Use the Inverse Property to find the number that makes the mathematical statement −5/7⋅[?]=1

Question

true.(1 point)
Responses

−57

Answer 1

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:

1. The reciprocal of $-\frac{5}{7}$ is $-\frac{7}{5}$.
2. Therefore, the number that satisfies the equation is $-\frac{7}{5}$.

So, $-\frac{5}{7}\cdot (-\frac{7}{5})=1$.

Thus, the answer you are looking for is:

$-\frac{7}{5}$