91Ó°ÊÓ

Understanding the order in which operations need to be carried out is crucial for simplifying algebraic expressions correctly. This hierarchy is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Let's look at how it applies to the exercise \( -8 - (-14) + 7 \). Here, the first thing we notice is the parentheses. According to PEMDAS, we deal with whatever is inside the brackets first. When we remove the parentheses by resolving the double negative, we are left with \( -8 + 14 + 7 \).

Since there are no exponents, multiplication, or division, we proceed to addition and subtraction. These are performed from left to right as they appear in the expression, leading us to the simplified result.

Handling negative numbers can be tricky, but there are some key rules that make working with them easier. For instance, subtracting a negative number is the same as adding its positive counterpart, because two negatives make a positive.

In our example, \( -8 - (-14) + 7 \), we encounter this situation with the term \( -(-14) \). This translates to the addition of 14, hence the expression simplifies to \( -8 + 14 + 7 \). It's important to remember that subtracting a larger number from a smaller one will result in a negative number, while adding a negative number is akin to subtraction.

Finally, summarizing the basic arithmetic operations within algebraic expressions comes down to addition, subtraction, multiplication, and division. Each operation follows specific rules that need to be applied consistently.

When combining positive and negative numbers, we use addition and subtraction, where the sign of the larger absolute number will determine the sign of the result. After resolving the brackets in our exercise, \( -8 + 14 + 7 \), we now add and subtract the numbers. Remember, when adding numbers with different signs, consider their absolute values and subtract the smaller from the larger, taking the sign of the larger value. The process in this case yields a straightforward sum of integers, leading to the final answer.