Adding Fractions Calculator
Add, subtract, and simplify fractions with step-by-step solutions
Calculate Fraction Operations
Fraction 1
Fraction 2+
Calculation Result
Expression
Result
Alternative Formats
Step-by-Step Solution
Example Calculations
Example 1: Same Denominators
Problem: 2/7 + 3/7
Solution: Add numerators: 2 + 3 = 5
Result: 5/7
Example 2: Different Denominators
Problem: 1/2 + 1/3
Step 1: Find LCD of 2 and 3: LCD = 6
Step 2: Convert: 1/2 = 3/6, 1/3 = 2/6
Step 3: Add: 3/6 + 2/6 = 5/6
Result: 5/6
Example 3: Mixed Numbers
Problem: 7/4 + 3/8
Step 1: Find LCD of 4 and 8: LCD = 8
Step 2: Convert: 7/4 = 14/8, 3/8 = 3/8
Step 3: Add: 14/8 + 3/8 = 17/8
Result: 17/8 or 2 1/8
Key Formulas
Same Denominators
Different Denominators
Least Common Denominator
Simplification
Fraction Rules
Same Denominator: Add/subtract numerators only
Keep denominator unchanged
Different Denominators: Find common denominator first
Use LCD for easier calculation
Simplify: Always reduce to lowest terms
Divide by GCD of numerator and denominator
Zero Denominator: Undefined fraction
Division by zero is not allowed
Real-World Applications
Cooking & Recipes
Combining ingredient measurements
Construction
Adding material lengths and measurements
Finance
Calculating parts of a whole
Education
Grade calculations and percentages
Understanding Fraction Addition and Subtraction
What are Fractions?
A fraction represents a part of a whole, written as a ratio of two numbers: numerator (top) and denominator (bottom). The denominator tells you how many equal parts make up the whole, while the numerator tells you how many of those parts you have.
Adding Fractions
When adding fractions with the same denominator, simply add the numerators and keep the same denominator. For different denominators, you must first find a common denominator (preferably the least common denominator) before adding.
Same denominators: a/c + b/c = (a+b)/c
Different denominators: Find LCD first
Step-by-Step Process
Step 1: Check denominators
Same? Add numerators. Different? Continue to step 2.
Step 2: Find LCD
Calculate the least common denominator of all fractions.
Step 3: Convert fractions
Make all fractions have the LCD as denominator.
Step 4: Add/subtract
Perform operation on numerators, keep LCD as denominator.
Step 5: Simplify
Reduce the fraction to its lowest terms.