Question

The multiplicative inverse of $-1\frac{1}{7}$

• A. $\frac{8}{7}$
• B. $\frac{-8}{7}$
• C. $\frac{7}{8}$
• D. $\frac{-7}{8}$

Answer 1

The correct option is D

$\frac{-7}{8}$

Multiplicative inverse of $-1\frac{1}{7}$

Explanation for correct option:

Option (D) $\frac{-7}{8}$

Change the given improper fraction $-1\frac{1}{7}$ into a proper fraction:

$-1\frac{1}{7}=\frac{-8}{7}$

The multiplicative inverse of a rational number is a number such that When multiplied by a rational number, gives the answer 1.

Assume $x$ as the multiplicative inverse of $-1\frac{1}{7}=\frac{-8}{7}$

Thus from definition from the multiplicative inverse:

$\begin{array}{rcl}\frac{-8}{7}\times x& =& 1\\ & \Rightarrow & x=\frac{-7}{8}\end{array}$

Hence , multiplicative inverse of $-1\frac{1}{7}$is $\frac{-7}{8}$.

And thus, Option (D) is the correct option.

Explanation for the incorrect option:

Since, the multiplicative option is $\frac{-7}{8}$ as calculated above which is not equivalent to the values mentioned in Option A , Option B, and Option C.

So, option A , Option B, and Option C are incorrect option

Hence, the correct option is Option (D)