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Simplifying expressions is a basic yet essential skill in arithmetic and algebra. When you see an expression, your goal is to reduce it to its simplest form. This means condensing the expression as much as possible, often by performing arithmetic operations like addition, subtraction, multiplication, and division. For example, in the expression \( (8-7)-9\), the first step is to focus on the part inside the parentheses since operations inside parentheses are performed first. Simplifying \( 8 - 7 \) gives us 1. Therefore, the original expression simplifies to 1 minus 9. Simplified forms are easier to understand and work with.

The order of operations is a fundamental principle in arithmetic and algebra, ensuring that everyone solves expressions in the same way. The standard order of operations can be remembered with the acronym PEMDAS:

• P: Parentheses first
• E: Exponents (or powers and roots, like squares and square roots)
• MD: Multiplication and Division (from left to right)
• AS: Addition and Subtraction (from left to right)

In the exercise given, \( (8-7)-9\), the parentheses indicate that we need to perform the subtraction inside them first. After evaluating \( 8 - 7 \) to get 1, we then move on to the next operation left to do, which is the subtraction outside the parentheses, resulting in \( 1 - 9 \).

Subtraction is one of the four basic arithmetic operations. It involves taking one number away from another. In the context of the given exercise \( (8-7)-9\), subtraction is used twice.

First, we subtract 7 from 8 inside the parentheses, yielding 1. Then, we subtract 9 from 1. To visualize subtraction, you can think of it as moving left on the number line. Starting from 1 and subtracting 9 moves you left to -8 because 9 steps left from 1 takes you past zero into negative numbers. This shows another important concept in arithmetic: subtracting a larger number from a smaller number results in a negative value. Always remember to perform subtraction with care, as it's easy to make mistakes with the order of numbers.