Welcome to our lesson on the order of operations. The order of operations is a fundamental set of rules that determines the correct sequence for evaluating mathematical expressions. Without these rules, the same expression could have multiple different answers. We use acronyms like PEMDAS or BODMAS to remember the correct order.
Let's break down PEMDAS step by step. P stands for Parentheses or Brackets - these are always calculated first. E stands for Exponents or Orders - powers and roots come next. M and D stand for Multiplication and Division - these have equal priority and are performed from left to right. Finally, A and S stand for Addition and Subtraction - these also have equal priority and are performed from left to right.
Let's work through a complete example step by step. We have the expression: 8 plus 2 times 3 squared minus the quantity 4 plus 2. First, we solve the parentheses: 4 plus 2 equals 6. Next, we calculate the exponent: 3 squared equals 9. Then we perform multiplication: 2 times 9 equals 18. Finally, we do addition and subtraction from left to right: 8 plus 18 equals 26, then 26 minus 6 equals 20.
Let's look at common mistakes people make with order of operations. The first mistake is ignoring parentheses and not doing them first. The second mistake is performing multiplication and division, or addition and subtraction, in the wrong order instead of left to right. The third mistake is forgetting to calculate exponents before other operations. For example, 6 plus 2 times 3 is not 24, but 12, because we multiply first, then add.
To summarize what we have learned: The order of operations is essential for getting consistent and correct results in mathematics. Remember PEMDAS to recall the correct sequence. Multiplication and division have equal priority and should be performed from left to right. The same applies to addition and subtraction. By following these rules systematically, you will always arrive at the correct answer.