1. What is the Fraction and Pattern Calculator?

This calculator performs operations on fractions and handles repeating decimal patterns. It can add, subtract, multiply, or divide fractions while accounting for any repeating patterns in the decimal results.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Numerator (unitless)
• \( b \) — Denominator (unitless)
• \( op \) — Operation (+, -, *, /)
• \( pattern \) — Optional repeating decimal pattern

Explanation: The calculator performs the specified operation on the fraction and can identify or apply repeating decimal patterns in the result.

3. Importance of Fraction Calculations

Details: Accurate fraction calculations are essential in mathematics, engineering, and sciences. Handling repeating patterns is particularly important for precise decimal representations.

4. Using the Calculator

Tips: Enter numerator and denominator as integers, select an operation, and optionally provide a repeating pattern. Denominator cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What are repeating decimal patterns?
A: Repeating patterns are sequences of digits that repeat infinitely in the decimal representation of a fraction (e.g., 0.333... has pattern "3").

Q2: How do I represent repeating patterns?
A: Enter the repeating sequence (e.g., for 0.142857142857..., enter "142857").

Q3: Can I calculate with mixed numbers?
A: Convert mixed numbers to improper fractions first (e.g., 1½ becomes 3/2).

Q4: What about non-repeating decimals?
A: The calculator works with both repeating and terminating decimals.

Q5: Are there limitations to this calculator?
A: Very large numbers or complex patterns may not be handled perfectly due to floating-point precision limits.