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\frac{2}{9}\times \frac{2}{3}=m
Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.
\frac{2\times 2}{9\times 3}=m
Multiply \frac{2}{9} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{4}{27}=m
Do the multiplications in the fraction \frac{2\times 2}{9\times 3}.
m=\frac{4}{27}
Swap sides so that all variable terms are on the left hand side.