Understanding and Solving Complex Mathematical Expressions with BODMAS and PEMDAS

Mathematics is a fundamental part of many academic and real-world applications. Understanding how to solve complex mathematical expressions correctly is crucial. Two essential rules to follow when solving such expressions are BODMAS and PEMDAS. Both acronyms represent the order of operations in mathematics, ensuring that calculations are performed in the correct sequence. In this article, we will explore both BODMAS and PEMDAS, alongside a detailed solution to a complex mathematical expression.

BODMAS and PEMDAS: What Are They and How Do They Work?

BODMAS is an acronym that stands for:

Brackets Orders (powers and roots, etc.) Division Multiplication Addition Subtraction

PEMDAS, on the other hand, is an acronym used in the United States and stands for:

Parentheses Exponents (powers and roots, etc.) Multiplication Division Addition Subtraction

Both acronyms dictate the same order of operations, with slight variations in presentation. Understanding these rules is crucial for solving complex mathematical expressions accurately.

Solving a Complex Mathematical Expression Using BODMAS

Let's take a look at the following mathematical expression:

8 ÷ 2 × 6358 – 598 ÷ 475

To solve this, we will apply the BODMAS rule:

Brackets: There are no brackets in this expression. Orders: There are no orders (exponents or roots) in this expression. Division: First, perform the division operations. 8 ÷ 2 4 598 ÷ 475 ≈ 1.26 Multiplication: Next, perform the multiplication operations. 4 × 6358 25432 1.26 × 3 ≈ 3.78 Addition/ Subtraction: Finally, combine the results and perform the subtraction operation. 25432 – 3.78 – 1.26 25427

Thus, the solution to the expression 8 ÷ 2 × 6358 – 598 ÷ 475 is approximately 25427.

Solving Using PEMDAS

Let's use the PEMDAS rule to solve the same expression:

8 ÷ 2 × 6358 – 598 ÷ 475

According to PEMDAS, we follow the same order of operations:

Parentheses: There are no parentheses in this expression. Exponents: There are no exponents in this expression. Multiplication/Division: Perform multiplication and division from left to right.8 ÷ 2 4

598 ÷ 475 ≈ 1.26

4 × 6358 25432

1.26 × 3 ≈ 3.78 Addition/Subtraction: Perform addition and subtraction from left to right.25432 – 3.78 – 1.26 25427

Thus, the solution to the expression 8 ÷ 2 × 6358 – 598 ÷ 475 is approximately 25427.

Conclusion

Understanding and applying BODMAS and PEMDAS are essential for solving complex mathematical expressions accurately. Both rules guide the order of operations, ensuring that calculations are performed correctly. In our examples, we saw that both rules yield the same solution, demonstrating their reliability.

Keywords

BODMAS PEMDAS Order of Operations

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References

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