Adding 3 Mixed Fractions Calculator

Formula for Adding Three Mixed Fractions:

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

First Mixed Fraction:

Second Mixed Fraction:

Third Mixed Fraction:

Result:

Decimal Equivalent:

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1. What is Adding Mixed Fractions?

Adding mixed fractions combines whole numbers with proper fractions. A mixed fraction like 2 1/3 represents 2 + 1/3. This calculator adds three mixed fractions together and provides the result in both simplified fraction and decimal forms.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

\( m, p, s \) — Whole number parts
\( n, q, t \) — Numerators
\( o, r, u \) — Denominators

Explanation: The calculator first converts each mixed fraction to an improper fraction, finds a common denominator, adds them together, and then simplifies the result back to a mixed fraction 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 the whole number, numerator, and denominator for each of the three mixed fractions. All denominators must be positive numbers. The calculator will show the result in both simplified fraction form and as a decimal.

5. Frequently Asked Questions (FAQ)

Q1: What if my result is an improper fraction?
A: The calculator will automatically convert it to a mixed number if possible (e.g., 7/3 becomes 2 1/3).

Q2: Can I use this with negative numbers?
A: This version only accepts positive numbers. For negative mixed fractions, you'd need to handle the signs separately.

Q3: What's the maximum number this can handle?
A: It's limited by PHP's integer size, but practical limits are much lower due to simplification steps.

Q4: Why do I need a common denominator?
A: Fractions can only be added directly when they have the same denominator, which is why we convert to equivalent fractions with a common denominator.

Q5: How is the simplification done?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction to its simplest form.