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Squared and Cubed Calculator Fractions

Fraction Calculations:

\[ \text{Square} = \left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2} \] \[ \text{Cube} = \left(\frac{a}{b}\right)^3 = \frac{a^3}{b^3} \]

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1. What is Fraction Squaring and Cubing?

Squaring a fraction means multiplying the fraction by itself, while cubing means multiplying the fraction by itself twice. These operations are fundamental in algebra and have applications in geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses these formulas:

\[ \text{Square} = \left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2} \] \[ \text{Cube} = \left(\frac{a}{b}\right)^3 = \frac{a^3}{b^3} \]

Where:

Explanation: To square or cube a fraction, you simply square or cube both the numerator and the denominator separately.

3. Practical Applications

Details: Squaring fractions is used in calculating areas, while cubing is used in volume calculations. These operations are also essential in probability calculations and scaling factors.

4. Using the Calculator

Tips: Enter the numerator and denominator of your fraction. The denominator cannot be zero. Results are displayed with 4 decimal places for precision.

5. Frequently Asked Questions (FAQ)

Q1: Can I enter decimal numbers?
A: Yes, the calculator accepts both whole numbers and decimals for numerator and denominator.

Q2: What happens if I enter zero as denominator?
A: Division by zero is undefined, so the calculator will not produce a result if denominator is zero.

Q3: How precise are the results?
A: Results are calculated with floating point precision and displayed with 4 decimal places.

Q4: Can this calculator handle mixed numbers?
A: No, you need to convert mixed numbers to improper fractions first before using this calculator.

Q5: Are negative fractions allowed?
A: Yes, the calculator works with negative fractions. Squaring will always produce positive results.

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