Fraction Calculator - Calculate with Fractions, Mixed Numbers & Decimals
All-in-one fraction calculator for multiple operations: add, subtract, multiply, divide fractions, simplify fractions, convert between decimals and fractions, work with mixed numbers, and handle big numbers. Perfect for students, professionals, and anyone working with fractions and decimals.
📋 Table of Contents
What are Fractions?
MathematicsA fraction represents a part of a whole, expressed as a ratio of two numbers: a numerator (top number) and a denominator (bottom number). For example, 3/4 means 3 parts out of 4 equal parts. Fractions are fundamental to mathematics, appearing in everyday contexts like cooking (1/2 cup flour), time (1/4 hour = 15 minutes), and money (1/4 dollar = 25 cents).
Fractions can be expressed in multiple forms: proper fractions (numerator smaller than denominator, like 3/4), improper fractions (numerator larger than denominator, like 5/3), and mixed numbers (whole number plus fraction, like 1 2/3). All these forms represent the same mathematical value but appear different.
Fractions and decimals are interchangeable ways of representing the same values. 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. Understanding conversions between these formats is essential for flexible mathematical thinking and problem-solving.
Understanding Fractions
Numerator and Denominator
The numerator (top number) indicates how many parts you have. The denominator (bottom number) indicates how many equal parts the whole is divided into. In 5/8, you have 5 parts out of a whole divided into 8 equal parts.
Equivalent Fractions
Equivalent fractions represent the same value: 1/2 = 2/4 = 3/6 = 4/8. Multiply or divide both numerator and denominator by the same number to create equivalent fractions. This principle underlies fraction simplification and common denominator operations.
Simplest Form (Lowest Terms)
A fraction in simplest form has no common factors between numerator and denominator except 1. Simplify by dividing both by their greatest common divisor (GCD). 6/9 simplifies to 2/3 (both divisible by 3).
Common Denominator
To add or subtract fractions, find a common denominator (ideally the least common multiple of the denominators). For 1/3 + 1/4, the LCD is 12, so convert to 4/12 + 3/12 = 7/12.
Mixed Numbers
Mixed numbers combine whole numbers and fractions: 2 1/3 means 2 + 1/3. Convert to improper fractions (numerator ≥ denominator) for calculations: 2 1/3 = 7/3. Convert back to mixed numbers for final answers.
Types of Fractions
Proper Fractions
Numerator is smaller than denominator: 3/4, 5/8, 1/2. Proper fractions represent values less than 1. They're called "proper" because they follow standard rules and conventions.
Improper Fractions
Numerator is greater than or equal to denominator: 5/3, 7/4, 8/8. Improper fractions represent values ≥ 1. They're often converted to mixed numbers for readability but are useful in calculations.
Mixed Numbers
Combination of whole number and proper fraction: 2 1/3, 5 3/4, 10 1/2. Mixed numbers make large fractions more readable. Convert to improper fractions for mathematical operations.
Unit Fractions
Numerator is 1: 1/2, 1/3, 1/8, 1/100. Unit fractions represent one part of the whole. All other fractions can be expressed as sums of unit fractions (Egyptian fraction representation).
Complex Fractions
Fractions where numerator or denominator (or both) contain fractions: (3/4)/(2/5). Simplify complex fractions by dividing: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.
Fraction Calculation Formulas
When denominators are equal, add numerators and keep the denominator
Find LCD, convert fractions, then add numerators
Similar to addition but subtract numerators after finding LCD
Multiply numerators together and denominators together
Multiply by the reciprocal of the second fraction
Divide both numerator and denominator by their GCD
Place decimal digits over appropriate power of 10, then simplify
Divide numerator by denominator
Multiply whole number by denominator, add numerator
Divide numerator by denominator to get whole and remainder
Fraction Calculator
Choose the operation you need and enter your values to calculate with fractions, mixed numbers, and decimals.
🔢 Fraction Operations
✂️ Simplify Fractions
🔄 Decimal/Fraction Converter
🔢 Mixed Numbers Calculator
How These Calculators Work
Basic Operations Calculator
Enter two fractions and select the operation. The calculator finds the least common denominator, performs the operation, and returns the result in fraction, decimal, and mixed number formats.
