Adding 3 Fractions Together

Fraction Addition Formula:

\[ \frac{a}{b} + \frac{c}{d} + \frac{e}{f} = \frac{a \times d \times f + b \times c \times f + b \times d \times e}{b \times d \times f} \]

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Sum Result:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Fraction Addition?

Adding fractions together requires finding a common denominator. For three fractions a/b, c/d, and e/f, the common denominator is the product of all three denominators (b×d×f). Each numerator is then adjusted by multiplying by the other denominators.

2. How Does the Calculator Work?

The calculator uses the fraction addition formula:

\[ \frac{a}{b} + \frac{c}{d} + \frac{e}{f} = \frac{a \times d \times f + b \times c \times f + b \times d \times e}{b \times d \times f} \]

Where:

\( a \) — First fraction numerator
\( b \) — First fraction denominator
\( c \) — Second fraction numerator
\( d \) — Second fraction denominator
\( e \) — Third fraction numerator
\( f \) — Third fraction denominator

Explanation: The calculator finds a common denominator, adjusts each numerator accordingly, sums them, and then simplifies the resulting fraction.

3. Importance of Common Denominator

Details: Fractions can only be added directly when they share the same denominator. The least common denominator (LCD) is the most efficient choice, but any common denominator (like the product of all denominators) works.

4. Using the Calculator

Tips: Enter all six values (numerators and denominators). Denominators cannot be zero. The calculator will show the unsimplified result, simplified fraction, and decimal approximation.

5. Frequently Asked Questions (FAQ)

Q1: What if denominators are the same?
A: The calculation simplifies to (a + c + e)/b, as the common denominator is already established.

Q2: How are negative fractions handled?
A: Negative numerators or denominators work normally. Two negatives make a positive.

Q3: What about mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 2½ becomes 5/2).

Q4: Why does the denominator get multiplied?
A: Multiplying denominators guarantees a common denominator, though it may not be the least common denominator.

Q5: Can I add more than three fractions?
A: Yes, the same principle extends to any number of fractions by multiplying all denominators and adjusting each numerator accordingly.