3 Fraction Calculator

3 Fraction Operation:

\[ \frac{a}{b} \pm \frac{c}{d} \pm \frac{e}{f} \]

Numerator 1 (a):

Denominator 1 (b):

Operation 1:

Numerator 2 (c):

Denominator 2 (d):

Operation 2:

Numerator 3 (e):

Denominator 3 (f):

Calculation Steps:

Final Result (Decimal):

Final Result (Fraction):

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1. What is the 3 Fraction Calculator?

The 3 Fraction Calculator performs sequential operations (addition or subtraction) on three fractions. It shows both the decimal and simplified fractional results, helping with mathematical computations involving multiple fractions.

2. How Does the Calculator Work?

The calculator performs operations in two steps:

\[ \frac{a}{b} \pm \frac{c}{d} = \text{Intermediate Result} \] \[ \text{Intermediate Result} \pm \frac{e}{f} = \text{Final Result} \]

Where:

\( a, c, e \) — Numerators
\( b, d, f \) — Denominators (must not be zero)
\( \pm \) — Addition or subtraction operation

Explanation: The calculator first performs the operation between the first two fractions, then uses that result to perform the operation with the third fraction.

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in mathematics, especially in algebra, physics, and engineering. This calculator helps visualize the step-by-step process of combining multiple fractions.

4. Using the Calculator

Tips: Enter all numerators and denominators (denominators must not be zero), select the operations between fractions, and click Calculate. The calculator will show both decimal and simplified fractional results.

5. Frequently Asked Questions (FAQ)

Q1: Why does the denominator have to be non-zero?
A: Division by zero is mathematically undefined. A zero denominator would make the fraction invalid.

Q2: How is the fraction simplified?
A: The calculator uses a continued fraction algorithm to find the closest simplified fraction representation of the decimal result.

Q3: Can I multiply or divide fractions?
A: This version only supports addition and subtraction. A future version may include multiplication and division.

Q4: What if the result is a whole number?
A: The fractional representation will show as number/1 (e.g., 5/1 for the whole number 5).

Q5: How precise is the fraction simplification?
A: The simplification is accurate to within 0.0001% of the decimal value.