Fraction & Ratio Calculator

Understanding fractions and ratios is essential in mathematics, science, cooking, engineering, finance, and everyday decision-making. Whether you're a student learning basic arithmetic or a professional working with data, proportions, or recipes, knowing how to simplify fractions, convert between mixed and improper forms, and simplify and scale ratiosempowers you to solve real-world problems accurately and efficiently.

Our free online Fraction & Ratio Calculator is designed to help you perform these operations instantly — from adding fractions like 3/4 + 1/2 to simplifying complex ratios such as 24:18. But beyond just getting answers, understanding the underlying concepts ensures you can verify results, avoid errors, and apply them confidently across different contexts.

What Is a Fraction?

A fraction represents a part of a whole. It consists of two numbers: the numerator (top number) and the denominator (bottom number). For example, in 3/5, the numerator 3 means we have three parts, and the denominator 5 indicates that one whole is divided into five equal parts.

There are three main types of fractions:

• Proper Fractions: The numerator is less than the denominator (e.g., 2/7)
• Improper Fractions: The numerator is greater than or equal to the denominator (e.g., 9/4)
• Mixed Numbers: A combination of a whole number and a proper fraction (e.g., 2 1/3)

You can convert between improper fractions and mixed numbers using division. For instance, 7/3 = 2 1/3 because 7 ÷ 3 = 2 remainder 1.

How to Simplify Fractions

To simplify a fraction, divide both the numerator and denominator by their Greatest Common Divisor (GCD). For example, to simplify 12/18, find the GCD of 12 and 18, which is 6. Then divide both numbers:12 ÷ 6 = 2 and 18 ÷ 6 = 3, resulting in 2/3.

Simplifying makes fractions easier to work with and compare. Our calculator automatically reduces any input fraction to its simplest form, whether you enter 4/8 or 100/150.

Performing Fraction Arithmetic

Adding, subtracting, multiplying, and dividing fractions follows specific rules:

• Addition/Subtraction: Requires a common denominator. For example, 1/4 + 1/6 = 3/12 + 2/12 = 5/12
• Multiplication: Multiply numerators and denominators directly: 2/3 × 4/5 = 8/15
• Division: Multiply by the reciprocal: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

These operations are crucial in algebra, physics, chemistry, and financial calculations. Our tool performs all four operations flawlessly, showing both simplified and mixed number results where applicable.

Understanding and Using Ratios

A ratio compares two quantities and shows how much of one thing there is relative to another. Written as A:B, it’s widely used in cooking (ingredient proportions), business (financial ratios), maps (scale ratios), and design (aspect ratios).

Like fractions, ratios can be simplified by dividing both terms by their GCD. For example, 12:8 simplifies to 3:2. You can also scale up a ratio — if a recipe calls for a 3:2 flour-to-sugar ratio and you want to triple it, multiply both sides: 9:6.

Ratios can be converted into fractions: 3:2 becomes 3/2 or 1 1/2. This flexibility allows for deeper analysis and integration with other mathematical tools.

Real-World Applications of This Calculator

• Cooking & Baking: Double a recipe written in fractions (1 1/2 cups × 2 = 3 cups)
• Homework Help: Check math assignments involving fraction addition or ratio simplification
• DIY Projects: Mix paint, concrete, or cleaning solutions using correct ratios
• Finance: Understand debt-to-income or price-to-earnings ratios more clearly
• Education: Teach students visual and practical uses of fractions and proportions

This free fraction and ratio calculator is mobile-friendly, works offline via browser cache, saves your history locally, and requires no sign-up — making it perfect for quick daily use.

Why Choose Our Free Online Tool?

Unlike many basic calculators, ours supports:

• ✅ Mixed numbers (2 3/4) and improper fractions (11/4) interchangeably
• ✅ Full arithmetic: addition, subtraction, multiplication, and division of fractions
• ✅ Automatic simplification using GCD reduction
• ✅ Ratio simplification and scaling features
• ✅ Calculation history with copy/share functionality
• ✅ Clean, intuitive interface without ads or distractions

Whether you're studying for a test, adjusting a recipe, or analyzing data, this tool gives you accurate results fast — while helping you learn the principles behind the math. Bookmark it today and make fractions and ratios simple again!