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\frac{a^{2}\times 2}{3a^{2}}
Divide \frac{a^{2}}{1} by \frac{3a^{2}}{2} by multiplying \frac{a^{2}}{1} by the reciprocal of \frac{3a^{2}}{2}.
\frac{2}{3}
Cancel out a^{2} in both numerator and denominator.