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Understanding how to combine numbers using algebraic addition is fundamental in mathematics. In algebra, addition involves combining like terms – terms that have the same variable raised to the same power. However, with integers, including negative numbers, we focus on combining the numbers based on their signs. When adding two negative numbers, we essentially combine their absolute values (the value of the number without considering its sign) and then assign a negative sign to the result.
For example, in the expression \( (-8) + (-6) \), we add the absolute values 8 and 6 to get 14 and then apply the negative sign to get \( -14 \). This process is quite straightforward but is essential to grasp as it forms the basis for more complex algebraic operations.

Arithmetic with negative numbers can initially seem confusing, but it's actually very logical once you understand the rules. Negative numbers represent values less than zero, often used to express a deficit or loss. The key with negative number arithmetic is to remember that when you add a negative number, you move to the left on the number line, symbolizing a decrease.
For instance, if we look at the expression \( (-2) + (-1) \), we are effectively combining two moves to the left on the number line. This results in moving left a total of 3 places, leading to \( -3 \). Similar rules apply for subtraction: when you subtract a negative, it's like moving to the right, which is equivalent to adding a positive. Including these concepts in homework and exercises helps students visualize the process, aiding in a stronger grasp of the subject.

Brackets play an important role in algebra – they indicate the order in which operations should be performed. According to the order of operations, expressions within brackets should be computed first before moving on to other operations.
In the example given, \( [(-8)+(-6)]+[(-2)+(-1)] \), we compute the sums inside the brackets before adding those results together.

Handling Multiple Brackets

Sometimes, you may encounter multiple brackets. In such cases, perform the operations inside the innermost brackets and work your way outward. This step-by-step approach ensures accuracy and prevents mistakes often made by rushing through the problem.

Bracket Operations and Negative Signs

Additionally, when they precede brackets, negative signs are distributed to each term within if you're multiplying or dividing. With addition and subtraction inside brackets, the terms retain their signs when summed, as seen in the exercise. After computing the sums within the brackets for our example, we added them together to find the overall sum, \( -17 \). This illustrates how bracket operations organize and clarify the steps needed to solve algebraic expressions.