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General Calculators

Ratio Calculator

Simplify ratios into lowest terms using greatest common divisor (GCD) and calculate decimal and percentage equivalents.

Simplified Ratio
3 : 4

Reduced from 36 : 48 using greatest common divisor

Decimal Equivalent:0.75
Percentage Proportion:75%

Ratio Simplification & Equivalence Mathematics

Simplifies mathematical ratios (A:B) into lowest integer terms using the Greatest Common Divisor (GCD/HCF), computing decimal ratio values and percentage shares.

Simplified Ratio = (A / GCD(A, B)) : (B / GCD(A, B)) | Fraction = A / (A + B)

Calculation Steps

  • 1Find the Greatest Common Divisor (GCD) of the two ratio terms using Euclidean algorithm.
  • 2Divide both terms by the GCD to find the simplified ratio in lowest terms.
  • 3Calculate decimal quotient: A / B.
  • 4Calculate part-to-whole percentages: [A / (A+B)] * 100 and [B / (A+B)] * 100.

Practical Example

Scenario: Simplify the ratio 48 : 72

Inputs: Ratio: 48 : 72

Calculation: GCD of 48 and 72 is 24. 48 / 24 = 2, 72 / 24 = 3.

Result: Simplified Ratio: 2 : 3 | Decimal: 0.6667 | Proportions: 40% and 60%

Assumptions & Disclaimers

Key Assumptions:

  • Both terms in the ratio must be non-zero positive numbers.
  • Ratios with decimals are multiplied by powers of 10 before simplification.

Ratios represent proportional relationships, not absolute quantities.

Frequently Asked Questions

Equivalent ratios are ratios that express the same relationship between numbers (for example, 2:3, 4:6, and 48:72 are all equivalent).

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