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Addition is one of the fundamental operations in mathematics that helps us combine quantities. When we talk about the addition of real numbers, we are combining any two numbers from the set of real numbers. The real numbers include all the numbers on the number line, such as integers, fractions, and decimals.
To add two real numbers, we simply calculate the sum of these values. It is crucial to remember that every number has a position on the number line, and the addition represents moving along this line. For example, positive numbers move us to the right while negative numbers move us to the left.
In the problem, we were tasked with adding two real numbers: 9 and -18. Real numbers can be added in any order due to the commutative property of addition, which is a handy rule. However, understanding the impact of negative numbers is important in this context.

Negative numbers are numbers that have a value less than zero and are found to the left of zero on the number line. When we add a negative number to another number, it is similar to subtracting the magnitude of that negative number. This might sound tricky, but with a bit of practice, it becomes quite natural.
For example, in the expression 9 + (-18), adding -18 is equivalent to taking away or subtracting 18 from 9. This is because adding a negative essentially moves you left on the number line, opposite to adding positive numbers.
It helps to visualize an addition like 9 + (-18) as starting at 9 on the number line and moving 18 units to the left to reach the final position of -9. This representation makes it easier to see how the numbers interact and change with one another.

When dealing with negative numbers in addition, it often simplifies things to think in terms of absolute values. The absolute value of a number is its distance from zero and is always a non-negative number, regardless of direction on the number line.
Subtracting a number means removing that amount, moving left on the number line. So, if we consider the absolute value in our problem, we're looking at \|\(-18\)|, the absolute value of -18, which is 18.
Thus, in the operation 9 + (-18), rather than thinking directly about combining the numbers, we can recognize that we are subtracting the absolute value of -18 (i.e., 18) from 9. This approach aligns with the rule that adding a negative number is the same as subtracting its absolute value.
Understanding this concept helps simplify operations with negative numbers and makes it easier to visualize and compute solutions accurately.