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When solving complex mathematical expressions, the order in which you perform operations is crucial. That's where PEMDAS comes in! PEMDAS, sometimes known by the mnemonic "Please Excuse My Dear Aunt Sally," helps remember the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

When you have an equation with several operations, always start with the operations inside the parentheses. Once you have simplified the expression within parentheses, look for exponents next. After handling parentheses and exponents, move on to multiplication and division, working from left to right. Finally, complete any addition and subtraction, also from left to right.

This ensures that everyone solves equations consistently and avoids the common pitfall of calculating in an incorrect order, which can lead to different and incorrect results.

When looking at a math expression, it's natural to move from left to right, solving as you go, but this doesn't always work due to the PEMDAS rule. Multiplication must be tackled before addition.

Think of multiplication as a more 'powerful' operation than addition. It significantly changes numbers with fewer operations. Therefore, in the exercise provided, the multiplication of 3 and 2 was solved first:

• We had the expression: \(20 - 3 \cdot 2 + 9\).
• We first computed \(3 \cdot 2 = 6\).
• Then, the expression became \(20 - 6 + 9\).

This prioritization keeps the integrity of mathematical operations, ensuring no errors occur by prematurely solving addition.

Once you have handled multiplication and division according to PEMDAS, you should solve any remaining operations from left to right, focusing on addition and subtraction. This step ensures that once the priority operations are completed, the remaining operations are handled in the correct sequence.

In the exercise example, after doing multiplication first, the expression became \(20 - 6 + 9\).

• Following left to right, start with 20 and 6, which gives \(20 - 6 = 14\).
• Next, add to the result: \(14 + 9 = 23\).

This straightforward left-to-right processing applies only after addressing operations of higher precedence, making sure no inadvertent mistakes alter the equation's outcome.