Adding and Subtracting Fractions Calculator – Guide & Formulas
Add and subtract fractions step by step. Handles like and unlike denominators, mixed numbers, and simplifies results to lowest terms.
Add and subtract fractions step by step. Enter fractions with like or unlike denominators, including mixed numbers, and get simplified results with clear working.
Key Takeaway
Use the free Adding and Subtracting Fractions Calculator to add and subtract fractions step by step. handles like and unlike denominators, mixed numbers, and simplifies results to lowest terms. Get instant results with step-by-step explanations.
How to Use the Adding and Subtracting Fractions Calculator
- Enter the first fraction (numerator and denominator) or a mixed number.
- Select addition (+) or subtraction (−).
- Enter the second fraction.
- Review the step-by-step solution showing LCD finding, conversion, and final simplified result.
The Formula
Variable Definitions
- a/b: The first fraction with numerator a and denominator b
- c/d: The second fraction with numerator c and denominator d
- LCD: Least Common Denominator — the smallest number divisible by both denominators
- GCD: Greatest Common Divisor — used to simplify the final fraction
Adding 2/3 + 5/8
Add two fractions with unlike denominators.
- Step 1: Find the LCD of 3 and 8. The LCD is 24.
- Step 2: Convert 2/3: (2 × 8)/(3 × 8) = 16/24.
- Step 3: Convert 5/8: (5 × 3)/(8 × 3) = 15/24.
- Step 4: Add numerators: 16 + 15 = 31. Result: 31/24.
- Step 5: Simplify: GCD(31, 24) = 1, so 31/24 = 1 7/24.
Frequently Asked Questions
How do I add fractions with the same denominator?
When denominators are the same (like fractions), simply add the numerators and keep the denominator. For example, 3/7 + 2/7 = 5/7.
How do I find the least common denominator?
The LCD is the least common multiple (LCM) of the two denominators. For example, LCM(4,6) = 12. List multiples of each denominator and find the smallest one they share.
What is a mixed number?
A mixed number combines a whole number and a fraction, like 2 3/4. To add/subtract mixed numbers, convert them to improper fractions first, then follow the standard procedure.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the result over the denominator. For example, 2 3/4 = (2 × 4 + 3)/4 = 11/4.
What does "simplify to lowest terms" mean?
Simplifying means dividing both numerator and denominator by their GCD. For example, 8/12 simplifies to 2/3 (GCD = 4). Always simplify your final answer.
How do I subtract fractions?
Subtraction works the same as addition: find a common denominator, convert both fractions, then subtract the numerators. The denominator stays the same.
What if I get a negative result?
A negative fraction means the second fraction was larger. You can write it as -(numerator/denominator) or move the negative sign to the numerator or denominator.
Can I add more than two fractions?
Yes. Process them two at a time from left to right, or find the LCD of all denominators at once and add all converted numerators together.