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Step 1:I'll solve this step-by-step using the proper LaTeX formatting:
Step 2:: Recall the rule for dividing fractions
When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal is found by flipping the numerator and denominator.
Step 3:: Set up the division
\frac{2}{9} \div \frac{1}{3}
Step 4:: Rewrite as multiplication by the reciprocal
\frac{2}{9} \times \frac{3}{1}
Step 5:: Multiply the numerators and denominators
\frac{2 \times 3}{9 \times 1}
Step 6:: Simplify
\frac{6}{9}
Step 7:: Reduce the fraction
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
Final Answer
Key Insight: Dividing by a fraction is the same as multiplying by its reciprocal. This method always works and simplifies the division process.
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