Adding Three Fractions Calculator

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:

Final Answer:

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1. What is Three Fractions Addition?

Adding three fractions involves finding a common denominator and then combining the numerators. The general formula is:

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

2. How Does the Calculator Work?

The calculator follows these steps:

Finds the common denominator by multiplying all denominators (b×d×f)
Converts each fraction to have this common denominator
Adds the numerators while keeping the common denominator
Simplifies the resulting fraction by finding the greatest common divisor (GCD)

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics, used in algebra, calculus, and real-world applications like measurements, ratios, and probability calculations.

4. Using the Calculator

Tips: Enter all six values (numerators and denominators for three fractions). Denominators must be positive integers. The calculator will show each step of the calculation process.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominators are the same?
A: The calculation becomes simpler - just add the numerators and keep the common denominator.

Q2: Can I use negative numbers?
A: Yes, numerators can be negative, but denominators must be positive.

Q3: What if my result is an improper fraction?
A: The calculator will show the improper fraction and its simplified form. You can convert it to a mixed number if needed.

Q4: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it.

Q5: Can I use decimals?
A: This calculator works with integers only. For decimal fractions, convert them to integers first (e.g., 0.5 = 1/2).