Multiplying 3 Fractions

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 numerator (a):

First denominator (b):

Second numerator (c):

Second denominator (d):

Third numerator (e):

Third denominator (f):

Product 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).

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

Explanation: The calculator multiplies all numerators together to get the result numerator, and all denominators together to get the result denominator, then simplifies the resulting fraction.

3. Importance of Fraction Multiplication

Details: Multiplying fractions is fundamental in mathematics and has applications in probability, ratios, scaling recipes, and many real-world problems involving 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 and its decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: What if one of the denominators is zero?
A: Division by zero is undefined. The calculator will not compute a result if any denominator is zero.

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

Q3: Can I use negative numbers?
A: Yes, the calculator handles negative numbers. A negative denominator will make the whole fraction negative.

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

Q5: How precise are the results?
A: The fractional result is exact. The decimal result is rounded to 4 decimal places for display.