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Adding or subtracting negative numbers is a fundamental concept in arithmetic. When you are combining negative numbers, keep in mind that you are essentially dealing with their absolute values. For instance, in the problem \(-4.2 + (-9.3)\), we notice both numbers are negative.

To combine these numbers, follow these steps:

1. Determine whether you are adding or subtracting. Here, it is addition because you have two negative numbers.
2. Add their absolute values: \(4.2 + 9.3 = 13.5\)
3. Attach the negative sign to the result because both original numbers are negative.

So, combining \(-4.2\) and \(-9.3\) gives us \(-13.5\).
This concept is straightforward if you remember that adding negatives means moving further into the negative side of the number line.

Understanding absolute value is crucial when working with negative numbers. The absolute value of a number is the distance of that number from zero on the number line, regardless of direction. In simple terms, it's the positive version of the number.

For example:

• The absolute value of \(-4.2\) is \| -4.2 | = 4.2\
• The absolute value of \(-9.3\) is \| -9.3 | = 9.3\

Using the absolute value makes it easier to perform arithmetic operations without worrying about the associated negative sign initially. You deal with the negative sign only after completing the combination of the absolute values.

Arithmetic operations with negative numbers follow specific rules that make calculations easier. When performing arithmetic operations like addition or subtraction, consider the absolute values of the numbers first.

In the given exercise:\(-4.2 + (-9.3)\):

• Recognize that you're adding two negative numbers.
• Combine their absolute values: 4.2 + 9.3 = 13.5
• Apply the negative sign to the result: -13.5

So the answer becomes \(-13.5\).

By understanding these rules and steps, you can easily perform arithmetic operations on negative numbers, ensuring accurate results without confusion.