The expression \( \frac{8x}{10} \) can be simplified to \( \frac{4x}{5} \). Whether \( \frac{4x}{5} \) is rational or irrational depends on the value of \( x \).
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If \( x \) is a rational number (like \( \frac{1}{2} \), \( 3 \), or \( -4 \)), then \( \frac{4x}{5} \) will also be a rational number, since the product and quotient of rational numbers are rational.
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If \( x \) is an irrational number (like \( \sqrt{2} \) or \( \pi \)), then \( \frac{4x}{5} \) will be irrational, since multiplying a rational number by an irrational number results in an irrational number.
In summary:
- \( \frac{8x}{10} \) is rational if \( x \) is rational.
- \( \frac{8x}{10} \) is irrational if \( x \) is irrational.
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