| Several operators and parentheses | A single result | Fraction expressions | 1/2 + 1/3 × 3/4 → 3/4 |
The table separates three families. Numeric expressions always give a number; expressions in x add conditions on the denominator; representations change how a rational number is written without changing its value. Here the roots row is the only one that can end in a decimal approximation.
An example from start to finish
Worked example: power and root of the same fraction
A square has a side of 3/4 of a unit. What fraction of a square unit does it cover, and how do you get back to the side?
- Square the numerator and denominator. 3² = 9 and 4² = 16, so (3/4)² = 9/16.
- Check that it cannot be simplified. 9 and 16 share no factor, so 9/16 is already in lowest terms.
- To go back, take the root of each part. √9 = 3 and √16 = 4, so the side is 3/4 again.
Result: the square covers 9/16 of the square unit.
Check: multiplying the side by itself, 3 × 3 over 4 × 4, gives back the result of the power.
With a root that is not exact, the way back fails: √(2/3) is not a fraction, and writing its decimal does not turn it into one. Powers of fractions and roots of fractions separate the two cases.
What you need to know before each group
Numeric expressions call for the rules of the four operations and the order among them. If you are still unsure about that order, review it in the main calculator, which has separate fields and steps for two fractions. Fraction expressions takes the whole expression on one line and respects the parentheses, and complex fractions solve the top and the bottom first.
Expressions in x call for knowing how to factor. Algebraic fractions cancels common factors without forgetting that (x²−1)/(x−1) leaves out x = 1. Equations with fractions apply the same idea: the candidate x = 1 shows up when solving, but it makes the denominator zero and is not a solution. Partial fractions needs you to supply the factored denominator; the tool does not discover it.
Representations need no algebra, only a fraction. Continued fractions expand it into whole-number coefficients that can be read as a chain of divisions, and Egyptian fractions split it into fractions with numerator 1. They are for studying how a number is written, not for replacing an everyday sum.
Tools and guides
The tools on this page take an input and return a result. Three guides explain why.
- The guide to algebraic fractions and domain tells why values of x are excluded and how to check a solution in the original equation.
- The guide to continued and Egyptian fractions explains how each form is obtained and where it stops.
- The guide on the zero denominator is the base for everything that has x in the denominator.
Sources: the English Wikipedia article Continued fraction says that any positive rational number can be expressed as a finite simple continued fraction, and the article Egyptian fraction defines an Egyptian fraction as a finite sum of distinct unit fractions (both consulted October 17, 2026).