Multiplying Three Fractions Calculator

Fraction Multiplication Formula:

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

Numerator 1 (a):

Denominator 1 (b):

Numerator 2 (c):

Denominator 2 (d):

Numerator 3 (e):

Denominator 3 (f):

Result (Decimal):

Result (Simplified Fraction):

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1. What is Fraction Multiplication?

Fraction multiplication involves multiplying the numerators together and the denominators together. For three fractions, the product is (a×c×e)/(b×d×f). This operation is fundamental in mathematics and has applications in scaling, ratios, and probability calculations.

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 and all denominators together, then simplifies the resulting fraction to its lowest terms.

3. Importance of Fraction Multiplication

Details: Multiplying fractions is essential in many real-world applications including cooking (adjusting recipes), construction (scaling measurements), and finance (calculating interest rates).

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators cannot be zero. The calculator will provide both decimal and simplified fraction results.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. All denominators must be non-zero values.

Q2: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction to its simplest form.

Q3: Can I enter negative fractions?
A: Yes, the calculator handles negative values. A negative in either numerator or denominator makes the fraction negative.

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

Q5: How precise are the results?
A: The decimal result shows 4 decimal places. The simplified fraction is exact.