How To Add 3 Fractions

Formula for adding three fractions:

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

First fraction numerator (a):

First fraction denominator (b):

Second fraction numerator (c):

Second fraction denominator (d):

Third fraction numerator (e):

Third fraction denominator (f):

Result:

Simplified Result:

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1. What is Fraction Addition?

Adding fractions involves finding a common denominator and then combining the numerators. When adding three fractions, we need to find a denominator that all three denominators divide into evenly.

2. How Does the Calculator Work?

The calculator uses the following 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:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction
\( e \) — Numerator of third fraction
\( f \) — Denominator of third fraction

Explanation: The formula finds the common denominator (b × d × f) and adjusts each numerator accordingly before adding them together.

3. Importance of Common Denominator

Details: Fractions can only be added directly when they have the same denominator. The common denominator is typically the least common multiple (LCM) of the individual denominators, though any common multiple will work.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be positive integers. The calculator will show both the raw result and the simplified fraction.

5. Frequently Asked Questions (FAQ)

Q1: Why can't denominators be zero?
A: Division by zero is mathematically undefined. A fraction with zero denominator doesn't represent a valid number.

Q2: What if I get a negative result?
A: Negative fractions are valid results when adding positive and negative fractions together.

Q3: How is the fraction simplified?
A: The calculator finds the greatest common divisor (GCD) of numerator and denominator and divides both by it.

Q4: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions before using this calculator.

Q5: What about reducing to lowest terms?
A: The simplified result is already in lowest terms, with no common factors between numerator and denominator.