Fraction Addition Calculator

Q: How do I add fractions with different denominators?

Find the Least Common Denominator (LCD), convert both fractions to equivalent fractions with that denominator, then add the numerators. Example: 1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12.

Q: How do I add fractions with the same denominator?

Simply add the numerators and keep the denominator. Example: 2/7 + 3/7 = (2+3)/7 = 5/7.

Q: How do I add mixed numbers?

Convert each mixed number to an improper fraction, then add using the LCD method. Example: 1 1/2 + 2 1/3 → 3/2 + 7/3 → LCD=6 → 9/6 + 14/6 = 23/6 = 3 5/6.

Q: Do I always need to simplify after adding?

Yes. After adding, check if the result can be simplified by dividing by the GCF. Example: 4/6 + 2/6 = 6/6 = 1. Or 2/8 + 2/8 = 4/8 = 1/2.

Q: What if the sum is an improper fraction?

Convert the improper fraction to a mixed number by dividing the numerator by the denominator. Example: 7/4 → 7÷4 = 1 remainder 3 → 1 3/4.

Add any two fractions with step-by-step solutions. See LCD conversion, common denominator method, and automatic simplification with interactive visual diagrams.

📐 Fraction Addition Calculator

Result

Visual Diagram

Definition

What is Fraction Addition Calculator?

A Fraction Addition Calculator adds two fractions together, showing the complete step-by-step process including finding the LCD, converting to common denominators, adding numerators, and simplifying the result.

Adding fractions is one of the four basic fraction operations. When fractions have the same denominator, addition is straightforward — add the numerators and keep the denominator. When denominators differ, both fractions must first be converted to equivalent fractions with a common denominator.

Fraction addition is used in cooking (combining ingredient amounts), construction (adding measurements), finance (adding fractional shares), and science (combining partial quantities).

Interactive Visualization

Formula

Fraction Addition Calculator Formula

Same Denominator: a/c + b/c = (a + b)/c

Different Denominators:

Find the LCD of the two denominators
Convert each fraction to an equivalent fraction with the LCD
Add the numerators: (a×d₂ + b×d₁) / LCD
Simplify the result

General formula: a/b + c/d = (a×d + c×b) / (b×d)

Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Examples

Worked Examples

1/3 + 1/4

LCD(3,4) = 12. Convert: 4/12 + 3/12 = 7/12. Result: 7/12.

2/5 + 3/10

LCD(5,10) = 10. Convert: 4/10 + 3/10 = 7/10. Result: 7/10.

3/8 + 5/8

Same denominator: (3+5)/8 = 8/8 = 1.

2/3 + 5/6

LCD(3,6) = 6. Convert: 4/6 + 5/6 = 9/6 = 3/2 = 1 1/2.

FAQ

Frequently Asked Questions

Common questions about the fraction addition calculator.

How do I add fractions with different denominators?

Find the Least Common Denominator (LCD), convert both fractions to equivalent fractions with that denominator, then add the numerators. Example: 1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12.

How do I add fractions with the same denominator?

Simply add the numerators and keep the denominator. Example: 2/7 + 3/7 = (2+3)/7 = 5/7.

How do I add mixed numbers?

Convert each mixed number to an improper fraction, then add using the LCD method. Example: 1 1/2 + 2 1/3 → 3/2 + 7/3 → LCD=6 → 9/6 + 14/6 = 23/6 = 3 5/6.

Do I always need to simplify after adding?

Yes. After adding, check if the result can be simplified by dividing by the GCF. Example: 4/6 + 2/6 = 6/6 = 1. Or 2/8 + 2/8 = 4/8 = 1/2.

What if the sum is an improper fraction?

Convert the improper fraction to a mixed number by dividing the numerator by the denominator. Example: 7/4 → 7÷4 = 1 remainder 3 → 1 3/4.