Add Three Fractions Calculator With Variables

Three Fractions Addition Formula:

\[ \frac{x}{y} + \frac{z}{w} + \frac{u}{v} = \frac{x \cdot w \cdot v + y \cdot z \cdot v + y \cdot w \cdot u}{y \cdot w \cdot v} \]

Numerator (x):

Denominator (y):

Numerator (z):

Denominator (w):

Numerator (u):

Denominator (v):

Result:

Decimal Value:

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1. What is the Three Fractions Addition Formula?

The three fractions addition formula calculates the sum of three fractions by finding a common denominator. It's essential for algebraic operations involving multiple fractional terms.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \frac{x}{y} + \frac{z}{w} + \frac{u}{v} = \frac{x \cdot w \cdot v + y \cdot z \cdot v + y \cdot w \cdot u}{y \cdot w \cdot v} \]

Where:

\( x, z, u \) — Numerators of the three fractions
\( y, w, v \) — Denominators of the three fractions

Explanation: The formula finds the common denominator (product of all denominators) and adjusts each numerator accordingly before summing them.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in algebra, physics, and engineering calculations. The three-fraction version extends this concept for more complex equations.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be non-zero. The calculator provides both fractional and decimal results.

5. Frequently Asked Questions (FAQ)

Q1: What if denominators have common factors?
A: The calculator automatically simplifies the final result by finding the greatest common divisor.

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

Q3: How precise are the results?
A: The fractional result is exact. The decimal result is rounded to 4 decimal places.

Q4: What if I get a zero denominator?
A: The calculator will not compute a result if any denominator is zero (division by zero is undefined).

Q5: Can this handle mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 2½ becomes 5/2).