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Ratio Simplifier

Simplifying a ratio reduces its terms to the smallest possible positive whole integers that share no common factor other than 1. This free Ratio Simpl

Mathematics
Formula & Methodology
Simplified Term A = A ÷ GCD(A, B) Simplified Term B = B ÷ GCD(A, B) GCD determined via Euclidean Algorithm

To simplify a two-term ratio A : B: 1. Determine the Greatest Common Divisor (GCD) of both numbers using Euclidean division. 2. Divide both A and B by the GCD. 3. Write the simplified ratio as (A ÷ GCD) : (B ÷ GCD). Because both terms are divided by the same non-zero factor, the proportional relationship remains unchanged.

Simplified Ratio (Lowest Terms)

2 : 3

Overview

Simplifying a ratio reduces its terms to the smallest possible positive whole integers that share no common factor other than 1. This free Ratio Simplifier uses the Euclidean Greatest Common Divisor (GCD) algorithm to reduce any ratio into its canonical lowest terms.

Unsimplified ratios like 24:36 or 100:250 make quantitative comparisons difficult. By reducing them to clean baseline expressions like 2:3 or 2:5, this tool clarifies financial debt-to-equity ratios, photography aspect ratios, and chemical mixture proportions.

Worked Examples

Example 1: Simplifying 24 : 36

Inputs: A = 24, B = 36

  1. Find GCD of 24 and 36: GCD(24, 36) = 12.
  2. Divide Term A: 24 ÷ 12 = 2.
  3. Divide Term B: 36 ÷ 12 = 3.
  4. Simplified Ratio: 2 : 3.
Final Answer: 2 : 3 (GCD = 12)

Example 2: Simplifying 100 : 250

Inputs: A = 100, B = 250

  1. GCD(100, 250) = 50.
  2. Divide: 100 ÷ 50 = 2; 250 ÷ 50 = 5.
  3. Simplified Ratio: 2 : 5.
Final Answer: 2 : 5

Example 3: Already Simplified Ratio (7 : 11)

Inputs: A = 7, B = 11

  1. 7 and 11 are prime numbers with GCD = 1.
  2. Ratio cannot be reduced further.
Final Answer: 7 : 11 (Already in lowest terms)

How to Use This Calculator

  1. Enter the first integer term in the A field.
  2. Enter the second integer term in the B field.
  3. Click "Calculate" to simplify the ratio.
  4. View the extracted GCD, fraction equivalent, and percentage breakdown below.
  5. Click "Reset" to simplify another ratio.

Reference Table

Original RatioGCD FactorSimplified RatioDecimal Value
10 : 20101 : 20.50
12 : 1643 : 40.75
24 : 36122 : 30.6667
50 : 75252 : 30.6667
100 : 250502 : 50.40

Frequently Asked Questions

What does it mean for a ratio to be in lowest terms?
A ratio is in lowest terms when its terms are coprime integers—meaning their Greatest Common Divisor is 1 and no integer greater than 1 divides both numbers evenly.
How do you simplify ratios with decimals (e.g. 2.5 : 3.5)?
Multiply both terms by 10 to clear the decimal (25 : 35), then simplify by dividing by their GCD of 5 to get 5 : 7.
Can negative numbers be used in a ratio?
Ratios comparing physical quantities (like mixing ingredients or screen dimensions) must be positive. Algebraic ratios preserve their sign.
What is a unit ratio (1 : n)?
A unit ratio divides both terms by Term A so the first term is exactly 1 (e.g. 2 : 3 becomes 1 : 1.5).
Is simplifying a ratio the same as simplifying a fraction?
Yes. Mathematically, simplifying the ratio A : B is identical to reducing the fraction A/B to lowest terms.

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Reviewed & Authored by: Dr. Elizabeth Vance, PhD Applied Mathematics · Last Updated: 2026-10-06
Computed via Euclidean greatest common divisor integer factorization.