➕➖ Adding and Subtracting Fractions Calculator
Add or subtract fractions with same or different denominators
How to Use This Calculator
Choose Operation
Select Addition (+) or Subtraction (➖) using the buttons at the top.
Enter Fractions
Enter numerator and denominator for both fractions. Works with different denominators.
Click Calculate
Press the calculate button to get the result with step-by-step solution and simplified form.
Formula
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Then simplify by dividing by GCD
Example 1: Add 1/4 + 1/6
LCD of 4 and 6 = 12
1/4 = 3/12, 1/6 = 2/12
3/12 + 2/12 = 5/12
Answer: 5/12
Example 2: Subtract 2/3 − 1/4
LCD of 3 and 4 = 12
2/3 = 8/12, 1/4 = 3/12
8/12 − 3/12 = 5/12
Answer: 5/12
Example 3: Add 5/8 + 3/8
Same denominator - just add numerators
5/8 + 3/8 = 8/8 = 1
Answer: 1
About Adding and Subtracting Fractions Calculator
The Adding and Subtracting Fractions Calculator performs both addition and subtraction operations on fractions. It automatically finds the lowest common denominator (LCD), converts fractions, performs the operation, and simplifies the result.
When to Use This Calculator
- Math Homework: Solve fraction addition and subtraction problems
- Recipe Adjustments: Combine or remove ingredient amounts
- Measurements: Add or subtract length, volume, or weight measurements
- Educational Use: Learn fraction operations with different denominators
- Real-World Problems: Solve practical fraction arithmetic
- Verification: Check manual calculations
Why Use Our Calculator?
- ✅ Both Operations: Add or subtract fractions in one tool
- ✅ Auto LCD: Automatically finds lowest common denominator
- ✅ Simplified Results: Shows answers in simplest form
- ✅ Step-by-Step: See complete calculation process
- ✅ Mixed Numbers: Converts to mixed number format when needed
- ✅ Completely Free: No registration required
Understanding Fraction Operations
To add or subtract fractions with different denominators:
- Step 1: Find the Lowest Common Denominator (LCD)
- Step 2: Convert both fractions to equivalent fractions with LCD
- Step 3: Add or subtract the numerators
- Step 4: Simplify by dividing by GCD if needed
Real-World Applications
Recipes: Combine 1/3 cup + 1/4 cup sugar. LCD = 12: 4/12 + 3/12 = 7/12 cup total.
Time: Add 1/2 hour + 1/3 hour work. LCD = 6: 3/6 + 2/6 = 5/6 hour total.
Money: Subtract 1/4 from 3/5 of your budget. LCD = 20: 12/20 − 5/20 = 7/20 remaining.
Tips for Using This Calculator
- Denominators cannot be zero
- Works with any positive or negative integers
- Results are automatically simplified to lowest terms
- Shows decimal equivalent for verification
- Use for fractions with different denominators
Frequently Asked Questions
Can I add fractions with different denominators?
Yes! The calculator automatically finds the LCD and converts both fractions to equivalent forms with the same denominator before adding or subtracting.
What is the LCD?
LCD stands for Lowest Common Denominator - the smallest number that both denominators divide into evenly. For 4 and 6, LCD = 12.
How do you simplify fractions?
Divide both numerator and denominator by their Greatest Common Divisor (GCD). For example, 8/12 simplifies to 2/3 (dividing by 4).
What if the result is an improper fraction?
The calculator will show both the improper fraction and its equivalent mixed number (e.g., 17/12 = 1 5/12).
Can I use negative fractions?
Yes, the calculator handles negative numbers. Enter negative numerators or denominators as needed.
Why simplify fractions?
Simplified fractions are in lowest terms, making them easier to understand and work with. It's the standard form for fraction answers.