Add Three Fractions Calculator With Different

Addition of Three Fractions Formula:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Sum Result:

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1. What is Three Fractions Addition?

Adding three fractions with different denominators requires finding a common denominator. The formula combines all three fractions into a single fraction by multiplying each numerator by the other denominators.

2. How Does the Calculator Work?

The calculator uses the 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 formula finds a common denominator (b×d×f) and adjusts each numerator accordingly before summing them.

3. Importance of Common Denominator

Details: To add fractions, they must have the same denominator. This calculator automatically finds the least common multiple of all denominators.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators cannot be zero. The calculator will simplify the result if possible.

5. Frequently Asked Questions (FAQ)

Q1: What if one denominator is zero?
A: Division by zero is undefined. All denominators must be positive integers.

Q2: Does the calculator simplify the result?
A: Yes, it provides both the raw result and simplified form (if different).

Q3: Can I use negative numbers?
A: Yes, the calculator handles negative numerators and denominators.

Q4: What's the maximum number size?
A: Limited by PHP's integer size (typically ±2 billion). For very large numbers, precision may be affected.

Q5: How is the decimal result calculated?
A: By dividing the final numerator by the denominator, rounded to 4 decimal places.