To find a fraction that makes the statement \( \frac{2}{10} < \text{fraction} < \frac{7}{11} \) true, we first convert the given fractions into decimal form for easier comparison.
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Calculate \( \frac{2}{10} \): \[ \frac{2}{10} = 0.2 \]
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Calculate \( \frac{7}{11} \): \[ \frac{7}{11} \approx 0.6363 \]
Now, we need a fraction that lies between \( 0.2 \) and \( 0.6363 \).
One simple choice is to find the midpoint between these two decimals: \[ \text{Midpoint} = \frac{0.2 + 0.6363}{2} \approx \frac{0.8363}{2} \approx 0.41815 \]
We can choose a simple fraction close to \( 0.41815 \). A common fraction to consider is \( \frac{2}{5} \), which equates to \( 0.4 \):
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Check \( \frac{2}{10} < \frac{2}{5} \): \[ 0.2 < 0.4 \quad \text{(True)} \]
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Check \( \frac{2}{5} < \frac{7}{11} \): \[ 0.4 < 0.6363 \quad \text{(True)} \]
Thus, a fraction that makes the statement true is:
\[ \frac{2}{5} \]
So, \[ \frac{2}{10} < \frac{2}{5} < \frac{7}{11} \]
Other fractions that may also work include \( \frac{3}{7} \approx 0.4286 \) or \( \frac{1}{3} \approx 0.3333 \). However, \( \frac{2}{5} \) is certainly acceptable.