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Understanding negative numbers is essential as they are numbers less than zero. They have a minus sign in front of them, which signifies their negative value. In mathematical operations, knowing how negative numbers interact with each other is very important.

When adding two negative numbers, the result is more negative. For example, adding -3 and -4 gives -7. Subtraction can be a bit tricky: subtracting a negative is like adding a positive. So,

• -8 - (-3) is the same as -8 + 3, which equals -5.

In multiplication, a negative number multiplied by a positive number results in a negative number. If you multiply two negative numbers, the result is positive. Understanding these basic rules allows you to handle more complex problems involving negative numbers effectively.

Division can initially seem complex, especially with negative numbers, but understanding the rules simplifies it greatly. When dividing numbers, it is crucial to consider the signs of the numbers involved.

The rules are straightforward:

• Dividing a positive number by another positive yields a positive result.
• Dividing a negative number by a positive number results in a negative number.
• Dividing a positive number by a negative number also results in a negative number.
• Finally, dividing two negative numbers results in a positive number.

To divide negative numbers correctly, apply the rule of dividing their absolute values (ignoring the signs) and determine the sign of the answer using the above rules. In the given exercise, dividing -150 by -25 results in 6 because two negatives make a positive.

Algebra is a branch of mathematics dealing with symbols and equations, enabling us to solve real-world problems in a structured way. It often involves finding the unknown number using operations like addition, subtraction, multiplication, and division.

An important aspect of algebra is working with expressions that include numbers and variables. In the scenario described in our problem, we're performing division, which is a basic algebraic operation. The exercise simplifies, using the division operation to manipulate numbers to achieve a result.

• Identify the variables and constants in an expression.
• Apply the rules of operations, such as division and multiplication.
• Simplify to solve for any unknowns.

The ability to handle operations like dividing negative numbers aids in solving more complex algebraic problems where different rules apply. As you become more comfortable with basic operations, algebraic expressions will gradually become easier to manipulate and solve.