Question

Find the multiplicative inverse of the following:
$ - 13,{\text{ - }}\dfrac{{13}}{{19}},{\text{ - }}\dfrac{5}{8}{\text{ }} \times {\text{ }} - \dfrac{3}{7}$
$
  {\text{A}}{\text{. - }}\dfrac{1}{{13}}{\text{; - }}\dfrac{{19}}{{13}}{\text{; }}\dfrac{{56}}{{15}} \\
  {\text{B}}{\text{. - }}\dfrac{1}{{13}}{\text{; }}\dfrac{{19}}{{13}}{\text{; }}\dfrac{{56}}{{15}} \\
  {\text{C}}{\text{. }}\dfrac{1}{{13}}{\text{; - }}\dfrac{{19}}{{13}}{\text{; }}\dfrac{{56}}{{15}} \\
  {\text{D}}{\text{. }}\dfrac{1}{{13}}{\text{; }}\dfrac{{19}}{{13}}{\text{; }}\dfrac{{56}}{{15}} \\
$

Answer 1

Hint – To find the multiplicative inverse we find the reciprocal of the number, i.e. flip the numerator and the denominator.

Complete step-by-step answer:

Given Data,
Multiplicative inverse of $ - 13,{\text{ - }}\dfrac{{13}}{{19}},{\text{ - }}\dfrac{5}{8}{\text{ }} \times {\text{ }} - \dfrac{3}{7}$
A multiplicative inverse or reciprocal for a number x, denoted by $\dfrac{1}{{\text{x}}}$ or ${{\text{x}}^{ - 1}}$, is a number which when multiplied by x yields the multiplicative identity, 1. Positive value of 1 only.

Multiplicative inverse of -13
Let the multiplicative inverse be x.
According to the definition x $\times$ -13 = 1
⟹x = $ - \dfrac{1}{{13}}$

Multiplicative inverse of $ - \dfrac{{13}}{{19}}$
Let the multiplicative inverse be x.
According to the definition x × $ - \dfrac{{13}}{{19}}$ = 1
⟹x = $ - \dfrac{{19}}{{13}}$

Multiplicative inverse of ${\text{ - }}\dfrac{5}{8}{\text{ }} \times {\text{ }} - \dfrac{3}{7}$,
I.e. Multiplicative inverse of $\dfrac{{15}}{{56}}$
Let the multiplicative inverse be x.
According to the definition x × $\dfrac{{15}}{{56}}$ = 1
⟹x = $\dfrac{{56}}{{15}}$

Hence the multiplicative inverses of $ - 13,{\text{ - }}\dfrac{{13}}{{19}},{\text{ - }}\dfrac{5}{8}{\text{ }} \times {\text{ }} - \dfrac{3}{7}$ are $ - \dfrac{1}{{13}}$, $ - \dfrac{{19}}{{13}}$ and $\dfrac{{56}}{{15}}$ respectively.
Hence Option A is the correct answer.

Note – In order to solve this type of question the key is to know the definition of a multiplicative inverse. It is important to look out for the sign on the number which finds the inverse.
Multiplication of signs are as follows:
(+) × (+) = (+)
(-) × (-) = (+)
(+) × (-) = (-)