Adding Fractions Calculator

Add, subtract, and simplify fractions with step-by-step solutions

Calculate Fraction Operations

Fraction 1

1/2

Fraction 2+

1/3

Calculation Result

Expression

1/2+1/3

Result

5/6
Simplified fraction

Alternative Formats

Fraction:
5/6
Mixed Number:
5/6
Decimal:
0.8333

Step-by-Step Solution

1
Original expression: 1/2 + 1/3
2
Find the LCD of denominators 2, 3: 6
3
Convert to common denominator:
4
1/2 = 1 × 3/2 × 3 = 3/6
5
1/3 = 1 × 2/3 × 2 = 2/6
6
Add numerators: 3 + 2 = 5
7
Result: 5/6

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

a/c + b/c = (a+b)/c

Different Denominators

a/b + c/d = (ad+bc)/(bd)

Least Common Denominator

LCD = LCM(denominator1, denominator2)

Simplification

Divide by GCD(numerator, denominator)

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.