To find which expression gives the product of \( \frac{14}{9} \), we can evaluate each provided option.
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For \( 2 \times \frac{7}{9} \): \[ 2 \times \frac{7}{9} = \frac{2 \times 7}{9} = \frac{14}{9} \]
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For \( 9 \times \frac{1}{7} \): \[ 9 \times \frac{1}{7} = \frac{9 \times 1}{7} = \frac{9}{7} \]
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For \( 9 \times \frac{2}{7} \): \[ 9 \times \frac{2}{7} = \frac{9 \times 2}{7} = \frac{18}{7} \]
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For \( 2 \times \frac{1}{9} \): \[ 2 \times \frac{1}{9} = \frac{2 \times 1}{9} = \frac{2}{9} \]
From these calculations, we can see that the only expression that results in \( \frac{14}{9} \) is:
\[ 2 \times \frac{7}{9} \]
So the correct answer is: \[ \boxed{2 \times \frac{7}{9}} \]