How to Use This Calculator
- Enter numerators and denominators: Input the top and bottom numbers for both fractions.
- Select arithmetic operator: Choose +, −, ×, or ÷.
- View step-by-step simplification: Watch the LCD common denominator search and GCD reduction.
Formula and Calculation Steps
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)Worked Examples and Reference Table
| Operation | Simplified Fraction | Decimal |
|---|---|---|
| 1/2 + 1/4 | 3/4 | 0.75 |
| 3/4 - 1/3 | 5/12 | 0.4167 |
| 2/3 × 3/5 | 2/5 | 0.40 |
| 4/5 ÷ 2/3 | 6/5 (1 1/5) | 1.20 |
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction to equivalent fractions with that common denominator, add the numerators, and reduce to simplest form.
How do you divide two fractions?
Multiply the first fraction by the reciprocal (the inverted form) of the second fraction: (a/b) ÷ (c/d) = (a/b) × (d/c).
What is a mixed number vs an improper fraction?
An improper fraction has a numerator larger than or equal to its denominator (e.g. 7/4). A mixed number expresses it as an integer plus a proper fraction (e.g. 1 3/4).
Can you simplify negative fractions?
Yes. Divide both numerator and denominator by their greatest common divisor (GCD) and place the negative sign in the numerator or in front of the fraction.
Why cannot a fraction have a denominator of zero?
Division by zero is mathematically undefined because there is no number that can be multiplied by zero to produce a non-zero numerator.