To solve the problem using area models for the division of fractions, we first convert \( \frac{2}{3} \) to sixths.
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Think: How many sixths are in \( \frac{2}{3} \)?
- We know that \( \frac{2}{3} = \frac{4}{6} \) because if we multiply both the numerator and the denominator of \( \frac{2}{3} \) by 2, we get \( \frac{2 \times 2}{3 \times 2} = \frac{4}{6} \).
Therefore, there are four sixths in the shaded \( \frac{2}{3} \).
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Setting up the equation: \[ \frac{2}{3} \div \frac{1}{6} = ? \] Since we found that \( \frac{2}{3} = \frac{4}{6} \), we can express the division as: \[ \frac{4}{6} \div \frac{1}{6} = 4 \]
Thus, \( \frac{2}{3} \div \frac{1}{6} = 4 \).
- Final statement: There are four equal parts of \( \frac{1}{6} \) in \( \frac{2}{3} \).
So the completed answer is:
There are four sixths in the shaded \( \frac{2}{3} \).
\( \frac{2}{3} \div \frac{1}{6} = 4 \)
There are four equal parts of \( \frac{1}{6} \) in \( \frac{2}{3} \).