Fraction With Mixed Number Calculator 3 Fractions

Mixed Number Addition Formula:

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

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:

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1. What is Mixed Number Addition?

Mixed number addition combines three mixed numbers (a combination of whole numbers and fractions) into a single simplified result. This calculator converts each mixed number to an improper fraction before performing the addition.

2. How Does the Calculator Work?

The calculator uses the following steps:

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

Convert each mixed number to improper fraction: \(\frac{a \times c + b}{c}\), \(\frac{d \times f + e}{f}\), \(\frac{g \times i + h}{i}\)
Find common denominator (c × f × i)
Convert all fractions to have common denominator
Add numerators
Simplify result by finding greatest common divisor
Convert back to mixed number if needed

3. Importance of Mixed Number Calculations

Details: Mixed number operations are fundamental in mathematics, engineering, and everyday measurements. Accurate calculation is essential for precise measurements in cooking, construction, and scientific applications.

4. Using the Calculator

Tips: Enter whole numbers, numerators, and denominators for all three fractions. Denominators must be positive integers. The calculator will automatically simplify the result to its lowest terms.

5. Frequently Asked Questions (FAQ)

Q1: What if one of my fractions is negative?
A: This calculator currently handles positive numbers only. For negative numbers, you would need to track the sign separately.

Q2: Can I add more than three fractions?
A: This calculator is designed for three fractions. For more fractions, you would need to perform multiple calculations.

Q3: What if my result is an improper fraction?
A: The calculator will automatically convert improper fractions to mixed numbers when appropriate.

Q4: Why do I need common denominators?
A: Fractions can only be directly added when they have the same denominator. Finding a common denominator allows for proper addition.

Q5: What if I enter zero as a denominator?
A: The calculator requires denominators to be positive integers. Division by zero is mathematically undefined.