Fraction Calculator
To add fractions, find the LCD and add numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. To subtract, same process but subtract. To multiply, multiply numerators and denominators: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the reciprocal: 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
Add, subtract, multiply, and divide fractions with step-by-step solutions. Supports mixed numbers, auto-simplifies results, and shows decimal equivalents. Perfect for students, teachers, and anyone working with fractions.
First Fraction
Second Fraction
Quick Reference: Fraction Operations
| Operation | Rule | Example |
|---|---|---|
| Addition | a/b + c/d = (ad + bc) / bd | 1/2 + 1/3 = 5/6 |
| Subtraction | a/b - c/d = (ad - bc) / bd | 3/4 - 1/4 = 1/2 |
| Multiplication | a/b × c/d = ac / bd | 2/3 × 3/4 = 1/2 |
| Division | a/b ÷ c/d = a/b × d/c | 1/2 ÷ 1/4 = 2 |
How to Use
- 1
Choose operation
Select Add, Subtract, Multiply, or Divide
- 2
Enter first fraction
Type the numerator and denominator (and whole number for mixed numbers)
- 3
Enter second fraction
Input the second fraction or mixed number
- 4
Calculate
Click Calculate or press Enter to see the result
- 5
View solution
See the simplified result, decimal equivalent, and step-by-step explanation
Frequently Asked Questions
- How do I add fractions with different denominators?
- To add fractions with different denominators, find the least common denominator (LCD), convert each fraction, then add the numerators. Example: 1/2 + 1/3. LCD of 2 and 3 is 6. Convert: 1/2 = 3/6, 1/3 = 2/6. Add: 3/6 + 2/6 = 5/6.
- How do I subtract fractions?
- Subtract fractions the same way you add them: find the LCD, convert fractions, then subtract numerators. Example: 3/4 - 1/3. LCD is 12. Convert: 3/4 = 9/12, 1/3 = 4/12. Subtract: 9/12 - 4/12 = 5/12.
- How do I multiply fractions?
- To multiply fractions, multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-cancel before multiplying to keep numbers smaller.
- How do I divide fractions?
- To divide fractions, multiply by the reciprocal of the second fraction (flip the second fraction, then multiply). Example: 5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4. The phrase "keep, change, flip" helps remember this: keep first fraction, change ÷ to ×, flip second fraction.
- How do I calculate with mixed numbers like 1 1/2?
- Convert mixed numbers to improper fractions first: multiply the whole number by the denominator and add the numerator. Example: 1 1/2 = (1×2 + 1)/2 = 3/2. Then perform the operation and convert back if needed. 3/2 + 1/3 = 9/6 + 2/6 = 11/6 = 1 5/6.
- How do I simplify a fraction?
- Find the Greatest Common Divisor (GCD) of numerator and denominator, then divide both by it. Example: 12/18. GCD(12,18) = 6. So 12/18 = 2/3. A fraction is fully simplified when numerator and denominator share no common factors other than 1.
- What is the least common denominator (LCD)?
- The LCD is the smallest number that both denominators divide into evenly. For 1/4 and 1/6, the LCD is 12 (since 12 is divisible by both 4 and 6). To find LCD: list multiples of each denominator until you find a common one, or use the formula LCD(a,b) = a×b / GCD(a,b).