3 Fraction Addition Calculator

Fraction Addition Formula:

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

First Fraction (a/b):

Second Fraction (c/d):

Third Fraction (e/f):

Sum of Fractions:

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1. What is Fraction Addition?

Fraction addition involves combining two or more fractions to form a single fraction. When adding fractions with different denominators, we first find a common denominator before adding the numerators.

2. How Does the Calculator Work?

The calculator uses the following formula to add three fractions:

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

Where:

a, c, e — Numerators of the fractions
b, d, f — Denominators of the fractions

Explanation: The calculator finds a common denominator by multiplying all three denominators together, then adds the adjusted numerators, and finally simplifies the resulting fraction.

3. Importance of Fraction Addition

Details: Adding fractions is a fundamental mathematical operation used in various fields including engineering, physics, cooking, and financial calculations. Understanding fraction addition is essential for solving more complex mathematical problems.

4. Using the Calculator

Tips: Enter the numerators and denominators for all three fractions. The denominators cannot be zero. The calculator will display the result in its simplest form.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. All denominators must be non-zero numbers.

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

Q3: Can I add more than three fractions?
A: This calculator is designed for three fractions, but the same principle applies to any number of fractions.

Q4: What if the result is an improper fraction?
A: The calculator will display the improper fraction in its simplest form. You may convert it to a mixed number if desired.

Q5: Does the order of fractions matter in addition?
A: No, fraction addition is commutative - you can add them in any order and get the same result.