Adding Mixed Fractions Calculator

Mixed Fractions 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 Fraction - Whole Number (m):

First Fraction - Numerator (n):

First Fraction - Denominator (o):

Second Fraction - Whole Number (p):

Second Fraction - Numerator (q):

Second Fraction - Denominator (r):

Result:

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From:	To:

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 simplifying back to mixed form if needed.

2. How Does the Calculator Work?

The calculator uses the following 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:

\( m \) — Whole number part of first fraction
\( n \) — Numerator of first fraction
\( o \) — Denominator of first fraction
\( p \) — Whole number part of second fraction
\( q \) — Numerator of second fraction
\( r \) — Denominator of second fraction

Explanation: The calculator first converts mixed numbers to improper fractions, finds a common denominator, adds them, and simplifies the result back to mixed form if possible.

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 whole numbers, numerators, and denominators for both fractions. Denominators must be positive integers. The calculator will show the result in simplest form, either as a proper fraction or mixed number.

5. Frequently Asked Questions (FAQ)

Q1: What if my denominators are different?
A: The calculator automatically finds a common denominator (the product of the two denominators) before adding.

Q2: Can I add more than two fractions?
A: This calculator handles two fractions at a time. For more fractions, add them two at a time using the intermediate results.

Q3: What if my result is an improper fraction?
A: The calculator will convert it to a mixed number if possible (when numerator ≥ denominator).

Q4: How does simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it.

Q5: Can I use negative numbers?
A: This version only accepts non-negative numbers for all inputs.