Simplify Ratio Calculator

Simplify any ratio to its lowest terms by dividing by the GCD. Supports two-part and three-part ratios.

Enter Ratio Values

Result

Simplified Ratio
3 : 2
lowest terms
Original Ratio12 : 8
GCD4
As Fraction3/2
As Decimal1.5

Step-by-Step Solution

12 : 8 = (12/4) : (8/4) = 3 : 2

How to Simplify a Ratio

Simplifying a ratio means reducing it to its smallest whole number form by dividing all parts by their Greatest Common Divisor (GCD). A simplified ratio expresses the same relationship between quantities using the smallest possible integers.

Step-by-Step Method

  1. If values are decimals, multiply all parts by a power of 10 to make them whole numbers.
  2. Find the GCD of all parts of the ratio.
  3. Divide each part by the GCD.
  4. The resulting ratio is in its simplest form.

Examples

24 : 16

GCD(24, 16) = 8

24:16 = 3:2

15 : 25 : 35

GCD(15, 25, 35) = 5

15:25:35 = 3:5:7

0.5 : 1.5

Multiply by 10: 5:15, GCD = 5

0.5:1.5 = 1:3

Ratios vs. Fractions

A two-part ratio a:b can be expressed as the fraction a/b. However, ratios can have three or more parts (like 2:3:5), which cannot be directly expressed as a single fraction. Ratios compare multiple quantities simultaneously.

Practical Uses of Ratios

  • Cooking recipes (e.g., flour to sugar ratio).
  • Map scales (e.g., 1:50000).
  • Mixing solutions (e.g., paint colors, concrete).
  • Financial analysis (e.g., debt-to-equity ratio).