2 3 Cube Calculator

Cube Calculation:

\[ \left(\frac{2}{3}\right)^3 = \frac{8}{27} \]

Result:

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1. What is the Cube of a Fraction?

The cube of a fraction is obtained by multiplying the fraction by itself three times. For example, (2/3)³ = (2/3) × (2/3) × (2/3) = 8/27.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \left(\frac{a}{b}\right)^3 = \frac{a^3}{b^3} \]

Where:

\( a \) — Numerator of the fraction
\( b \) — Denominator of the fraction

Explanation: The calculator cubes both the numerator and denominator separately, then simplifies the resulting fraction if possible.

3. Mathematical Explanation

Details: Cubing a fraction follows the same rules as integer exponents. The operation is equivalent to multiplying the fraction by itself three times.

4. Using the Calculator

Tips: Enter the numerator and denominator of your fraction. The denominator must be a positive integer. The calculator will compute the cube and simplify the result if possible.

5. Frequently Asked Questions (FAQ)

Q1: Why does cubing a fraction make it smaller?
A: When you cube a proper fraction (between 0 and 1), the result gets smaller because you're multiplying three numbers less than 1 together.

Q2: What if I cube an improper fraction?
A: Improper fractions (greater than 1) will become larger when cubed, following the same mathematical rules.

Q3: How does the simplification work?
A: The calculator finds the greatest common divisor (GCD) of the cubed numerator and denominator to simplify the fraction.

Q4: Can I cube negative fractions?
A: Yes, the calculator handles negative numerators (but not denominators). The cube of a negative fraction will be negative.

Q5: What's special about cubing vs. squaring?
A: Cubing preserves the sign of the original fraction (negative remains negative), while squaring always makes the result positive.