Question

Which of the following will make the statement true: 3/11
, 13/5
, 1?

3/11⋅
_____>3/11

Answer 1

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:

1. **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.

2. **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.

3. **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 **\( \frac{13}{5} \)**.