Fraction Calculator
How to Work with Fractions
Addition & Subtraction
Find a common denominator, then add or subtract numerators:
a/b ± c/d = (a×d ± c×b) / (b×d)
Multiplication
a/b × c/d = (a×c) / (b×d) — then simplify by GCF.
Division
Multiply by the reciprocal: a/b ÷ c/d = (a×d) / (b×c)
Frequently Asked Questions
What is 3/4 + 2/3?
LCD of 4 and 3 = 12. Convert: 9/12 + 8/12 = 17/12 = 1 5/12.
How do I simplify a fraction?
Divide both numerator and denominator by their GCF (Greatest Common Factor). To simplify 18/24: GCF(18,24) = 6. 18÷6 = 3, 24÷6 = 4. Simplified: 3/4.
What is a mixed number?
A mixed number combines a whole number and a proper fraction: 2 3/4 = 2 + 3/4 = 11/4 as an improper fraction. To convert: multiply whole number by denominator, add numerator: 2×4+3 = 11/4.
Simplification
Divide both parts by their GCF. Example: GCF(12,8) = 4 → 12/8 = 3/2.
Quick Reference
| Operation | Formula | Example | Result |
|---|---|---|---|
| Addition | (a×d + b×c) / (b×d) | 1/2 + 1/3 | 5/6 |
| Subtraction | (a×d − b×c) / (b×d) | 3/4 − 1/4 | 1/2 |
| Multiplication | (a×c) / (b×d) | 2/3 × 3/4 | 1/2 |
| Division | (a×d) / (b×c) | 1/2 ÷ 1/4 | 2 |
