Fraction Calculator Division Multiplication Addition

Fraction Operation Formula:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Result:

Decimal Result:

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1. What is the Fraction Calculator?

This calculator performs combined operations of division, multiplication, and addition on three fractions. It computes (a/b) × (c/d) + (e/f) and provides the result in both fractional and decimal forms.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

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

Explanation: The calculator first multiplies the first two fractions (a/b × c/d = (a×c)/(b×d)), then adds the third fraction by finding a common denominator (b×d×f).

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in mathematics, physics, engineering, and many real-world applications like cooking, construction, and financial calculations.

4. Using the Calculator

Tips: Enter all numerators and denominators as integers. Denominators cannot be zero. The calculator automatically simplifies the resulting fraction to its lowest terms.

5. Frequently Asked Questions (FAQ)

Q1: Why does the denominator have to be positive?
A: While mathematically fractions can have negative denominators, by convention we keep denominators positive and show the sign in the numerator.

Q2: How does the calculator simplify fractions?
A: It uses the greatest common divisor (GCD) algorithm to reduce the fraction to its simplest form.

Q3: What if I get a negative result?
A: Negative results are valid and indicate the combined value is less than zero. The calculator properly handles negative signs in either numerator or denominator.

Q4: Can I enter mixed numbers?
A: This calculator requires proper fractions. Convert mixed numbers to improper fractions first (e.g., 1½ = 3/2).

Q5: What about division of fractions?
A: Division (a/b ÷ c/d) is equivalent to multiplication by the reciprocal (a/b × d/c). You can use this calculator by swapping c and d for division operations.