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How do I add, subtract, multiply, or divide fractions?

Add, subtract, multiply, and divide fractions. Simplify fractions and convert between fractions, decimals, and percentages.

What This Calculator Is

A fraction calculator performs addition, subtraction, multiplication, and division with fractions, providing results in both fractional and decimal form. It automatically simplifies fractions to their lowest terms and handles mixed numbers, eliminating the tedious manual work of fraction arithmetic.

Who This Calculator Is For

Students learning or reviewing fraction operations, professionals in fields requiring precise fractional measurements (cooking, construction), and anyone who occasionally needs fraction math but doesn't remember the rules.

When to Use This Calculator

Use this calculator when combining recipe ingredients with fractional measurements, solving homework problems, working on construction or crafting projects, or whenever you need to add, subtract, multiply, or divide fractions.

Inputs

3
4
1
2

Results

Sum (Simplified)

5/4

Difference1/4
Product3/8
Quotient3/2

Results are for informational purposes. Verify calculations for critical applications.

Insights

Fraction results

Sum: 5/4 • Difference: 1/4 • Product: 3/8 • Quotient: 3/2

How Fraction Is Calculated

For addition/subtraction, find a common denominator. For multiplication, multiply numerators and denominators. For division, multiply by the reciprocal. Then simplify using the greatest common divisor.

Sum = (n1*d2 + n2*d1) / (d1*d2), simplified
Difference = (n1*d2 - n2*d1) / (d1*d2), simplified
Product = (n1*n2) / (d1*d2), simplified
Quotient = (n1*d2) / (d1*n2), simplified
All results reduced via greatest common divisor (GCD)
Where:
n1/d1 = first fraction numerator/denominator (defaults 1/2), n2/d2 = second fraction (defaults 1/4)
Assumptions:
Zero denominators are replaced with 1 to avoid division errors (so a 0 denominator fraction is silently treated as a whole number over 1)
Simplified fraction with denominator 1 displayed as a whole number; negative denominators normalized to positive with sign moved to numerator
Quotient denominator (d1*n2)=0 treated as 1

Key Takeaways

  • •To add fractions: find common denominator, add numerators, keep denominator
  • •To multiply fractions: multiply numerators together, multiply denominators together
  • •To divide fractions: flip the second fraction and multiply
  • •Always simplify by dividing both numerator and denominator by their GCD
  • •Convert to decimals by dividing numerator by denominator

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How do I calculate percentages?

Calculate percentages, percentage changes, and percentage differences. Find what percent one number is of another.

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