Fraction Calculator With 3 Fractions Multiplication

Fraction Multiplication Formula:

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

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Multiplication Result:

Decimal Value:

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1. What is Fraction Multiplication?

Fraction multiplication involves multiplying the numerators together and the denominators together. For three fractions a/b, c/d, and e/f, the product is (a×c×e)/(b×d×f). The result is typically simplified to its lowest terms.

2. How Does the Calculator Work?

The calculator uses the fraction multiplication formula:

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

Where:

\( a \) — First fraction numerator
\( b \) — First fraction denominator
\( c \) — Second fraction numerator
\( d \) — Second fraction denominator
\( e \) — Third fraction numerator
\( f \) — Third fraction denominator

Explanation: The calculator multiplies all numerators together, all denominators together, then simplifies the resulting fraction by dividing both numerator and denominator by their greatest common divisor (GCD).

3. Importance of Fraction Multiplication

Details: Multiplying fractions is fundamental in mathematics, used in scaling recipes, calculating probabilities, solving algebraic equations, and many real-world applications involving ratios and proportions.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators cannot be zero. The calculator will show both the fractional result (simplified if possible) and the decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be non-zero.

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

Q3: Can I enter negative fractions?
A: Yes, the calculator handles negative values. The sign rules follow standard mathematical conventions.

Q4: What about mixed numbers?
A: Convert mixed numbers to improper fractions before entering them (e.g., 2½ becomes 5/2).

Q5: How precise is the decimal result?
A: The decimal is rounded to 4 decimal places for readability.