Adding 3 Fractions Calculator With Whole Numbers

Formula for adding two fractions with a whole number:

\[ \frac{a}{b} + \frac{c}{d} + e = \frac{a \times d + b \times c + e \times b \times d}{b \times d} \]

Result:

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1. What is the Adding Fractions Formula?

The formula for adding two fractions with a whole number combines them into a single fraction. It finds a common denominator and properly incorporates the whole number into the numerator.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \frac{a}{b} + \frac{c}{d} + e = \frac{a \times d + b \times c + e \times b \times d}{b \times d} \]

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction
\( e \) — Whole number to add

Explanation: The formula first finds a common denominator (b×d), then converts all terms to have this denominator before adding them together.

3. Importance of Fraction Addition

Details: Adding fractions with whole numbers is fundamental in mathematics, used in recipes, construction, measurements, and various real-world applications where quantities need to be combined.

4. Using the Calculator

Tips: Enter numerators and denominators for both fractions, plus any whole number to add. Denominators must be positive integers. The calculator will simplify the result if possible.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: The calculator requires positive denominators. Division by zero is undefined in mathematics.

Q2: How does the calculator simplify fractions?
A: It finds the greatest common divisor (GCD) of numerator and denominator, then divides both by this number.

Q3: Can I add more than two fractions?
A: This calculator handles two fractions plus a whole number. For more fractions, you would need to add them sequentially.

Q4: What if my result is an improper fraction?
A: The calculator shows the result as-is, but you may convert it to a mixed number if desired.

Q5: Can I use negative numbers?
A: Yes, the calculator works with negative numerators and whole numbers, but denominators must remain positive.