Add Fractions Together Calculator

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 of Fractions:

Decimal Result:

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1. What is Fraction Addition?

Fraction addition is the process of combining two or more fractions into a single fraction. To add fractions with different denominators, we first find a common denominator, then add the numerators while keeping the common denominator.

2. How Does the Calculator Work?

The calculator uses the following formula to add three fractions:

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

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 (the product of all denominators), then combines the numerators appropriately.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics and has applications in engineering, physics, chemistry, and everyday measurements. Understanding fraction addition is crucial for solving more complex mathematical problems.

4. Using the Calculator

Tips: Enter numerators and denominators for all three fractions. Denominators must be positive numbers. The calculator will show both the fractional result (simplified if possible) and the decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What if I only have two fractions to add?
A: You can leave the third fraction as 0/1 (enter 0 for numerator and 1 for denominator).

Q2: Why do denominators need to be positive?
A: Division by zero is undefined, and negative denominators can be confusing (though mathematically valid). We enforce positive denominators for simplicity.

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

Q4: Can I add more than three fractions?
A: This calculator is designed for three fractions, but you can chain calculations by using the result as one of the inputs in a new calculation.

Q5: What about mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 2½ becomes 5/2).