To find the number that makes the statement \(-\frac{5}{7} \cdot [?] = 1\) true, we can use the concept of the Inverse Property of multiplication, which states that a number multiplied by its multiplicative inverse (or reciprocal) equals 1.
The multiplicative inverse of \(-\frac{5}{7}\) can be found by taking the reciprocal and changing its sign:
- The reciprocal of \(-\frac{5}{7}\) is \(-\frac{7}{5}\).
- Therefore, the number that satisfies the equation is \(-\frac{7}{5}\).
So, \(-\frac{5}{7} \cdot \left(-\frac{7}{5}\right) = 1\).
Thus, the answer you are looking for is:
\(-\frac{7}{5}\)