Question

Use the Inverse Property to find the number that makes the mathematical statement - 5/7 x [?]= 1 true.
A. 5/7
B. - 5/7
C. 7/5
D. - 7/5

Answer 1

To solve the equation \(-\frac{5}{7} \times [?] = 1\), we can use the concept of the inverse property. The inverse property states that a number multiplied by its reciprocal (or multiplicative inverse) equals 1.

We can find the multiplicative inverse of \(-\frac{5}{7}\):

The reciprocal (inverse) of \(-\frac{5}{7}\) is \(-\frac{7}{5}\).

Now, we can plug this back into our equation:

\[
-\frac{5}{7} \times -\frac{7}{5} = 1
\]

Thus, the number that makes the statement true is:

**D. -\frac{7}{5}**