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Find the multiplicative inverse of the following.
(i) -13
(ii) \( \frac{-13}{19} \)
(iii) \( \frac{1}{5} \)
Given: (i) -13
(ii) $-\frac{13}{19}$
(iii) $\frac{1}{5}$
To find: We have to find the multiplicative inverse of the given numbers.
Solution:
Multiplying a number by its multiplicative inverse results in 1.
Now,
i) - 13
Let the multiplicative inverse be = a
So,
- 13 x a = 1
$a\ =\ -\frac{1}{13}$
Therefore, multiplicative inverse of -13 is $-\frac{1}{13}$.
ii) $-\frac{13}{19}$
Let the multiplicative inverse be = a
So,
$-\frac{13}{19} \ \times \ a\ =\ 1$
$\Longrightarrow \ a\ =\ -\frac{19}{13}$
Therefore, the multiplicative inverse of $-\frac{13}{19}$ is $-\frac{19}{13}$.
iii) $\frac{1}{5}$
Let the multiplicative inverse be = a
So,
$\frac{1}{5} \ \times \ a\ =\ 1$
$\Longrightarrow \ a\ =\ 5$
Therefore, the multiplicative inverse of $\frac{1}{5}$ is 5.