Question

What is the sum of additive inverse and multiplicative inverse of -7?

Answer 1

Hint: Use the fact that the additive inverse of a number a is –a and its multiplicative inverse is \[\dfrac{1}{a}\]. Substitute \[a=-7\] in the above expression. Add the two values to get the sum of multiplicative inverse and additive inverse of -7.

Complete step-by-step answer:
We have to calculate the sum of additive inverse and multiplicative inverse of number -7.
We know that the additive inverse of any number ‘a’ is ‘-a’.
Substituting \[a=-7\] in the above expression, we have the additive inverse of -7 to be \[=-\left( -7 \right)=7\].
We know that the multiplicative inverse of any number ‘a’ is \[\dfrac{1}{a}\].
Substituting \[a=-7\] in the above expression, we have, the multiplicative inverse of -7 to be \[=\dfrac{1}{-7}=\dfrac{-1}{7}\].
Thus, the additive and multiplicative inverse of -7 is 7 and \[\dfrac{-1}{7}\] respectively.
We will now add the two numbers to find the sum of additive inverse and multiplicative inverse of -7.
So, the sum of 7 and \[\dfrac{-1}{7}\] is \[=7+\left( \dfrac{-1}{7} \right)\].
Taking LCM, we have, the sum \[=7+\left( \dfrac{-1}{7} \right)=\dfrac{49-1}{7}=\dfrac{48}{7}\].
Hence, the sum of additive inverse and multiplicative inverse of -7 is \[\dfrac{48}{7}\].

Note: Additive inverse of a number is the number, which added to the number, yields a result 0. For any real number, we can obtain its additive inverse by reversing the sign of the number, i.e., reversing the sign of positive number will give a negative number of same magnitude and reversing the sign of a negative number will give positive number of same magnitude. Multiplicative inverse (or reciprocal) of any number is the number which when multiplied with the number gives the multiplicative identity 1. To find the multiplicative inverse of a number, divide 1 by the number.