Fraction Calculator

Perform operations with fractions including addition, subtraction, multiplication, and division. Convert between mixed numbers and improper fractions with ease.

Whole Number 1 Optional: Enter 0 if using simple fraction

Numerator 1 Top number of the first fraction

Denominator 1 Bottom number of the first fraction

Operation

Whole Number 2 Optional: Enter 0 if using simple fraction

Numerator 2 Top number of the second fraction

Denominator 2 Bottom number of the second fraction

Output Format

Quick Examples:

How to Use This Calculator

Enter the whole number (if any), numerator, and denominator for your first fraction
Select the operation you want to perform (addition, subtraction, multiplication, or division)
Enter the whole number (if any), numerator, and denominator for your second fraction
Choose your preferred output format (improper fraction, mixed number, decimal, or all)
Click Calculate to see the result in your selected format

Formula Used


            Addition: a/b + c/d = (ad + bc) / bd

            Subtraction: a/b - c/d = (ad - bc) / bd

            Multiplication: a/b × c/d = ac / bd

            Division: a/b ÷ c/d = ad / bc

Where:

a = Numerator of the first fraction
b = Denominator of the first fraction
c = Numerator of the second fraction
d = Denominator of the second fraction

Example Calculation

Real-World Scenario:

A recipe calls for 1/2 cup of flour and 1/3 cup of sugar. To find the total amount of dry ingredients needed, we need to add these fractions.

Given:

First fraction = 1/2
Second fraction = 1/3
Operation = Addition

Calculation:

1/2 + 1/3 = (1×3 + 2×1) / (2×3) = (3 + 2) / 6 = 5/6

Result: The total amount of dry ingredients needed is 5/6 cup.

Why This Calculation Matters

Practical Applications

Cooking and baking measurements
Construction and carpentry calculations
Financial calculations with interest rates

Key Benefits

Accurate results without manual errors
Time-saving for complex fraction operations
Helps visualize fractions in different formats

Common Mistakes & Tips

A common mistake is adding or subtracting numerators and denominators directly (e.g., 1/2 + 1/3 = 2/5). Always find a common denominator first by multiplying the denominators together or finding the least common multiple.

After performing operations, always simplify your result by dividing both the numerator and denominator by their greatest common divisor. For example, 6/8 should be simplified to 3/4.

When dividing by a fraction, remember to multiply by its reciprocal. For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2, not 1/2 ÷ 1/4 = 1/8.

Frequently Asked Questions

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, then add the numerator. Place this result over the original denominator. For example, 2 3/4 = (2×4+3)/4 = 11/4.

Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator, and the denominator stays the same. For example, 11/4 = 2 remainder 3, so 11/4 = 2 3/4.

Find the least common multiple (LCM) of the denominators. You can do this by listing multiples of each denominator until you find a common one, or by using prime factorization. For example, the LCM of 4 and 6 is 12.

References & Disclaimer

Mathematical Disclaimer

This fraction calculator provides accurate mathematical results based on standard fraction operations. Results are presented in simplified form when possible. For educational purposes, we recommend understanding the manual process of fraction operations in addition to using this calculator.

References

Math is Fun - Fractions - Comprehensive guide to understanding and working with fractions
Khan Academy - Fraction Arithmetic - Video tutorials and practice exercises for fraction operations
Calculator Soup - Fraction Calculators - Additional resources and examples for fraction calculations

Accuracy Notice

This calculator performs calculations using standard JavaScript floating-point arithmetic, which may have minor precision limitations for extremely large or complex fractions. For academic or professional use, verify important calculations manually or with specialized mathematical software.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

Connect with LinkedIn

Tags:

math arithmetic fraction formula calculation

Related Calculators