Add 3 Fractions

Addition of Three Fractions:

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

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Sum Result:

Decimal Value:

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1. What is Three Fraction Addition?

Adding three fractions involves finding a common denominator and combining the numerators. The calculator uses the mathematical formula to add three fractions efficiently, providing results in both fractional and decimal forms.

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:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction
\( e \) — Numerator of third fraction
\( f \) — Denominator of third fraction

Explanation: The calculator finds a common denominator (product of all denominators) and combines the numerators accordingly, then simplifies the result.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics, used in various fields including engineering, physics, and finance. Understanding this operation is essential for solving more complex mathematical problems.

4. Using the Calculator

Tips: Enter all six values (numerators and denominators for three fractions). Denominators cannot be zero. The calculator will provide both fractional and decimal results.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be non-zero.

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

Q3: Can I enter negative fractions?
A: Yes, the calculator handles negative values in numerators or denominators.

Q4: What if the result is a whole number?
A: The calculator will display the whole number when the simplified denominator is 1.

Q5: How precise is the decimal result?
A: The decimal result is rounded to 4 decimal places for readability.