Education
Simplify Calculator
Pick a mode and enter your numbers. The tool reduces fractions using GCD, simplifies square roots by extracting perfect-square factors, and reduces ratios by their greatest common divisor.
e.g. 18
e.g. 24
Scope
This tool simplifies fractions (using GCD), square roots (pulling out perfect-square factors), and integer ratios. It is not a full symbolic algebra system; for full algebraic simplification (variables, polynomials, complex expressions), use a computer algebra system like Wolfram Alpha or SymPy.
Simplified fraction
3 / 4
Decimal 0.75
Fractions are reduced by dividing by GCD(numerator, denominator). Square roots are simplified by extracting all perfect-square factors. Ratios are reduced by dividing every part by the GCD of the whole list.
Examples
18 / 24
GCD 6 · simplified 3/4 · 0.75
√72
6√2 · ≈ 8.485
12 : 18
GCD 6 · reduced 2 : 3
12 : 18 : 24
reduced 2 : 3 : 4
How it works
All three modes use the Euclidean algorithm to find the GCD, then divide. The square-root mode scans for perfect-square factors up to √n.
Fraction · divide numerator and denominator by GCD
Square root · √(a² × b) = a × √b
Ratio · divide every part by GCD of all parts
Related calculators
- Fraction calculator for adding, subtracting, multiplying, and dividing fractions.
- Square root calculator for decimal and simplified square roots.
- GCF calculator for the greatest common factor of any set of numbers.
- LCM calculator for the least common multiple.
- All education calculators.
Frequently asked questions
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that GCD. For example, 18/24 has GCD 6, giving 3/4. The simplified form is unique (up to sign): a fraction is in lowest terms when GCD = 1.
Factor the radicand into a product of a perfect square and a remainder. For example, √72 = √(36 × 2) = 6√2. The calculator pulls out every perfect-square factor automatically, leaving the smallest possible number under the radical.
Find the GCD of all parts of the ratio, then divide each part by that GCD. For example, 12:18 has GCD 6, giving 2:3. The same procedure works for ratios with more than two parts: 12:18:24 has GCD 6, giving 2:3:4.
No. This is a numeric simplifier, not a computer algebra system. For symbolic simplification (combining like terms, factoring polynomials, simplifying rational expressions with variables), use a CAS such as Wolfram Alpha, SymPy, or a similar tool.
Decimals aren't in scope here. Convert the decimal to a fraction first (move the decimal point and reduce), then use this calculator's fraction mode. For repeating decimals, use a fraction-from-decimal converter.
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