91Ó°ÊÓ

When simplifying expressions, following the rules around the order of operations is crucial. The order of operations, commonly remembered through the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)), dictates the sequence in which different mathematical operations should be performed to ensure consistent and accurate results.

For example, in the expression \( (2.3 - 3.8)^2 \), you must start by solving the operation inside the parentheses before doing any squaring. By evaluating the expression inside the parentheses first, you simplify calculations and ensure that each step is orderly.

Always remember:

• Perform operations inside Parentheses first.
• Exponents (and roots) come next.
• Then work on Multiplication and Division, from left to right.
• Finally, perform any Addition and Subtraction, from left to right.

Subtraction is one of the basic arithmetic operations and is crucial for simplifying expressions. It involves taking one number away from another. When dealing with subtraction in algebraic expressions, pay close attention to the signs of the numbers involved. The result could be a positive or negative number.

In the given problem, you need to subtract 3.8 from 2.3: \((2.3 - 3.8) = -1.5\). Since 3.8 is larger than 2.3, the outcome is a negative number, -1.5. When subtracting larger numbers from smaller ones, it's helpful to think about moving left on the number line to better understand why the result is negative.

Steps for simple subtraction:

• Align the numbers by their decimal points if they have them.
• Subtract each column starting from the rightmost digit.
• Borrow from the next column if needed.

Understanding and practicing subtraction helps in solving more complex expressions accurately.

Squaring a number means multiplying that number by itself. In mathematical notation, squaring is represented by an exponent of 2. For example, \((-1.5)^2\) means \((-1.5 \times -1.5)\). The result of any number squared is always positive because a negative number times a negative number equals a positive number.

In the given exercise:

• You first simplify the expression inside the parentheses: \((2.3 - 3.8) = -1.5\).
• You then square the result: \((-1.5)^2 = (-1.5 \times -1.5) = 2.25\).

Remember, squaring amplifies the magnitude of a number. Practicing squaring helps solidify your understanding of exponents and prepares you for more advanced math topics.

To summarize, follow these steps:

• Makes sure to perform any operations inside parentheses first.
• Then, apply the exponent to square the result.
• Simplify any multiplications to get the final answer.