Ratio Simplifier

How the Ratio Simplifier Works

The Ratio Simplifier converts both values (A and B) into whole numbers, then finds their greatest common factor (GCF). By dividing each number by the GCF, the ratio is reduced to its simplest form.

Formula:
Simplified Ratio = (A ÷ GCF) : (B ÷ GCF)

This process ensures accuracy whether A and B are integers, fractions, or decimals.

How to Simplify a Ratio (Step-by-Step)

Case 1: When A and B are Whole Numbers

1. List the factors of A.
2. List the factors of B.
3. Find the GCF(A, B).
4. Divide both numbers by the GCF.
5. Write the simplified ratio as A : B.

If GCF = 1, the ratio is already in its simplest form.

Example: Simplify 6 : 10

• Factors of 6 = 1, 2, 3, 6
• Factors of 10 = 1, 2, 5, 10
• GCF = 2
• 6 ÷ 2 = 3, 10 ÷ 2 = 5
• Simplified ratio = 3 : 5

Case 2: When A and B are Not Whole Numbers

If A or B are decimals, fractions, or mixed numbers, the simplification process includes a few extra steps:

1. Convert mixed numbers to improper fractions.
2. If either value is a decimal, multiply both by the same power of 10 to remove decimal points.
3. If one value is a fraction and the other a whole number, convert both to fractions (e.g., 5 = 5/1).
4. If both are fractions with like denominators, multiply both by that denominator to convert them to whole numbers.
5. If both are fractions with unlike denominators, find the LCD (Least Common Denominator), rewrite both fractions with it, and multiply through to get whole numbers.
6. Once both values are whole numbers, find the GCF and divide.

Example: Simplify 8 : 36

• Factors of 8 = 1, 2, 4, 8
• Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
• GCF = 4
• 8 ÷ 4 = 2, 36 ÷ 4 = 9
• Simplified ratio = 2 : 9

If you work frequently with ratios and fractions, you can also try the Ratio to Fraction Calculator to convert ratios directly into fraction form for further calculations.

Simplifying Ratios with Decimals or Fractions

Let’s simplify a ratio with decimals:
Example: Simplify 2.5 : 1.25

• Multiply both numbers by 100 to remove decimals: 250 : 125
• GCF = 125
• Divide both by 125 → 2 : 1

Result: 2 : 1

Now an example with fractions:
Example: Simplify ½ : ¼

• Find LCD = 4
• Convert to whole numbers: (½ × 4) : (¼ × 4) → 2 : 1
• Simplified ratio = 2 : 1

This process ensures ratios are consistently reduced to the cleanest, most comparable format.

Why Simplifying Ratios Matters

Simplifying ratios is crucial because it provides clearer comparisons and eliminates redundancy. For instance:

• A ratio of 50 : 100 simplifies to 1 : 2 — a more readable and meaningful representation.
• In design and media, aspect ratios (like 16:9) define visual proportions, often calculated using the Aspect Ratio Calculator for screen dimensions and layouts.

Simplified ratios also improve accuracy in budgeting, financial analysis, and statistical reporting.

The Ratio Simplifier reduces any ratio — whether made up of decimals, fractions, or whole numbers — to its lowest terms by finding the greatest common factor (GCF). This not only standardizes data but also enhances understanding in both mathematical and real-world applications.

By simplifying ratios, you can make comparisons clearer, identify relationships faster, and apply consistent proportions in financial, design, or statistical contexts.

Try it now:
Use the Ratio Simplifier on CalculatorCave to simplify any ratio instantly and view the complete solution steps.