Fractions Calculator With Different Denominators

Fraction Operation:

\[ \frac{a}{b} \text{ op } \frac{c}{d} = \frac{(a \times \frac{LCM}{b}) \text{ op } (c \times \frac{LCM}{d})}{LCM} \]

Numerator 1 (a):

Denominator 1 (b):

Operation:

Numerator 2 (c):

Denominator 2 (d):

Result:

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1. What is the Fractions Calculator?

This calculator performs arithmetic operations (addition, subtraction, multiplication, division) on fractions with different denominators. It finds the Least Common Multiple (LCM) to handle different denominators and simplifies the final result.

2. How Does the Calculator Work?

The calculator uses the following approach:

\[ \frac{a}{b} \text{ op } \frac{c}{d} = \frac{(a \times \frac{LCM}{b}) \text{ op } (c \times \frac{LCM}{d})}{LCM} \]

Where:

\( a \) — Numerator of first fraction
\( b \) — Denominator of first fraction
\( c \) — Numerator of second fraction
\( d \) — Denominator of second fraction
\( op \) — Operation (+, -, *, /)
\( LCM \) — Least Common Multiple of denominators

Explanation: For addition and subtraction, the calculator converts fractions to equivalent fractions with common denominator (LCM) before performing the operation. For multiplication and division, it follows standard fraction arithmetic rules.

3. Importance of LCM in Fractions

Details: The Least Common Multiple is essential for adding or subtracting fractions with different denominators. It represents the smallest number that both denominators divide into evenly, allowing for proper fraction conversion.

4. Using the Calculator

Tips: Enter numerators and denominators (must be positive integers), select the operation. The calculator will show the result in simplest form.

5. Frequently Asked Questions (FAQ)

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

Q2: How does the calculator simplify fractions?
A: It divides both numerator and denominator by their Greatest Common Divisor (GCD).

Q3: What if the result is a whole number?
A: The calculator will display it as a whole number (e.g., 4 instead of 4/1).

Q4: Can I use negative numbers?
A: Yes, numerators can be negative but denominators must be positive.

Q5: How precise are the results?
A: Results are exact fractions, not decimal approximations, maintaining full precision.