Question

If the multiplicative inverse of \[\dfrac{{15}}{3}\] is $\dfrac{a}{b}$ . Then find the value of $(a + b)$ .

Answer 1

Hint: The multiplicative inverse of a real number is always the reciprocal of it. For example, the multiplicative inverse of $\dfrac{a}{b}$ is $\dfrac{b}{a}$ .
Here the sign of the number will never be changed.
Moreover, the multiplicative inverse of a number $t$ will be just $\dfrac{1}{t}$ .
To find $(a + b)$ we have to add the numerator and denominator of the reciprocal.

Complete step-by-step answer:
We are given a fraction $\dfrac{{15}}{3}$ .
We first have to find the multiplicative inverse of the number.
Then we have to find the sum of the numerator and denominator.
Here, to find the multiplicative inverse we just have to interchange the numerator with the denominator and vice versa. This is similar to finding the reciprocal of a number.
$\therefore $ The multiplicative inverse of $\dfrac{{15}}{3}$ is $\dfrac{3}{{15}}$ .
We can also check that the product of $\dfrac{{15}}{3}$ and $\dfrac{3}{{15}}$ is $1$ .
Here $a = 3,b = 15$ .
Now we have to find the sum of the numerator and denominator.
$\therefore (a + b) = 3 + 15 = 18$
Hence, the required value of $(a + b)$ is $18$ .

Note: If we multiply a number by its multiplicative inverse then the product will be $1$ . This comes from the definition of a multiplicative inverse. It is very important to remember that sign doesn’t have any impact on the multiplicative inverse. One should be very careful while finding the multiplicative inverse. In case if a number or fraction has a negative sign the negative sign will appear in the final answer. One must remember the multiplicative inverse of a complex number is very different from that of a real number and the same logic does not apply there.