Question

What will be the additive inverse of -3 / 9, -9 / 11, 5 / 7?

Answer 1

Hint: In this question we can use the fact that the sum of an integer and additive inverse of that integer is always zero. This means we have to find the integer whose sum with the given integer brings the answer zero.

Complete step by step answer:
We have to find the additive inverse of -3/9, -9/11, 5/7.
First, we will find the additive inverse of -3/9.
Let the additive inverse of -3/9 be x.
The sum of integers and its additive inverse is zero. So,
$\dfrac{{ - 3}}{9} + x = 0$
$x = \dfrac{3}{9}$.
So, the additive inverse of -3/9 is 3/9.
Similarly, we will find additive inverse of -9/11 and 5/7.
Let the additive inverse of -9/11 is y. so,
$\dfrac{{ - 9}}{{11}} + y = 0$
$y = \dfrac{9}{{11}}$.
So, the additive inverse of -9/11 is 9/11.
Let the additive inverse of 5/7 be z.
$\dfrac{5}{7} + z = 0$
$z = \dfrac{{ - 5}}{7}$
So, the additive inverse of 5/7 is -5/7.
Hence, the additive inverse of -3/9, -9/11 and 5/7 are 3/9, 9/11 and -5/7 respectively.

Note:
 We can also find the additive inverse of any integer just by changing their sign; the sum of any two integers can only be negative when the value of both the integers are same but the signs are different. While changing the sign of integers we must be very careful that we must not make any changes in the digit of the integers but only their signs. We have to make a positive integer as negative integer and negative integer as positive integer by changing their sign only.