91Ó°ÊÓ

Simplifying expressions is an important skill in prealgebra. It involves combining and reducing terms to make the expression easier to work with.Many expressions include numbers, variables, or both. In this exercise, we worked strictly with numbers to simplify the given expression: \[(-20-5) \div 5 - 15\] Here are the ways you commonly simplify expressions:

• Combine like terms if there are any.
• Perform operations following the order of operations.

For this example, the expression starts with a subtraction inside parentheses. Inside the parentheses, we have \(-20 - 5\). First, simplify this to \(-25\), so the expression becomes \(-25 \div 5 - 15\). From here, continue to perform division or multiplication before addressing any additional addition or subtraction to fully simplify the expression.

Order of operations is crucial for correctly solving expressions. It provides a systematic approach to reach the right answer.The order is famously remembered by the acronym PEMDAS:

• P: Parentheses - Do calculations inside parentheses first.
• E: Exponents - Address powers and square roots.
• M and D: Multiplication and Division - From left to right.
• A and S: Addition and Subtraction - From left to right.

In our problem, parentheses came first. We simplified \(-20 - 5\) inside the parentheses. Next, division was at the forefront with \(-25 \div 5\) yielding \(-5\). Finally, subtraction gave the final answer as \(-20\). Following this order ensures calculations are done correctly.

Integer arithmetic is the set of operations that involve whole numbers, which can be positive, negative, or zero. Understanding how to perform arithmetic with integers is foundational in math.In our expression, all numbers involved were integers: \(-20\), \(-5\), \(-25\), and \(15\).Performing subtraction: When subtracting, think of moving along a number line. For example: \(-20 - 5\) means moving 5 steps left from \(-20\).Performing division: This operation is straightforward. You divide two integers like \(-25 \div 5\) and the negative sign indicates the result is negative.Performing subtraction again at the end ensures you understand how addition of negative numbers works: \(-5 - 15\) calculated as moving further to the left yields \(-20\). These basic operations with integers are essential for tackling more complex algebraic problems.