91Ó°ÊÓ

Simplification is the process of making an expression easier to work with or understand. In this exercise, we simplify a mathematical expression step-by-step.

To simplify, you need to follow the order of operations, sometimes remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This helps you decide which operation to perform first in an expression that has multiple operations.

For the given problem \(-32 - 8 \div 4 - (-2)\), we will simplify it step-by-step, considering the rules of PEMDAS.

Always look for groupings and perform operations inside parentheses first. Even if there are no explicit parentheses, consider the operations performed first as critical groupings.

Division is one of the four primary arithmetic operations. In this exercise, division must be handled before addition or subtraction as per the order of operations.

In the expression \(-32 - 8 \div 4 - (-2)\), identify the division part first: \( 8 \div 4 = 2\).

Once you perform the division, the expression transforms into \(-32 - 2 - (-2)\). Notice that eliminating fractions or more complex divisions early simplifies the remaining steps and reduces potential mistakes.

By carefully handling division early in the equation-solving process, you will maintain consistency and accuracy in your work.

Subtracting negative numbers can be tricky, but remembering some rules makes it easier. In this step, recognize that subtracting a negative number is equivalent to adding the positive of that number.

For example, in the expression \(-32 - 2 - (-2)\), subtracting -2 is the same as adding +2: \(-32 - 2 + 2\).

Understanding this rule: \(a - (-b) = a + b\) is fundamental when simplifying expressions involving negative numbers. Subtracting a negative changes the sign to positive and effectively becomes addition. Always simplify negative subtractions before combining all terms for the final simplification.

In our example, after addressing this rule, you end up combining remaining terms to get the final simplified result \-32\.