Adding Fractions Calculator Mixed Numbers

Mixed Numbers Addition Formula:

\[ (m \frac{n}{o}) + (p \frac{q}{r}) = \frac{(m \times o + n) \times r + (p \times r + q) \times o}{o \times r} \]

First Whole Number (m):

First Numerator (n):

First Denominator (o):

Second Whole Number (p):

Second Numerator (q):

Second Denominator (r):

Result (Improper Fraction):

Result (Simplified):

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1. What is Mixed Numbers Addition?

Mixed numbers addition combines whole numbers and fractions. A mixed number consists of an integer and a proper fraction (like 2 1/3). Adding them requires converting to improper fractions first.

2. How Does the Calculator Work?

The calculator uses the mixed numbers addition formula:

\[ (m \frac{n}{o}) + (p \frac{q}{r}) = \frac{(m \times o + n) \times r + (p \times r + q) \times o}{o \times r} \]

Where:

\( m \) — First whole number
\( n \) — First numerator
\( o \) — First denominator
\( p \) — Second whole number
\( q \) — Second numerator
\( r \) — Second denominator

Explanation: The formula converts mixed numbers to improper fractions, finds a common denominator, adds them, and simplifies the result.

3. Importance of Mixed Numbers Calculation

Details: Adding mixed numbers is essential in everyday measurements (cooking, construction) and advanced mathematics. Proper calculation ensures accurate results.

4. Using the Calculator

Tips: Enter whole numbers, numerators, and denominators for both mixed numbers. Denominators must be positive integers. The calculator will return results as both improper fraction and simplified form.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominators are different?
A: The calculator automatically finds a common denominator by multiplying the denominators together.

Q2: How is the result simplified?
A: The calculator uses the greatest common divisor (GCD) to reduce the fraction to its simplest form.

Q3: Can I add more than two mixed numbers?
A: This calculator handles two numbers at a time. For more numbers, add them sequentially.

Q4: What if I get an improper fraction result?
A: The calculator shows both the improper fraction and its simplified mixed number form.

Q5: Can I use negative numbers?
A: This calculator is designed for positive numbers only.