Simplify Fractions Calculator
Enter a fraction to simplify. The calculator finds the greatest common divisor (GCD) of numerator and denominator, then divides both by the GCD to produce the simplest form.
Decimal/Fraction Converter
Convert decimals to fractions by placing the decimal digits over the appropriate power of 10, then simplifying. Convert fractions to decimals by dividing numerator by denominator.
Mixed Numbers Calculator
Convert mixed numbers to improper fractions using the formula: (whole × denominator + numerator) / denominator. Convert improper fractions to mixed numbers by dividing numerator by denominator.
Big Number Handling
These calculators handle large numerators and denominators accurately, maintaining precision even with numbers in the millions. Large fractions are automatically simplified to manageable forms.
Uses of Fraction Calculators
Student Learning and Homework
Students use fraction calculators to check homework, verify calculations, and learn fraction concepts. Seeing multiple representation forms (fraction, decimal, mixed number) reinforces understanding.
Cooking and Baking
Recipes often use fractional measurements (1/2 cup, 3/4 teaspoon). Doubling or halving recipes requires fraction multiplication and division. Calculators quickly convert between measurement units.
Construction and Carpentry
Measurements in inches and feet frequently involve fractions (5 3/8 inches). Calculations for cutting materials, calculating areas, and material quantities rely on fraction mathematics.
Financial Planning
Interest rates, stock prices, and probability calculations use fractions and decimals. Converting between formats helps with financial analysis and investment decisions.
Medicine and Healthcare
Dosage calculations often involve fractions: 1/2 tablet, 3/4 teaspoon. Accurate fraction arithmetic is critical for patient safety in pharmaceutical contexts.
Engineering and Science
Complex calculations in physics, chemistry, and engineering frequently involve fractions. Unit conversions and dimensional analysis require fraction operations.
Music and Art
Musical timing (1/4 note, 3/8 time signature) and proportional measurements in visual arts depend on fractions. Understanding these relationships enhances creative work.
Frequently Asked Questions
A proper fraction has numerator smaller than denominator (3/4, 1/2), representing a value less than 1. An improper fraction has numerator greater than or equal to denominator (5/3, 8/8), representing a value ≥ 1. Both are mathematically valid; improper fractions are often converted to mixed numbers for readability.
Find the least common denominator (LCD) of the two denominators. Convert each fraction to an equivalent fraction with the LCD as denominator. Add the numerators and keep the LCD as the denominator. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Simplifying fractions reduces them to simplest form, making them easier to understand and work with. 6/9 and 2/3 are equivalent, but 2/3 is simpler. Simplified fractions are the standard for final answers in mathematics.
Multiply fractions by multiplying numerators together and denominators together: (3/4) × (2/5) = 6/20 = 3/10. Divide fractions by multiplying by the reciprocal: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.
The GCD is the largest number that divides both the numerator and denominator evenly. For 12/18, the GCD is 6 (both divisible by 6). Dividing both by 6 gives 2/3. Finding the GCD is essential for simplifying fractions.
Yes, all terminating and repeating decimals can be converted to fractions. Terminating decimals (0.75 = 3/4) convert easily. Repeating decimals (0.333... = 1/3) also convert but may require algebraic manipulation for repeating patterns.
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For 2 1/3: (2 × 3 + 1)/3 = 7/3. This conversion is necessary for fraction arithmetic operations.
Master Fractions with Confidence
Fractions are foundational to mathematics and appear in countless real-world applications. Whether you're a student mastering fraction arithmetic, a professional needing quick calculations, or someone working on recipes and measurements, these fraction calculators provide accurate, instant results for all your fraction needs.
These calculators not only provide answers but help you understand fraction relationships by showing results in multiple formats (fractions, decimals, mixed numbers). This multi-format approach deepens mathematical understanding and builds confidence in working with fractions.
Note: These calculators handle fractions and mixed numbers of any size. For educational purposes, work through problems manually first to understand the concepts, then use calculators to verify your work and explore variations quickly.