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When simplifying mathematical expressions, the order in which you perform operations can change the result. This is where PEMDAS is handy! It is an acronym for guiding the sequence:

• P – Parentheses
• E – Exponents
• M – Multiplication
• D – Division
• A – Addition
• S – Subtraction

In PEMDAS, multiplication and division share the same level of priority, which means you perform them as you encounter them from left to right. It's like reading a book; you don't skip random lines. Similarly, perform addition and subtraction as they appear from left to right. Following this sequence accurately is crucial for getting the correct answer in expressions like \( 2 \cdot 9 \div 3 \cdot 18 \). Taking these steps helps ensure you don't skip over any operations.

Multiplication is one of the basic operations in arithmetic. It involves finding the product of numbers. In the expression \( 2 \cdot 9 \div 3 \cdot 18 \), multiplication occurs twice.

Beginning with Multiplication

The expression starts with \( 2 \cdot 9 \). To simplify, you multiply these two numbers: \( 2 \times 9 = 18 \). Think of this process as grouping, like making sets of nine twice.

Final Multiplication

After dividing, you multiply again. From Step 3 where the result was 6, multiply by 18, getting \( 6 \times 18 = 108 \). This operation scales the number, which is like adding six sets eighteen times. Multiplication is efficient because it allows you to add groups quickly, resulting in fewer calculations.

Division is the process of determining how many times a number is contained within another. In our expression, division is right in the middle, following the first multiplication.

Performing Division

Starting from the result of the first multiplication, 18, you perform division by 3, which is executing \( 18 \div 3 \). This operation breaks 18 into 3 equal parts, and each part is 6. This step is important as it contributes to solving the whole expression methodically. Ensuring you follow the left-to-right rule in division and multiplication will make sure you end up with the right result. Here, the division doesn't just reduce the number; it is essential for finding the accurate middle ground before proceeding to the final multiplication. So whenever you face division as seen in this expression, approach it methodically, breaking the numbers into simpler parts to avoid mistakes.