3 Fraction Addition Calculator

Fraction Addition Formula:

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

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 3 Fraction Addition?

Adding three fractions involves finding a common denominator and combining the numerators. The result is a new fraction that represents the sum of the three original fractions.

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 least common denominator (LCD) by multiplying all denominators, then adjusts each numerator accordingly before adding them together.

3. Importance of Fraction Addition

Details: Adding fractions is fundamental in mathematics, used in various real-world applications like cooking, construction, and financial calculations where parts of wholes need to be combined.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators must be positive integers. The calculator will provide both the fractional result (simplified if possible) and decimal equivalent.

5. Frequently Asked Questions (FAQ)

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

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

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

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

Q5: Does the order of fractions matter?
A: No, addition is commutative - the order doesn't affect the result.