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⚖️ Ratio Simplifier

Enter a:b to automatically simplify to the lowest integer ratio

:
Given A:B = C:D, enter A, B, C to find D
:
8
Simplified Ratio
3:4
= 0.75 = 75%
Ratio Value
0.75
Percentage
75%
D Value
8

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Ratio Simplifier Guide

The Ratio Simplifier tool automatically reduces an input ratio a:b to its simplest integer form, while also displaying the ratio value (decimal form) and percentage. Additionally, it supports finding the fourth value D given A:B=C:D.

A ratio expresses the relative size relationship between two quantities and is widely used in mathematics, engineering, cooking, and finance. Simplifying ratios to their lowest terms is a fundamental skill for understanding data relationships — just like simplifying fractions, the simplest ratio more intuitively reflects the essential relationship between two quantities. This tool uses the GCD algorithm to ensure results are in the simplest integer ratio.

Ratio Formulas

【Simplification】a:b → (a÷g) : (b÷g), where g=GCD(a,b)

【Ratio Value】ratio = a / b
【Percentage】percent = (a/b) × 100%

【Fundamental Property】If A:B = C:D
then A×D = B×C (cross multiplication equality)
D = (B×C) / A (find unknown term)

【Multiple Ratios】a:b:c can be simplified step by step: first simplify a:b, then find common factor with c

Practical Examples

📋
【Example 1】Simplify ratio 15:20 GCD(15,20)=5 15÷5 : 20÷5 = 3:4 Ratio value=0.75, Percentage=75% 【Example 2】Map scale 1:250000 Actual distance 50km, map distance? 1:250000 = x:5000000cm x = 5000000/250000 = 2cm 【Example 3】Recipe ratio 3:2:1 (cement:sand:gravel) Total 600kg material needed Cement = 600×3/6 = 300kg Sand = 600×2/6 = 200kg Gravel = 600×1/6 = 100kg 【Example 4】Find D: A:B=6:9, C=18 6:9 = 18:D D = (9×18)/6 = 27 Verification: 6/9=0.667, 18/27=0.667 ✓

Important Notes

💡
- Both numbers in a ratio should be positive; negative ratios are uncommon in practice - Simplified ratio terms should be coprime integers (GCD=1) - The order of a:b matters — a:b ≠ b:a (unless a=b) - A ratio greater than 1 means the first term is larger; less than 1 means the second is larger - When finding D, A cannot be 0 (as it is the divisor)

Application Scenarios

  • - Cooking & baking: Scale recipes up or down (e.g. adjust an 8-serving recipe to 4 servings)
  • - Cartography: Scale conversions, actual distance vs. map distance
  • - Construction: Concrete mix ratios (cement:sand:gravel golden ratio)
  • - Finance & investment: Asset allocation ratios, stock-bond ratios, position management
  • - Graphic design: Image scaling with aspect ratio preservation, screen resolution adaptation

Ratios, Fractions, and Percentages

Ratios, fractions, and percentages are essentially three different expressions of the same concept: the ratio 3:4 is equivalent to the fraction 3/4, which equals 75%. Which expression to choose depends on the context — ratios emphasize "comparative relationship," fractions emphasize "part to whole," and percentages emphasize "proportion degree."

The golden ratio (≈1.618:1 or ≈0.618:1) is the most famous special ratio, widely found in artistic composition, architectural design, and nature (such as the spiral of nautilus shells). Understanding the essence of ratios helps better grasp quantitative relationships.

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