Simplifying Calculator
Simplify fractions, square roots, and algebraic expressions with step-by-step solutions. Enter any fraction, radical, or expression and get the simplified form instantly.
Simplify a Fraction
Quick examples:
Enter numerator and denominator to simplify
Three Modes
Simplify fractions using GCD, radicals by pulling out perfect square factors, and expressions by combining like terms.
Step-by-Step
Every simplification shows every step, from finding the GCD to extracting the perfect square factor, clearly numbered.
Instant Results
Results update as you type. Includes decimal form, mixed number representation, and whether the expression is already simplified.
Fraction Simplification Examples
| Original Fraction | GCD | Simplified | Decimal | Mixed Number |
|---|---|---|---|---|
| 12/18 | 6 | 2/3 | 0.667 | - |
| 16/24 | 8 | 2/3 | 0.667 | - |
| 45/60 | 15 | 3/4 | 0.75 | - |
| 100/250 | 50 | 2/5 | 0.4 | - |
| 36/48 | 12 | 3/4 | 0.75 | - |
| 7/3 | 1 | 7/3 | 2.333 | 2 1/3 |
| 22/8 | 2 | 11/4 | 2.75 | 2 3/4 |
Radical Simplification Examples
| Original | Perfect Square Factor | Simplified | Decimal |
|---|---|---|---|
| √12 | 4 | 2√3 | 3.464 |
| √18 | 9 | 3√2 | 4.243 |
| √50 | 25 | 5√2 | 7.071 |
| √72 | 36 | 6√2 | 8.485 |
| √98 | 49 | 7√2 | 9.899 |
| √200 | 100 | 10√2 | 14.142 |
| √45 | 9 | 3√5 | 6.708 |
| √7 | 1 | √7 (already simplified) | 2.646 |
Why Simplifying Matters
Simplified expressions are not just about tidiness - they are functionally easier to work with. When you carry unsimplified fractions through a multi-step problem, errors compound. Simplifying at each step keeps numbers smaller and arithmetic more manageable.
In higher math, simplified radicals are required in exact answers. A teacher marking an exam will not accept √50 when 5√2 is the simplified form. Similarly, leaving 12/18 instead of 2/3 in a probability or ratio problem signals that simplification was skipped.
For algebraic expressions, combining like terms reduces the size of expressions before you plug in values or continue solving. This reduces the chance of arithmetic errors and helps you see the structure of an equation more clearly.