Adding Mixed Fractions Calculator 3 Fractions

Mixed Fractions Addition Formula:

\[ (a \frac{b}{c}) + (d \frac{e}{f}) + (g \frac{h}{i}) = \frac{(a \times c + b) \times i \times f + (d \times f + e) \times b \times i + (g \times i + h) \times b \times f}{c \times f \times i} \]

First Fraction - Whole Number:

First Fraction - Numerator:

First Fraction - Denominator:

Second Fraction - Whole Number:

Second Fraction - Numerator:

Second Fraction - Denominator:

Third Fraction - Whole Number:

Third Fraction - Numerator:

Third Fraction - Denominator:

Result (Simplified):

Improper Fraction:

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1. What is Mixed Fractions Addition?

Mixed fractions (also called mixed numbers) combine whole numbers and proper fractions. Adding them requires converting to improper fractions first, finding a common denominator, adding, and then converting back to mixed form if needed.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ (a \frac{b}{c}) + (d \frac{e}{f}) + (g \frac{h}{i}) = \frac{(a \times c + b) \times i \times f + (d \times f + e) \times b \times i + (g \times i + h) \times b \times f}{c \times f \times i} \]

Where:

\( a, d, g \) — Whole number parts
\( b, e, h \) — Numerators
\( c, f, i \) — Denominators

Explanation: Each mixed number is converted to an improper fraction, then all fractions are converted to have a common denominator before adding.

3. Importance of Mixed Fractions

Details: Mixed fractions are commonly used in everyday measurements (like cooking or construction) where quantities often include whole units plus fractional parts.

4. Using the Calculator

Tips: Enter the whole number, numerator and denominator for each of the three fractions. Denominators must be positive integers. The calculator will show both simplified mixed form and improper fraction results.

5. Frequently Asked Questions (FAQ)

Q1: What if my fraction can be simplified further?
A: The calculator automatically simplifies the result to its lowest terms.

Q2: Can I use this for subtracting fractions?
A: No, this is specifically for addition. For subtraction, you would need a different calculator.

Q3: What if I enter a numerator larger than the denominator?
A: The calculator will still work, treating it as an improper fraction in the mixed number.

Q4: Why show both mixed and improper results?
A: Different situations call for different forms - mixed numbers are more intuitive, while improper fractions are often easier for further calculations.

Q5: What's the largest denominator I can use?
A: Technically limited by PHP's integer size, but practically any reasonable denominator will work.