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Negative numbers are numbers that are less than zero. They are represented by placing a minus sign before the number. Negative numbers can be found on the left side of zero on a number line, opposite of positive numbers.
For example,

• -2 is a negative number, it is less than 0.
• When you add a negative number, you actually move further left on the number line.

Negative numbers behave differently in arithmetic operations compared to positive numbers.
When you add a negative number to a positive number, you're essentially subtracting the two numbers. For example, if you calculate 5 + (-3), it's the same as 5 - 3, which equals 2.
Understanding how negative numbers work in operations is crucial for solving algebraic expressions like the one in the exercise, where you need to handle both positive and negative results.

Multiplication is one of the four elementary mathematical operations that allow you to find the total of adding a number to itself a certain number of times. For the multiplication of negative numbers,

• When multiplying a negative number by a positive number, the result is always negative.
• When multiplying two negative numbers, the result turns positive.
• When multiplying a positive number by another positive number, the result is positive.

For example, in the exercise, we start with
-2 times 9, which results in -18 because you multiply a negative number by a positive number.
Understanding multiplication rules helps when dealing with complex algebraic expressions because following these rules ensures the calculation is accurate.

The order of operations is a fundamental concept in mathematics that dictates the rules used to clarify which procedures to perform first in order to ensure consistent results. This concept is sometimes remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

This order helps in evaluating expressions systematically.
For instance, in our given exercise -2(9) - 2(5)(10), you first perform the multiplication parts because there are no parentheses or exponents.
Then, results from the multiplication are summed. This approach ensures calculations yield the correct answer by respecting the hierarchy in mathematical operations.