Why Are People So Confused About PEMDAS?

PEMDAS is a widely recognized acronym that helps students and professionals remember the order of operations in mathematics. However, despite its simplicity, many individuals struggle to grasp its correct application. This article explores the reasons behind this confusion and provides insights to clarify these misconceptions.

Order of Multiplication/Division and Addition/Subtraction

One of the primary reasons for confusion regarding PEMDAS is the misconception that multiplication always comes before division and addition before subtraction. In reality, multiplication and division, as well as addition and subtraction, are at the same level of precedence. They should be performed from left to right as they appear in the expression. For example, consider the expression 8 / 4 * 2 1 - 3. According to PEMDAS, we should:

The key point to remember is to work left to right when dealing with multiplication and division, or addition and subtraction.

Misinterpretation of Parentheses

Another common source of confusion is the misinterpretation of parentheses. While parentheses are used to alter the order of operations, learners often struggle to understand their proper usage. When parentheses are applied, operations inside them are performed first, regardless of the external operators. Consider the expression (3 2) * 4 - 1. First, perform the operation inside the parentheses: 3 2 5. Then, multiply the result by 4: 5 * 4 20. Finally, subtract 1: 20 - 1 19.

Incorrectly ignoring the parentheses can lead to significant errors in the calculation. It is crucial to follow the order of operations strictly, especially when dealing with nested parentheses.

Complex Expressions

As expressions become more complex, maintaining the correct order of operations becomes challenging. This is particularly true when multiple layers of parentheses are involved. For instance, consider the expression (2 * (3 4) - 1) / (5 - 3). First, solve the nested parentheses: 3 4 7 and 5 - 3 2. Next, perform the multiplication and subtraction inside the first set of parentheses: 2 * 7 - 1 14 - 1 13. Finally, divide the result by 2: 13 / 2 6.5.

This example highlights the importance of systematically breaking down complex expressions into simpler parts, adhering to the order of operations.

Inconsistent Teaching Methods

Different teachers or educational systems may emphasize different aspects of the order of operations, leading to confusion among students. For instance, some use acronyms like BIDMAS (Brackets, Indices, Division and Multiplication, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). While the underlying principles are the same, the differences in acronyms can cause cognitive dissonance for students.

Real-Life Applications

People often perform calculations in everyday life without strict adherence to the order of operations. This can lead to misunderstandings when encountering problems that strictly require a specific order, especially in fields like engineering, finance, and science. Understanding and applying PEMDAS correctly ensures accurate results in all mathematical calculations.

Conclusion

To mitigate confusion, it is essential to practice with a variety of examples and reinforce the importance of following the order of operations systematically. Educators and trainers can also help by using consistent teaching methods and providing clear explanations of the rules. By fostering a deeper understanding of PEMDAS, individuals can avoid common pitfalls and excel in their mathematical endeavors.