Math Toolfraction calculatorUpdated 2026

Fractions Calculator with Step-by-Step Reduction

Add, subtract, multiply, and divide fractions and mixed numbers with common denominator steps and simplified results.

Fraction Arithmetic

Simplified Fraction Result
Invalid
Decimal Equivalent: 0
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How Fractions Calculator Works: Mathematical Formula & Steps

Adds, subtracts, multiplies, and divides rational numbers using the Least Common Multiple (LCM) of denominators and simplifies to lowest terms via Greatest Common Divisor (GCD).

Fraction Arithmetic & Common Denominators
a/b ± c/d = (ad ± bc) / bd | a/b × c/d = ac / bd | (a/b) ÷ (c/d) = ad / bc
Where:
  • a, c (Numerators): Top parts representing fractional counts.
  • b, d (Denominators): Bottom parts representing total equal divisions.

Worked Real-World Example: Step-by-Step Calculation

To illustrate how the fraction calculator works in practice, consider the following real scenario:

Adding 3/4 + 2/5 Step by Step

Scenario: Add fractions with unlike denominators: 3/4 and 2/5.

Step 1: Find common denominator (LCM of 4 and 5)
LCM(4, 5) = 20
Step 2: Convert 3/4 to twentieths
3/4 = (3×5)/(4×5) = 15/20
Step 3: Convert 2/5 to twentieths
2/5 = (2×4)/(5×4) = 8/20
Step 4: Add numerators over common denominator
(15 + 8) / 20 = 23/20
Final Result: Result is 23/20 (improper fraction), which equals 1 3/20 (mixed number) or 1.15 in decimal form.

Key Takeaways & Best Practices

  • To divide fractions, multiply by the reciprocal of the second fraction (keep, change, flip).
  • Always reduce final fractions by dividing both numerator and denominator by their greatest common divisor (GCD).

International & Multi-Currency Standards

Whether you are evaluating calculations in the United States (USD), United Kingdom (GBP), Eurozone (EUR), South Africa (ZAR), Australia (AUD), Canada (CAD), or India (INR), everycalculator dynamically formats outputs according to regional accounting notations and dual metric/imperial conversions.

Related Search Terms & Common Queries

This calculator is designed to provide immediate answers for popular search queries including:

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Frequently Asked Questions

How do you add fractions with different denominators?

Find the least common denominator (LCD), convert each fraction so they share this denominator, add the numerators together while keeping the denominator identical, and simplify the fraction to lowest terms.

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