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Negative numbers are numbers that are less than zero. They are represented with a minus sign (-) in front of the number. When dealing with negative numbers in operations like division and multiplication, there are specific rules to follow. For example, dividing two negative numbers results in a positive number. Likewise, multiplying two negative numbers also results in a positive number. These rules help maintain consistency and allow us to make accurate calculations. Understanding how negative numbers interact with each other is crucial for solving problems involving these numbers.
Here's a recap of important rules to remember:

• Negative × Negative = Positive
• Negative ÷ Negative = Positive
• Negative × Positive = Negative
• Negative ÷ Positive = Negative

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a positive value or zero. For example, both the absolute value of \-3 and \3 is \3 because each is three units away from zero.
When performing operations like division or multiplication, it can be helpful to consider the absolute values first. This eliminates any confusion related to the signs of the numbers.
In our initial exercise of dividing \-4.24 \ by \-8, we first considered the absolute values, which are \4.24 and \8 respectively. After performing the division$$ \frac{4.24}{8} $$, we get 0.53. Since both our original numbers were negative, we apply the rule for division of negative numbers, resulting in a positive answer.

Multiplication is one of the four fundamental arithmetic operations and represents the addition of a number to itself a certain number of times. When working with negative numbers, it's important to note the rule: A negative number multiplied by another negative number results in a positive product. Conversely, a negative number multiplied by a positive number results in a negative product.
To check the result of a division operation, we can use multiplication to verify the answer. For instance, in the problem \-4.24 \ \div(-8) = 0.53, we multiply the quotient by the divisor:$$0.53 \times (-8) = -4.24$$.
Since the product is \-4.24, the same as our original dividend, the division operation is confirmed to be correct. Understanding multiplication thoroughly equips you with the tools to verify results and ensure accuracy in mathematical operations.