To determine which of the given numbers (3/11, 13/5, or 1) can be multiplied by \( \frac{3}{11} \) to make the product greater than \( \frac{3}{11} \), we will analyze each one:
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Calculation with 3/11: \[ \frac{3}{11} \cdot \frac{3}{11} = \frac{9}{121} \] Since \( \frac{9}{121} \) is less than \( \frac{3}{11} \), this does not satisfy the condition.
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Calculation with 13/5: \[ \frac{3}{11} \cdot \frac{13}{5} = \frac{39}{55} \] Next, we compare \( \frac{39}{55} \) to \( \frac{3}{11} \). To do this, we can cross multiply: \[ 39 \cdot 11 = 429 \quad \text{and} \quad 3 \cdot 55 = 165 \] Since \( 429 > 165 \), it follows that \( \frac{39}{55} > \frac{3}{11} \). Thus, \( \frac{13}{5} \) works.
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Calculation with 1: \[ \frac{3}{11} \cdot 1 = \frac{3}{11} \] This equals \( \frac{3}{11} \), which does not satisfy the condition of being greater.
From the above calculations, the only number that makes \( \frac{3}{11} \cdot x > \frac{3}{11} \) true is \( \frac{13}{5} \).
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