Two possible rational numbers between \(-\frac{2}{3}\) and \(\frac{1}{2}\) are

Concept

A rational number \(x\) lies strictly between two bounds \(a\) and \(b\) when \(a<x<b\).

To compare fractions, rewrite them with a common positive denominator; multiplying a numerator and its denominator by the same non-zero number preserves the value.

Application

1. Rewrite the bounds with denominator 6: \(-\frac{2}{3}=-\frac{4}{6}\) and \(\frac{1}{2}=\frac{3}{6}\). Thus a candidate must satisfy \(-\frac{4}{6}<x<\frac{3}{6}\).

2. For \(\left(\frac{2}{6},\frac{3}{5}\right)\), \(\frac{2}{6}\) lies inside the interval, whereas \(\frac{3}{5}=0.6>\frac{1}{2}\).

3. For \(\left(-\frac{2}{6},\frac{2}{6}\right)\), both \(-\frac{2}{6}=-\frac{1}{3}\) and \(\frac{2}{6}=\frac{1}{3}\) lie strictly between \(-\frac{2}{3}\) and \(\frac{1}{2}\).

4. For \(\left(-\frac{1}{6},\frac{4}{6}\right)\), \(-\frac{1}{6}\) lies inside the interval, whereas \(\frac{4}{6}=\frac{2}{3}>\frac{1}{2}\).

5. Exactly one listed pair passes the interval test, so the set-level choices claiming more than one pair or no pair do not apply.

Cross-check

In decimals, the interval is approximately \((-0.667,0.5)\). The values \(-\frac{1}{3}\approx-0.333\) and \(\frac{1}{3}\approx0.333\) are both strictly inside it.

Therefore, the required pair is \(\left(-\frac{2}{6},\frac{2}{6}\right)\).