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Negative numbers are values less than zero. They are represented with a minus sign (e.g., -1, -2, -3). When dealing with negative numbers in mathematical operations, it's important to understand their properties. A negative number is the opposite of a positive number. For example, -5 is the opposite of 5. Negative numbers are often used to represent loss, deficit, or values below a certain point.
When performing operations with negative numbers, pay attention to their signs. Adding a negative number is like subtracting, and subtracting a negative number is like adding. Multiplying and dividing with negative numbers involves specific rules, which we will discuss next.

When multiplying numbers, the sign of the result depends on the signs of the numbers being multiplied. Here are the key rules:

• Positive × Positive = Positive (e.g., 2 × 3 = 6)
• Negative × Positive = Negative (e.g., -2 × 3 = -6)
• Positive × Negative = Negative (e.g., 2 × -3 = -6)
• Negative × Negative = Positive (e.g., -2 × -3 = 6)

Understanding these rules helps in simplifying expressions involving multiplication with negative numbers. For example, in the expression \(-6(-9)\), you apply the fourth rule. Since both numbers are negative, their product is positive. Thus, \(-6 \times -9 = 54\).

Mathematical operations include addition, subtraction, multiplication, and division. Each operation has specific rules and properties that govern how numbers interact.
When working with multiplication, it's important to follow the correct order: first multiply the absolute values of the numbers, then apply the appropriate sign based on the multiplication rules discussed earlier. For instance, in the expression \(-6 \times -9\), first multiply the absolute values (6 × 9 = 54), then determine the sign. Since both numbers are negative, the result is positive, giving you 54.
Breaking down each step helps in understanding and correctly applying mathematical operations, ensuring accurate results in problem-solving.