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A numerical expression is a mathematical phrase involving numbers and operations such as addition, subtraction, multiplication, and division. In simpler terms, it includes the numbers and the mathematical symbols that we use to perform calculations.

For instance, in the expression \(16 - 40\), we can identify two numbers—16 and 40—and the operation of subtraction. The goal when working with numerical expressions is to simplify them, which means performing the operations to find the simplest form or value of the expression.

To simplify, always follow the correct order of operations. In the case of subtraction, you only need to subtract one number from another, as shown:

• Perform the operation 16 - 40
• Get the result -24

This process of simplifying the numerical expression helps make more complex equations easier to handle.

Whenever you see a fraction, like \(\frac{16-40}{8}\), it is composed of two main parts: the numerator and the denominator. Understanding these parts is crucial in simplifying fractions.

The **numerator** is the top part of the fraction. It represents the number of parts we have or are considering. In the example \(\frac{16-40}{8}\), before simplification, the numerator is \(16-40\). Once simplified, it becomes \(-24\).

The **denominator** is the bottom part of the fraction. It tells us into how many equal parts the numerator is divided. In our case, the denominator is 8. Therefore, the fraction \(\frac{-24}{8}\) means we have -24 parts divided into 8 equal groups.

Simplifying a fraction often involves performing interactions with both the numerator and the denominator to achieve the simplest form. By breaking these components into simpler parts, the overall calculation becomes more straightforward.

The division of integers involves dividing whole numbers. This is a straightforward but essential aspect of algebra simplification. In this practice, you can apply the division process to numbers regardless of their signs.

In our problem, after simplifying, the fraction \(\frac{-24}{8}\) needs to be solved through division. This involves the integer -24 being divided by 8. Here's how:

• -24 divided by 8 is calculated as
• If you divide 24 by 8, you get 3. However, since one number is negative, the result becomes negative, hence -3.

The main rule here is, when dividing two integers with different signs, the result is always negative. Conversely, if the signs were the same, the result would be positive. This principle aids in accurately determining the result of integer divisions.