Fraction Calculator - Free Online Math Tool

Advanced fraction calculator with addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Perfect for students, teachers, and professionals.

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Fraction Calculator

Add, subtract, multiply, and divide fractions

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Operation

First Fraction

Numerator

Denominator

Second Fraction

Numerator

Denominator

How to Use Fraction Calculator

Step 1: Select Operation

Choose from addition (+), subtraction (-), multiplication (×), or division (÷).

Step 2: Enter Fractions

Input the numerator and denominator for both fractions. The calculator will automatically calculate the result.

3/4 + 1/6 = 11/12

Fraction Operations & Properties

Addition & Subtraction

Fractions require a common denominator. The calculator finds the least common multiple (LCM) automatically.

3/4 + 1/6 = (3×6)/(4×6) + (1×4)/(6×4) = 18/24 + 4/24 = 22/24 = 11/12

Multiplication & Division

Multiply numerators and denominators directly. For division, multiply by the reciprocal.

3/4 × 1/6 = (3×1)/(4×6) = 3/24 = 1/8

Frequently Asked Questions

What is a fraction and why is it important in mathematics?

A fraction represents a part of a whole, consisting of a numerator (top number) and denominator (bottom number). Fractions are essential for representing values between whole numbers, ratios, percentages, and many real-world applications like cooking, construction, and scientific calculations.

What is the easiest way to add fractions with different denominators?

Find the least common multiple (LCM) of the denominators, convert each fraction to have that common denominator, then add the numerators. Our calculator automatically handles this process for you. For example: 3/4 + 1/6 = 9/12 + 2/12 = 11/12.

How do I convert a decimal to a fraction?

Write the decimal as a fraction with the decimal places as the denominator (e.g., 0.75 = 75/100), then simplify by finding the greatest common divisor (GCD) of the numerator and denominator. 0.75 becomes 3/4.

What's the difference between proper and improper fractions?

A proper fraction has a numerator smaller than the denominator (e.g., 3/4), while an improper fraction has a numerator equal to or larger than the denominator (e.g., 5/4). Improper fractions can be converted to mixed numbers.

Why do I need to learn fractions if I have a calculator?

Understanding fractions helps you interpret results, catch errors, and solve problems when calculators aren't available. It also builds mathematical thinking skills essential for advanced topics like algebra and calculus.

How can I practice fractions effectively?

Start with simple problems and gradually increase complexity. Use visual aids like pie charts and number lines, practice with real-world examples, and use our fraction calculator to check your work and build confidence.

What are equivalent fractions and how do I find them?

Equivalent fractions have the same value but different numerators and denominators (e.g., 1/2 = 2/4 = 3/6). To find equivalent fractions, multiply or divide both the numerator and denominator by the same non-zero number.

How do I simplify fractions to their lowest terms?

To simplify fractions, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD. For example, 8/12 simplifies to 2/3 because the GCD of 8 and 12 is 4.

What is the least common denominator (LCD) and why is it important?

The LCD is the smallest number that is a multiple of all denominators in a set of fractions. It's essential for adding and subtracting fractions with different denominators, as it allows you to convert them to equivalent fractions with the same denominator.

How do I multiply fractions step by step?

To multiply fractions: 1) Multiply the numerators together, 2) Multiply the denominators together, 3) Simplify the result if possible. For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2.

How do I divide fractions using the reciprocal method?

To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second fraction. For example, 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2 2/3.

What are the common fraction operations used in real life?

Fraction operations are used in cooking (recipe scaling), construction (measurements), finance (interest calculations), science (concentration ratios), and many other fields where precise part-to-whole relationships are important.

How do I convert mixed numbers to improper fractions?

To convert mixed numbers to improper fractions: 1) Multiply the whole number by the denominator, 2) Add the numerator, 3) Place the result over the original denominator. For example, 2 1/3 = (2×3 + 1)/3 = 7/3.

How do I convert fractions to percentages?

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 = 75%. Our calculator can handle these conversions automatically.

What are complex fraction problems and how do I solve them?

Complex fraction problems involve multiple operations in sequence. Break them down step by step, follow the order of operations (PEMDAS), and use visual representations when helpful. For example: (2/3 + 1/4) × (3/5 - 1/2) = 11/12 × 1/10 = 11/120.

How accurate are fraction calculator results?

Our calculator provides exact fraction results using precise mathematical algorithms. For decimal conversions, results are accurate to 6 decimal places, which is sufficient for most academic and professional applications.

What are the key features of a professional fraction calculator?

Professional fraction calculators should support all four operations (addition, subtraction, multiplication, division), handle mixed numbers, provide step-by-step solutions, convert between fractions and decimals, simplify results, and work with both proper and improper fractions.

How do fractions appear in everyday life?

Fractions appear in time (quarter past 3), money (half dollar), sports (three-quarters of the game), cooking (3/4 cup of flour), construction (5/8 inch thickness), and measurements (half inch). Understanding fractions helps you navigate the world more effectively!

What are the different types of fractions I should know?

The main types are: proper fractions (numerator < denominator), improper fractions (numerator ≥ denominator), mixed numbers (whole number + fraction), and equivalent fractions (same value, different form). Each type has specific uses and conversion methods.

How do I solve fraction word problems?

For fraction word problems: 1) Read carefully and identify what's being asked, 2) Determine which operation to use, 3) Set up the problem with fractions, 4) Solve step by step, 5) Check your answer makes sense in the original context.

Can I use this calculator for complex fraction expressions?

Yes! Our calculator can handle complex expressions involving multiple operations, mixed numbers, and various fraction types. It automatically follows the order of operations and provides step-by-step solutions for educational purposes.