Understanding the Order of Operations in Mathematical Expressions

When dealing with mathematical expressions, it is crucial to understand and apply the correct order of operations. This ensures that calculations are done in a consistent and accurate manner. In this article, we will explore the concepts of BODMAS and PEMDAS, and how they can be used to solve the expression 62 ÷ 2 – 3 x 3 6 x 2.

BODMAS and PEMDAS: An Overview

Both BODMAS and PEMDAS stand for acronyms that represent the same set of operations but with different ordering. BODMAS is commonly used in the UK and India, while PEMDAS is more popular in the US and other English-speaking countries.

BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction)

BODMAS is a mnemonic used to remember the order in which operations should be performed in a mathematical expression:

B - Brackets (groups) O - Orders (exponents) D - Division M - Multiplication A - Addition S - Subtraction

PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

PEMDAS is another mnemonic that explains the same set of operations:

P - Parentheses (groups) E - Exponents (orders) M - Multiplication D - Division A - Addition S - Subtraction

Although the names are different, both BODMAS and PEMDAS follow the same rule: perform operations in the order of their precedence, from highest to lowest.

Applying BODMAS to Solve the Expression

The expression 62 ÷ 2 – 3 x 3 6 x 2 can be tackled using the BODMAS rule as follows:

Step-by-Step Solution Using BODMAS

First, we deal with the division: 62 ÷ 2 31. Next, we handle the subtraction and multiplication in the given order: 31 - 3 28. Then, we perform the multiplication of the remaining terms: 28 x 3 84. Finally, we complete the remaining multiplication: 6 x 2 12. Substituting the values back into the expression: 31 - 3 x 3 12. Now, we perform the remaining multiplication: 3 x 3 9. So, the expression becomes: 31 - 9 12. The final step is to perform the subtraction: 31 - 9 22, and then: 22 12 96.

Thus, the correct solution to the expression 62 ÷ 2 – 3 x 3 6 x 2 is 96.

Applying PEMDAS to Solve the Expression

Using the PEMDAS rule for the same expression:

Step-by-Step Solution Using PEMDAS

First, we calculate the division: 62 ÷ 2 31. Next, we perform the subtraction and multiplication in the given order: 31 - 3 28. Then, we multiply the remaining terms: 28 x 3 84. After that, we complete the remaining multiplication: 6 x 2 12. Substituting the values back into the expression: 28 x 3 12. Now, we perform the remaining multiplication: 3 x 12 36. So, the expression becomes: 84 x 36. Finally, we perform the multiplication: 84 x 36 96.

The correct solution to the expression 62 ÷ 2 (–) 3 (×) 3 6 (×) 2 is 96.

Conclusion

The expression 62 ÷ 2 – 3 x 3 6 x 2 evaluates to 96 when solved in accordance with the order of operations, BODMAS or PEMDAS. It is essential to apply these rules correctly to avoid common mistakes and ensure accurate results in mathematical computations.

FAQs

What is the difference between BODMAS and PEMDAS?

Both BODMAS and PEMDAS represent the same order of operations: Brackets/Parents, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right). The difference lies in the names: BODMAS is commonly used in the UK and India, while PEMDAS is popular in the US and other English-speaking countries.

Why is the order of operations important?

The order of operations ensures that everyone arrives at the same answer when solving mathematical expressions. Without a universally agreed order, the same expression could yield multiple results, leading to inconsistencies and confusion. By following BODMAS or PEMDAS, we maintain the integrity and consistency of mathematical computations.

What are some common mistakes to avoid?

Misinterpreting the order of operations, leading to incorrect results. Misunderstanding the precedence of multiplication and division, which are performed from left to right. Ignoring the evaluation of brackets or parentheses before performing other operations. Forgetting to perform operations from left to right when they have the same precedence.

References

1. Huettemann, T. (2014). Mathematics 1A: A skills practice consolidation workbook for Year 11 12 students. Retrieved from [Reference URL]

2. Khan Academy. (2023). Order of operations. Retrieved from