Multiply Three Fractions Calculator

Fraction Multiplication Formula:

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

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Product Result:

Simplified Form:

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). This operation is fundamental in mathematics and has applications in various fields including physics, engineering, and probability.

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 to get the product numerator, and all denominators together to get the product denominator. It 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 essential for solving problems in algebra, calculating probabilities, scaling recipes in cooking, determining areas in geometry, and solving rate problems in physics and engineering.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). Denominators cannot be zero. The calculator will show the product in three forms: the raw multiplied fraction, simplified form, and decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: Can I multiply more than three fractions?
A: Yes, the same principle applies - multiply all numerators together and all denominators together, then simplify.

Q2: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator will not accept zero as a denominator.

Q3: How is the simplified form calculated?
A: The calculator finds the greatest common divisor (GCD) of the numerator and denominator, then divides both by this value.

Q4: Can I enter negative fractions?
A: Yes, negative values are accepted. The calculator will properly handle the sign in the result.

Q5: What about mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 2½ becomes 5/2) before using the calculator.