Question

Use the Inverse Property to find the number that makes the mathematical statement −5/7⋅[?]=1
true.(1 point)
Responses

−7/5
negative Start Fraction 7 over 5 End Fraction

−5/7
negative Start Fraction 5 over 7 End Fraction

5/7
Start Fraction 5 over 7 End Fraction

7/5

Answer 1

To find the number that makes the equation \(-\frac{5}{7} \cdot [?] = 1\) true, we can use the concept of the inverse property.

The inverse property states that a number multiplied by its multiplicative inverse (or reciprocal) equals 1.

The multiplicative inverse of \(-\frac{5}{7}\) can be found by flipping the fraction and changing the sign:

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

So, setting up the equation:
\[
-\frac{5}{7} \cdot \left(-\frac{7}{5}\right) = 1
\]
This confirms that \(-\frac{7}{5}\) is the correct answer.

Thus, the number that makes the mathematical statement true is:

\(-\frac{7}{5}\) (negative Start Fraction 7 over 5 End Fraction).