Skip to main content
Calculator Answers

Simplify Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A simplify calculator is a comprehensive math utility designed to reduce algebraic and arithmetic expressions to their simplest form. The tool simplifies proper and improper fractions by dividing the numerator and denominator by their greatest common divisor, reduces ratios, and simplifies radical expressions by extracting perfect-square factors from inside square roots. Students, teachers, and professionals use this calculator to check math homework, verify algebraic solutions, and present clean mathematical values.

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.

Quick Answer

Reduce fractions, radicals, and ratios to their simplest forms. Enter your expression to calculate the simplified mathematical value.

What to simplify

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

Simplified fraction

3 / 4

Decimal 0.75

Original18 / 24
GCD6
Simplified3 / 4
Decimal0.75

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.

Was this helpful?

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

Learn the concept

These guides explain the idea this tool computes, with worked examples and the distinctions readers most often trip over.

What Is a Term in Math? Counting terms, like terms, and why 3xy is one term not three.What Is a Constant in Math? The fixed part of an expression, and what it does to a graph.What Is a Variable in Math? Why letters are used, and when a letter is not a variable.What Is a Coefficient in Math? The number multiplying a variable, including the invisible 1.

Related calculators

Related Calculators

More tools from Education

Fraction CalculatorAdd fractions, subtract, multiply, divide, and simplify fractions. Convert fraction to decimal and convert improper fractions to mixed numbers with step by step work.

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.