As the absolute value of a negative number increases, the value of the negative number also increases.
This statement is not correct. The value of a negative number increases as its absolute value decreases. Let's see why:
The absolute value of a number is its distance from zero on the number line, regardless of whether the number is positive or negative. For example, the absolute value of -3 is 3 because it is 3 units away from zero.
As we increase the absolute value of a negative number, we are moving it further away from zero on the number line. Therefore, the value of the negative number actually decreases.
For example, let's consider the negative number -2. Its absolute value is 2, and it is 2 units away from zero on the number line. If we increase the absolute value to 3, the negative number becomes -3, which is now 3 units away from zero.
So, as the absolute value of a negative number increases, the value of the negative number decreases.