**Additive Inverse of -7/9**

To find the additive inverse of a number, we need to find a number that, when added to the given number, results in zero. In other words, the additive inverse of a number is the number that, when added to the original number, gives us a sum of zero.

In this case, we are given the number -7/9. To find its additive inverse, we need to find a number that, when added to -7/9, gives us zero.

**Step 1: Understand the concept of additive inverse**

The concept of additive inverse is based on the fact that for any real number 'a', its additive inverse is denoted as -a, and the sum of 'a' and its additive inverse is always zero.

**Step 2: Find the additive inverse**

To find the additive inverse of -7/9, we need to find a number that, when added to -7/9, gives us zero.

Let's denote the additive inverse of -7/9 as 'x'. So, we have:

-7/9 + x = 0

**Step 3: Solve for 'x'**

To solve for 'x', we need to isolate it on one side of the equation. We can do this by subtracting -7/9 from both sides of the equation:

x = -(-7/9) [subtracting -7/9 from both sides]

x = 7/9

Therefore, the additive inverse of -7/9 is 7/9.

**Summary:**

The additive inverse of -7/9 is 7/9. When -7/9 is added to 7/9, the sum is zero. The concept of additive inverse states that for any real number 'a', its additive inverse is denoted as -a, and the sum of 'a' and its additive inverse is always zero. In this case, -7/9 is added to its additive inverse, resulting in a sum of zero.

7/9