Adding Three Fractions Calculator

Formula for adding three fractions:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Result:

Decimal Result:

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1. What is Three Fractions Addition?

Adding three fractions involves finding a common denominator and then combining the numerators. The result is a new fraction that represents the sum of the three original fractions.

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 the common denominator by multiplying all three denominators together, then adjusts each numerator accordingly before adding them together.

3. Importance of Fractions Addition

Details: Adding fractions is fundamental in mathematics and has applications in various fields including engineering, physics, and everyday measurements. 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 provide both the exact fractional result (simplified if possible) and a decimal approximation.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative result?
A: Negative results are valid and indicate the sum of the fractions is negative. This occurs when the combined negative numerators outweigh the positive ones.

Q2: Why must denominators be positive?
A: By mathematical convention, denominators cannot be zero (undefined) or negative (sign is carried by the numerator).

Q3: How does simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by this number to simplify the fraction.

Q4: Can I enter decimal numbers?
A: The calculator accepts decimal inputs, but for exact fractional results, it's best to enter fractions in their original form.

Q5: What if my result is an improper fraction?
A: Improper fractions (where numerator > denominator) are valid results. You may convert to a mixed number if desired.