➗ Fraction Calculator
Enter any two fractions to add, subtract, multiply, or divide them - and get a complete step-by-step solution showing every stage of the working. Results are automatically simplified and shown as both a fraction and a decimal. Includes mixed number conversion and a side-by-side fraction comparison tool.
➗ Fraction Calculator
📝 Step-by-Step Solution
✂️ Fraction Simplifier
Enter a fraction to reduce it to its simplest form.
🔄 Decimal → Fraction
Convert any decimal to a fraction.
⚖️ Compare Two Fractions
Find out which fraction is larger, smaller or equal.
📋 Common Fractions Reference
| Fraction | Simplified | Decimal | Percentage | Notes |
|---|
📐 Fraction Formulas
Addition & Subtraction
Find the LCM (Least Common Multiple) of denominators, then add/subtract numerators.
a/b − c/d = (a×d − c×b) / (b×d) [then simplify]
Example: 1/2 + 1/3
= (1×3 + 1×2) / (2×3)
= (3 + 2) / 6
= 5/6
Multiplication
Multiply numerators together, multiply denominators together, then simplify.
Example: 2/3 × 3/4
= (2×3) / (3×4)
= 6/12 = 1/2
Division
Multiply by the reciprocal (flip the second fraction).
Example: 1/2 ÷ 1/4
= 1/2 × 4/1
= 4/2 = 2
Simplification (GCD Method)
Divide both numerator and denominator by their Greatest Common Divisor (GCD).
Example: 12/18
GCD(12,18) = 6
= (12÷6) / (18÷6) = 2/3
GCD (Euclidean Algorithm)
while b ≠ 0:
temp = b
b = a mod b
a = temp
return a
GCD(12, 18):
18 mod 12 = 6 → GCD(12, 6)
12 mod 6 = 0 → GCD(6, 0) = 6
Mixed Number ↔ Improper Fraction
Improper → Mixed: n/d = (n÷d) remainder (n mod d)
= whole (remainder/d)
Example: 2 3/4 = (2×4+3)/4 = 11/4
Example: 11/4 = 2 remainder 3 = 2 3/4
❓ Frequently Asked Questions
Fraction Calculator - All Four Operations With Step-by-Step Workings
Fractions are one of the areas of mathematics where students most commonly make mistakes - and where the mistakes are most easy to understand once the method is clear. Whether you're adding fractions for a recipe, dividing fractions in an algebra problem, or simplifying a result for a test, the key is following the same logical steps every time. This calculator shows exactly those steps, so you can see how the answer was reached, not just what it is.
Adding and Subtracting Fractions - The Common Denominator Method
You can only add or subtract fractions when they have the same denominator - because the denominator tells you what size the pieces are, and you can only combine pieces of the same size. When denominators are different, you first need to convert both fractions to equivalent fractions with the same denominator.
The most efficient approach is to find the Least Common Multiple (LCM) of the two denominators - this gives the smallest common denominator, which keeps the numbers manageable:
- Find the LCM of the two denominators
- For each fraction, multiply top and bottom by the factor that makes the denominator equal the LCM
- Add or subtract the numerators (denominator stays the same)
- Simplify the result by dividing by the GCD
Example: 2/3 + 3/4. LCM of 3 and 4 = 12. Convert: 2/3 = 8/12, 3/4 = 9/12. Add: 8/12 + 9/12 = 17/12. As a mixed number: 1 and 5/12.
Multiplying and Dividing Fractions - The Simpler Operations
Unlike addition, multiplication and division of fractions don't require a common denominator - making them the easier pair of operations once you know the pattern:
Multiplying Fractions
- Multiply numerators: top × top
- Multiply denominators: bottom × bottom
- Simplify the result
- Formula: (a/b) × (c/d) = (a×c)/(b×d)
- Example: 2/3 × 3/4 = 6/12 = 1/2
- Tip: cross-cancel before multiplying to keep numbers small - divide a top by a bottom if they share a factor
Dividing Fractions
- Flip the second fraction (find its reciprocal)
- Then multiply as normal
- Formula: (a/b) ÷ (c/d) = (a/b) × (d/c) = (a×d)/(b×c)
- Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3
- Memory trick: "Keep, Change, Flip" - keep the first fraction, change ÷ to ×, flip the second
Simplifying Fractions - Finding the GCD
A fraction is fully simplified (or "in lowest terms") when the only number that divides both the numerator and denominator is 1. To simplify, find the Greatest Common Divisor (GCD) - the largest number that divides both - and divide both parts by it.
Example: simplify 36/48. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. GCD = 12. 36÷12 = 3, 48÷12 = 4. Simplified: 3/4.
Quick shortcut: if both numbers are even, divide by 2. Keep halving until one is odd. Then check for other common factors (3, 5, 7...). The Euclidean algorithm is the most efficient method for large numbers: GCD(48, 36) = GCD(36, 12) = GCD(12, 0) = 12.
Mixed Numbers and Improper Fractions - Converting Between Them
An improper fraction has a numerator larger than the denominator (e.g., 11/4). A mixed number combines a whole number and a proper fraction (e.g., 2 and 3/4). Converting between them:
- Improper → Mixed: Divide numerator by denominator. Quotient = whole number, remainder = new numerator. Example: 11/4 → 11÷4 = 2 remainder 3 → 2 and 3/4.
- Mixed → Improper: Multiply whole number by denominator, add the numerator, keep the denominator. Example: 2 and 3/4 → (2×4)+3 = 11 → 11/4.
When performing arithmetic with mixed numbers, it's usually easiest to convert them to improper fractions first, do the calculation, then convert back. The calculator handles this automatically.