Add Three Fractions Calculator

Three Fractions 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):

Result:

Decimal Value:

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1. What is Three Fractions Addition?

Adding three fractions involves finding a common denominator and then combining the numerators. The formula calculates the sum of three fractions by multiplying each numerator by the other denominators to create equivalent fractions with a common denominator.

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 formula finds a common denominator (b×d×f) 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. Understanding this operation is crucial for solving more 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 do we need a common denominator?
A: Fractions can only be directly added when they have the same denominator. A common denominator allows us to combine the fractions properly.

Q2: What if one denominator is a multiple of the others?
A: The calculator still works, but the result could be simplified further. Our calculator automatically simplifies the final fraction.

Q3: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions. For example, 2½ becomes 5/2.

Q4: What if I enter zero for a denominator?
A: The calculator requires denominators to be positive. Division by zero is undefined in mathematics.

Q5: How does simplification work?
A: The calculator finds the greatest common divisor (GCD) of numerator and denominator and divides both by this number.