Fraction Calculator With 3 Numbers Add

Fraction Addition Formula:

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

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?

Three fraction addition involves finding a common denominator and then summing 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:

\( a \) — First fraction numerator
\( b \) — First fraction denominator
\( c \) — Second fraction numerator
\( d \) — Second fraction denominator
\( e \) — Third fraction numerator
\( f \) — Third fraction denominator

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

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics, used in various fields including engineering, physics, and finance. It's essential for combining ratios or parts of wholes.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be positive integers. The calculator will provide both fractional and decimal results.

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. Check your input values if this was unexpected.

Q2: Why does the denominator have to be positive?
A: In mathematics, division by zero is undefined and negative denominators are conventionally made positive by adjusting the numerator sign.

Q3: How is the simplified form calculated?
A: The calculator uses the greatest common divisor (GCD) to reduce the fraction to its simplest form.

Q4: Can I use decimal numbers?
A: The calculator accepts decimal inputs for numerators but requires integers for denominators.

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