Adding Multiply Fractions Calculator

Fraction Operations:

\[ \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \] \[ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \]

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Operation:

Result:

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1. What is Fraction Addition/Multiplication?

Fraction operations are fundamental mathematical calculations. Addition of fractions requires a common denominator, while multiplication is performed by multiplying numerators and denominators directly.

2. How Does the Calculator Work?

The calculator uses these mathematical formulas:

\[ \text{Addition: } \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \] \[ \text{Multiplication: } \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \]

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction

Explanation: The calculator automatically simplifies the result to its lowest terms using the greatest common divisor (GCD).

3. Importance of Fraction Operations

Details: Understanding fraction operations is essential for algebra, measurements, ratios, and many real-world applications like cooking, construction, and science.

4. Using the Calculator

Tips: Enter all four values (two numerators and two denominators), select the operation, and click Calculate. Denominators cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: Why do we need common denominators for addition?
A: Fractions represent parts of a whole, and to add them meaningfully they must be parts of the same size (denominator).

Q2: Can I enter negative fractions?
A: Yes, the calculator handles negative values in numerators or denominators.

Q3: What if my result is an improper fraction?
A: The calculator shows the result as-is. You may convert it to a mixed number if desired.

Q4: How does simplification work?
A: The calculator divides numerator and denominator by their greatest common divisor (GCD).

Q5: What if denominators are equal?
A: For addition, the result denominator remains the same (a/b + c/b = (a+c)/b).