Sum Of 3 Fractions

Fraction Addition Formula:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Sum Result:

Decimal Value:

Simplified Fraction:

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1. What is Sum Of 3 Fractions?

The Sum Of 3 Fractions calculator computes the addition of three fractions using the common denominator method. It provides results in both fractional and decimal forms, along with simplification when possible.

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:

\( a, c, e \) — Numerators of the three fractions
\( b, d, f \) — Denominators of the three fractions (must be non-zero)

Explanation: The calculator finds a common denominator by multiplying all denominators together, then combines the numerators accordingly.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics, with applications in ratios, proportions, measurements, and various real-world calculations.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be non-zero. The calculator will display the result in three formats: original fraction, decimal equivalent, and simplified fraction.

5. Frequently Asked Questions (FAQ)

Q1: What if I enter zero for a denominator?
A: The calculator requires non-zero denominators. Division by zero is mathematically undefined.

Q2: How does the simplification work?
A: The calculator uses the greatest common divisor (GCD) to reduce the fraction to its simplest form.

Q3: Can I enter negative numbers?
A: Yes, the calculator accepts negative values for numerators but denominators must be positive.

Q4: What's the precision of decimal results?
A: Decimal results are rounded to 4 decimal places for readability.

Q5: Does this work for mixed numbers?
A: No, convert mixed numbers to improper fractions first (e.g., 1½ becomes 3/2).