To divide two fractions, you can multiply the first fraction by the reciprocal of the second fraction.
So, to calculate \( \frac{2}{3} \div \frac{12}{19} \), you do the following:
\[ \frac{2}{3} \div \frac{12}{19} = \frac{2}{3} \times \frac{19}{12} \]
Now, multiply the numerators and the denominators:
\[ = \frac{2 \times 19}{3 \times 12} = \frac{38}{36} \]
Next, simplify \( \frac{38}{36} \):
Both 38 and 36 can be divided by 2:
\[ \frac{38 \div 2}{36 \div 2} = \frac{19}{18} \]
Therefore, the answer is
\[ \frac{19}{18} \]
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