Ratio of Three Numbers Calculator

Simplify the ratio of three numbers (a:b:c) and view proportions with step-by-step solutions.

Enter Three Numbers

Result

Simplified Ratio
--
Original Ratio--
Simplified Ratio--
GCD--
Total Parts--
A proportion--
B proportion--
C proportion--

Step-by-Step Solution

A : B : C = simplified

Understanding Three-Part Ratios

A three-part ratio compares three quantities simultaneously. Written as A:B:C, it shows the relative sizes of three values. Simplifying a three-part ratio involves dividing all three numbers by their greatest common divisor (GCD).

How to Simplify a Three-Part Ratio

  1. Find the GCD of all three numbers: GCD(A, B, C) = GCD(GCD(A, B), C)
  2. Divide each number by the GCD
  3. The result is the simplified ratio in lowest terms

Proportions from Ratios

Finding Proportions

Each part's proportion is its share of the total.

Proportion of A = A / (A + B + C)

Percentage Split

Convert each proportion to a percentage.

% of A = (A / Total) x 100

Decimal Ratios

Divide everything by the smallest value to see relative sizes.

Normalize: A/min : B/min : C/min

Real-World Examples

Three-part ratios appear in many contexts: mixing paint colors (red:blue:yellow), dividing profits among three partners, recipe ingredients, concrete mix ratios (cement:sand:gravel), and asset allocation in investment portfolios.

Handling Decimals

  • If any of the numbers are decimals, multiply all three by a power of 10 to make them whole numbers first.
  • Then find the GCD and simplify normally.
  • The ratio 0.5 : 1.5 : 2.0 becomes 5 : 15 : 20 = 1 : 3 : 4.