The multiplicative inverse of $\frac{12}{5}$ equal to:

Question

Accepted Answer

The correct option is (3):

To find the multiplicative inverse of a number, we need to find another number such that their product is 1. This other number is also known as the reciprocal.

For a fraction $\frac{a}{b}$, its multiplicative inverse is $\frac{b}{a}$, provided that $a 
eq 0$ and $b 
eq 0$.

In this problem, the given number is $\frac{12}{5}$.
Let the multiplicative inverse be $x$.
According to the definition, $\frac{12}{5} 	imes x = 1$.
To find $x$, we can multiply both sides by the reciprocal of $\frac{12}{5}$, which is $\frac{5}{12}$.
So, $x = 1 	imes \frac{5}{12}$
$x = \frac{5}{12}$

Let's check our answer:
$\frac{12}{5} 	imes \frac{5}{12} = \frac{12 	imes 5}{5 	imes 12} = \frac{60}{60} = 1$.
Thus, the multiplicative inverse of $\frac{12}{5}$ is $\frac{5}{12}$.

The incorrect option is (1):
1 is the multiplicative identity, not the multiplicative inverse of $\frac{12}{5}$. The product of $\frac{12}{5}$ and 1 is $\frac{12}{5}$, not 1.

The incorrect option is (2):
\-1 is not the multiplicative inverse. The product of $\frac{12}{5}$ and -1 is $-\frac{12}{5}$, not 1.

The incorrect option is (4):
The multiplicative inverse of 0 is undefined because division by zero is not possible. Also, for any non-zero number, multiplying it by 0 will always result in 0, not 1.