Divide Fractions Calculator 3 Fractions

Division Formula for Three Fractions:

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

First Fraction (a/b):

Second Fraction (c/d):

Third Fraction (e/f):

Quotient (fraction):

Decimal Value:

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1. What is Fraction Division?

Fraction division is a mathematical operation that determines how many times one fraction fits into another. For three fractions, it's calculated by dividing the first fraction by the second, then dividing that result by the third fraction.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

Where:

\( \frac{a}{b} \) — First fraction
\( \frac{c}{d} \) — Second fraction
\( \frac{e}{f} \) — Third fraction

Explanation: Division of fractions is performed by multiplying by the reciprocal. For three fractions, we multiply the first fraction by the reciprocal of the second, then multiply that result by the reciprocal of the third.

3. Importance of Fraction Division

Details: Understanding fraction division is essential in many real-world applications including cooking, construction, science experiments, and financial calculations where proportional relationships are important.

4. Using the Calculator

Tips: Enter the numerator and denominator for each of the three fractions. All values must be integers greater than 0. The calculator will provide both the simplified fractional result and its decimal equivalent.

5. Frequently Asked Questions (FAQ)

Q1: Why do we multiply by the reciprocal when dividing fractions?
A: Multiplying by the reciprocal is mathematically equivalent to division and simplifies the calculation process.

Q2: What if one of my denominators is zero?
A: Division by zero is undefined. The calculator requires all denominators to be positive integers.

Q3: How does the calculator simplify the result?
A: It finds the greatest common divisor (GCD) of the numerator and denominator and divides both by this number.

Q4: Can I use this for mixed numbers?
A: First convert mixed numbers to improper fractions before using this calculator.

Q5: What if my result is an improper fraction?
A: The calculator shows the result as an improper fraction. You may convert it to a mixed number if desired.