Fractions Greater Than 2/3

Comparison Rule:

\[ \frac{a}{b} > \frac{2}{3} \text{ if } a \times 3 > b \times 2 \]

Result:

Greater Than 2/3?:

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1. What is the 2/3 Fraction Comparison?

This calculator determines whether a given fraction is greater than the fraction 2/3. It uses the mathematical rule that compares the cross-products of the fractions.

2. How Does the Calculator Work?

The calculator uses the following comparison rule:

\[ \frac{a}{b} > \frac{2}{3} \text{ if } a \times 3 > b \times 2 \]

Where:

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

Explanation: This method avoids division and potential floating-point inaccuracies by using cross-multiplication.

3. Importance of Fraction Comparison

Details: Comparing fractions is fundamental in mathematics, useful in probability calculations, ratios, and many real-world applications like cooking, construction, and financial analysis.

4. Using the Calculator

Tips: Enter the numerator and denominator (must be positive integers). The denominator cannot be zero. The calculator will show whether your fraction is greater than 2/3.

5. Frequently Asked Questions (FAQ)

Q1: Why use cross-multiplication instead of division?
A: Cross-multiplication avoids floating-point rounding errors and works perfectly with integers.

Q2: What if my denominator is zero?
A: Division by zero is undefined. The calculator requires a positive denominator.

Q3: Can I compare fractions to other values?
A: This calculator specifically compares to 2/3, but the same method works for any fraction comparison.

Q4: Does this work for negative fractions?
A: The calculator currently only handles positive numbers, as negative fractions require additional sign considerations.

Q5: How is this useful in real life?
A: Comparing fractions helps in situations like determining better deals (price per unit), mixing ratios, or analyzing statistical probabilities.