Add 3 Fractions Calculator

Addition of Three Fractions Formula:

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

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 of Fractions:

Decimal Result:

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1. What is Three Fractions Addition?

Adding three fractions involves finding a common denominator and then adding the numerators. The result is typically simplified to its lowest terms.

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 denominators together, then calculates the equivalent numerators and sums them.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics and has applications in various fields including engineering, physics, and everyday measurements.

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: Why do we need a common denominator?
A: Fractions can only be directly added when they have the same denominator, as they represent parts of the same whole.

Q2: What if my denominators are the same?
A: If denominators are identical, simply add the numerators and keep the denominator the same.

Q3: How does simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction to its simplest form.

Q4: Can I add mixed numbers with this calculator?
A: First convert mixed numbers to improper fractions, then use the calculator.

Q5: What if I get a negative result?
A: Negative results are valid and indicate the sum is less than zero.