The additive inverse of a number is the value that, when added to the original number, results in zero. In other words, it is the opposite of the given number on the number line. To find the additive inverse of -7/-6, we need to understand and apply the concept of the additive inverse.

Understanding the Additive Inverse:
The concept of the additive inverse is based on the fact that every number has a corresponding opposite value. For any number 'a', its additive inverse is denoted as '-a'. When 'a' and '-a' are added together, the result is always zero.

Finding the Additive Inverse of -7/-6:
To find the additive inverse of -7/-6, we can follow these steps:

Step 1: Determine the given number
The given number is -7/-6.

Step 2: Simplify the given number
To simplify -7/-6, we need to divide -7 by -6. Dividing a negative number by a negative number results in a positive value. Therefore, -7/-6 simplifies to 7/6.

Step 3: Calculate the additive inverse
To find the additive inverse, we place a negative sign in front of the simplified value. Thus, the additive inverse of 7/6 is -7/6.

Explanation:
The additive inverse of -7/-6 is -7/6. This means that when we add -7/6 to 7/6, the result will be zero. It is important to note that the additive inverse preserves the sign of the number, but the numerator and denominator remain the same. The negative sign indicates the opposite direction on the number line.

Visual Representation:
To further understand the concept visually, we can represent -7/6 and its additive inverse on a number line. The number line has zero at its center, with positive values to the right and negative values to the left.

-7/6 would be represented to the left of zero, indicating a negative value. Its additive inverse, -(-7/6) or 7/6, would be represented to the right of zero, indicating a positive value. The distance between -7/6 and 7/6 is the sum of the two, which is zero.

Conclusion:
The additive inverse of -7/-6 is -7/6. By understanding the concept of the additive inverse, we can find the opposite value of a given number. The additive inverse is crucial in various mathematical operations and helps establish a balance between positive and negative values. Remember, the additive inverse preserves the sign of the number while flipping its direction on the number line.

Sice denominator and numerator both have a minus sign so both the sign will be cancelled. so now additive inverse of -7/-6 is -7/6