Adding Three Fractions Calculator With Different

Fraction Addition Formula:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Sum Result:

Decimal Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Three Fraction Addition?

Adding three fractions with different denominators requires finding a common denominator. The calculator uses the mathematical principle of cross-multiplication to combine the fractions accurately.

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 the least common denominator by multiplying all denominators together, then 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. Understanding this operation is crucial for solving 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 fractional and decimal results, simplified to lowest terms when possible.

5. Frequently Asked Questions (FAQ)

Q1: Why can't denominators be zero?
A: Division by zero is mathematically undefined. Denominators must be non-zero integers.

Q2: How does the calculator simplify fractions?
A: It uses the greatest common divisor (GCD) algorithm to reduce fractions to their simplest form.

Q3: Can I use negative numbers?
A: Yes, numerators can be negative, but denominators must be positive.

Q4: What if the result is an improper fraction?
A: The calculator displays improper fractions as-is. You may convert to mixed numbers if desired.

Q5: How precise is the decimal result?
A: The decimal is rounded to 4 decimal places for readability while maintaining reasonable precision.