Fraction Calculator With Multiplication And Division

Fraction Calculation Formula:

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

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Result:

Decimal Value:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Fraction Multiplication and Division?

This calculator performs multiplication and division operations on three fractions. The operation follows the mathematical rule: (a/b) × (c/d) ÷ (e/f) = (a×c×f)/(b×d×e).

2. How Does the Calculator Work?

The calculator uses the following formula:

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

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 by finding the greatest common divisor.

3. Importance of Fraction Calculations

Details: Fraction operations are fundamental in mathematics, science, engineering, and everyday life. Understanding how to multiply and divide fractions is essential for solving complex problems.

4. Using the Calculator

Tips: Enter all six values (three numerators and three denominators). None of the denominators can be zero. The calculator will show the result in both fractional and decimal form.

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 values.

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 use negative numbers?
A: Yes, the calculator handles negative numbers in both numerators and denominators.

Q4: What if the result is a whole number?
A: The calculator will show it as a fraction (e.g., 5/1) and also as a decimal (5.0).

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