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When solving mathematical expressions, it's crucial to follow a set of rules known as the Order of Operations. These rules help ensure consistency and clarity in solving equations. A common tool used to remember these rules is the acronym PEMDAS (or BODMAS in some countries):

• Parentheses/Brackets
• Exponents/Orders (i.e., powers and roots, etc.)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

For the problem given: \(12 - 9 \div 3\), it's important to first identify which operations are present. In this case, we have both division and subtraction.
According to the order of operations, we must perform division before subtraction. This order helps maintain a standard approach so everyone arrives at the same answer when solving expressions. Ignoring the order can lead to incorrect results and misunderstandings in communication.

Division is one of the four basic mathematical operations. It represents the process of splitting a number into equal parts. In the context of our exercise, we are dividing 9 by 3.
Here's how division works in practical terms:

• Determine the dividend: The number to be divided. Here, it is 9.
• Identify the divisor: The number you are dividing by. In this case, it is 3.
• Compute the quotient: The result of the division. For this problem, dividing 9 by 3 gives us 3.

After carrying out the division, we update our expression by replacing the division operation with its result, simplifying it from \(12 - 9 \div 3\) to \(12 - 3\). Division can sometimes be tricky, but with practice, determining the quotient becomes intuitive. Working carefully through each step prevents errors and leads to accurate results.

Subtraction is a mathematical operation that involves taking one number away from another. It helps us determine the difference between numbers. In our simplified expression \(12 - 3\), we need to perform subtraction.
Let's break down the subtraction operation:

• Identify the minuend: the number from which another number is to be subtracted. In this exercise, it's 12.
• Recognize the subtrahend: the number that is to be subtracted, which is 3 in this problem.
• Calculate the difference: This is the result of the subtraction. Subtracting 3 from 12 gives us 9.

Subtraction is a straightforward process but requires careful attention to the numbers involved. This ensures the correct computation of the difference. By understanding and applying subtraction, we arrive at the final simplified answer of 9 for our expression.