Fraction Calculator With Three Fractions Worksheet

Formula:

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

First Fraction Numerator (a):

First Fraction Denominator (b):

Second Fraction Numerator (c):

Second Fraction Denominator (d):

Third Fraction Numerator (e):

Third Fraction Denominator (f):

Result:

Decimal Result:

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1. What is Three Fraction Operation?

This calculator performs operations on three fractions using the formula: a/b - c/d + e/f. It provides both fractional and decimal results, simplifying the final answer when possible.

2. How Does the Calculator Work?

The calculator uses the following formula:

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

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 finds a common denominator (b×d×f) and performs the operations in the numerator, then simplifies the result.

3. Importance of Fraction Operations

Details: Understanding fraction operations is fundamental in mathematics, essential for algebra, calculus, and real-world applications like cooking, construction, and financial calculations.

4. Using the Calculator

Tips: Enter all six values (numerators and denominators). Denominators must be positive integers. The calculator will show the result in both fractional and decimal forms.

5. Frequently Asked Questions (FAQ)

Q1: Why can't denominators be zero?
A: Division by zero is mathematically undefined. Denominators must be positive integers.

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, numerators can be negative, but denominators must be positive.

Q4: What if the result is a whole number?
A: The calculator will show it as a fraction (e.g., 4/1) and also as a decimal.

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