How To Add 3 Fractions Calculator

Fraction Addition Formula:

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

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 of Fractions:

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1. What is Fraction Addition?

Adding fractions combines two or more fractional quantities into a single fraction. To add fractions with different denominators, we first find a common denominator before adding the numerators.

2. How Does the Calculator Work?

The calculator uses the fraction addition formula:

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

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 by multiplying all denominators together, then adjusts each numerator accordingly before summing them up.

3. Importance of Common Denominator

Details: Fractions can only be directly added when they share 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 un-simplified and simplified results when applicable.

5. Frequently Asked Questions (FAQ)

Q1: Can I add more than three fractions?
A: Yes, the same principle applies - find a common denominator and sum all adjusted numerators.

Q2: What if my denominators are the same?
A: If denominators are identical, simply add the numerators and keep the same denominator.

Q3: How do I simplify the resulting fraction?
A: Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by this number.

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

Q5: What if I get a negative result?
A: Negative results are valid and indicate the sum is less than zero. The same calculation rules apply.