Adding Three Fraction Calculator

Three 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):

Result:

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1. What is Three Fraction Addition?

Three fraction addition involves finding a common denominator for all three fractions and then adding their numerators. The result is a new fraction that represents the sum of the original three fractions.

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:

\( \frac{a}{b} \) — First fraction
\( \frac{c}{d} \) — Second fraction
\( \frac{e}{f} \) — Third fraction

Explanation: The calculator finds a common denominator (b×d×f) and then adds the adjusted numerators.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics and has applications in various fields including engineering, physics, and finance. Understanding fraction operations is essential for solving complex mathematical problems.

4. Using the Calculator

Tips: Enter numerators and denominators for all three fractions. Denominators must be positive integers. The calculator will display the result in both unsimplified and simplified forms (if simplification is possible).

5. Frequently Asked Questions (FAQ)

Q1: What if I enter a zero denominator?
A: The calculator requires denominators to be positive integers. Division by zero is undefined.

Q2: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by this number.

Q3: Can I enter negative fractions?
A: Yes, numerators can be negative, but denominators must remain positive.

Q4: What if the result is an improper fraction?
A: The calculator displays the result as-is. You may convert it to a mixed number if desired.

Q5: Does this work for decimal fractions?
A: This calculator is designed for integer numerators and denominators. For decimals, convert them to fractions first.