Understanding Mathematical Expressions: Solving 9 8 ÷ 2 - 2 with PEMDAS/BODMAS

Mathematics often requires a specific order of operations to solve expressions correctly. This article will walk you through the process using the expression '9 8 ÷ 2 - 2', emphasizing the importance of following the PEMDAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) rules.

What is 9 8 ÷ 2 - 2?

Let's break down the expression 9 8 ÷ 2 - 2 step by step to understand the correct solution.

Step-by-Step Breakdown

Parentheses/Brackets: In this particular example, there are no parentheses or brackets to be considered. Thus, we move to the next step. Exponents/Orders: There are no exponents or orders in this expression, so we continue. Multiplication and Division: According to PEMDAS/BODMAS, we first perform any multiplication or division from left to right. In this case, we have the division: 8 ÷ 2 4. Addition and Subtraction: After performing the division, we substitute 4 back into the expression, resulting in 9 4 - 2. Now, we perform the subtraction: 9 - 2 7.

The Final Answer

By following the correct order of operations, we find that the expression 9 8 ÷ 2 - 2 simplifies to 11. This is the correct solution based on the orders of operations.

Alternative Expressions

Let's also consider a similar expression, 72 ÷ 18 - 18. Applying the same rules:

We first perform the division: 72 ÷ 18 4. Next, we perform the subtraction: 4 - 18 -14.

Therefore, the result of 72 ÷ 18 - 18 is -14.

Common Mistakes and Clarifications

Solving mathematical expressions can be straightforward when you follow the correct order of operations. However, it's not uncommon to encounter confusion with certain types of expressions. It's crucial to remember that:

Division should always be performed before subtraction or addition. Classical order of operations applies to all mathematical expressions. Always simplify inside any parentheses or brackets first if they are present.

Additional Examples

Let's look at a few more examples to solidify the concept:

98 ÷ 2 - 2 First, perform the division: 98 ÷ 2 49. Then, perform the subtraction: 49 - 2 47. 11 As there are no operations to perform, the value remains 11.

Conclusion

Mathematical expressions, whether simple or complex, require a consistent application of the order of operations to arrive at the correct answer. By adhering to the PEMDAS/BODMAS rules, you can solve expressions with confidence and accuracy. Remember to always perform divisions before subtraction or addition, and you'll be well on your way to solving any mathematical expression effectively.