Adding 3 Fractions Calculator

Adding Three Fractions 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:

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1. What is the Adding 3 Fractions Formula?

The formula for adding three fractions calculates the sum by finding a common denominator and adding the numerators. The common denominator is the product of all three denominators, and each numerator is multiplied by the other two denominators.

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 (b×d×f) and adjusts each numerator accordingly before summing them up.

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 crucial for solving more complex mathematical problems.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be positive integers. The calculator will display both the fractional result (simplified if possible) and the decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: Why do we need a common denominator to add fractions?
A: Fractions represent parts of a whole. To add them meaningfully, they must represent parts of the same-sized whole, which is achieved by using a common denominator.

Q2: What if one of the denominators is zero?
A: Division by zero is undefined in mathematics. The calculator requires all denominators to be positive integers.

Q3: 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 number to simplify the fraction.

Q4: Can this calculator handle negative fractions?
A: Yes, negative numerators can be entered, but denominators must remain positive.

Q5: What's the advantage of this method over finding the least common denominator?
A: While finding the LCD results in simpler calculations, this method is more straightforward for programming and works universally for any three fractions.