⚖️ Ratio Calculator
Simplify ratios to lowest terms
Understanding Ratios
A ratio is a comparison between two or more numbers that shows their relative sizes. Ratios are written with a colon (:) or as a fraction.
How to Simplify Ratios
To simplify a ratio, divide both numbers by their Greatest Common Divisor (GCD). This gives you the simplest form of the ratio while maintaining the same proportional relationship.
Real-World Applications
- Cooking: Recipe scaling (2:3 ratio of flour to sugar)
- Finance: Investment allocation and portfolio balancing
- Construction: Mixing concrete (1:2:3 ratio of cement:sand:gravel)
- Design: Aspect ratios for screens and images (16:9, 4:3)
- Business: Profit margins and financial ratios
Relationship Between Ratios and Fractions
A ratio can be expressed as a fraction. For example, the ratio 3:4 can be written as the fraction 3/4. Both represent the same proportional relationship, but ratios are often used when comparing quantities, while fractions represent parts of a whole.
Frequently Asked Questions
What is a ratio and how is it used?
A ratio is a mathematical expression that compares two or more quantities. It shows how many times one value contains or is contained within another. Ratios are used in cooking, finance, construction, design, and many other fields to maintain proportional relationships.
How do I simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers, then divide each number by the GCD. For example, to simplify 12:16, find GCD(12,16) = 4, then divide: 12÷4 = 3 and 16÷4 = 4, giving you 3:4.
What is the difference between a ratio and a fraction?
While ratios and fractions are related, they serve different purposes. A fraction represents a part of a whole (3/4 means 3 parts out of 4 total parts), while a ratio compares two separate quantities (3:4 means for every 3 of one thing, there are 4 of another). A ratio can be converted to a fraction, but the interpretation differs.
How do I convert a ratio to a percentage?
To convert a ratio to a percentage, first convert it to a fraction by dividing the first number by the second, then multiply by 100. For example, the ratio 3:4 becomes 3÷4 = 0.75, then 0.75 × 100 = 75%.
Can ratios have more than two numbers?
Yes! Ratios can compare three or more quantities. For example, a concrete mix might use a 1:2:3 ratio of cement:sand:gravel. To simplify multi-part ratios, divide all numbers by their common factor.
What is the golden ratio?
The golden ratio is a special ratio approximately equal to 1.618:1 (or 1:1.618). It appears frequently in nature, art, and architecture and is considered aesthetically pleasing. It's represented by the Greek letter phi (φ) and equals (1+√5)/2.