Understanding and Solving Complex Arithmetic Expressions

Arithmetic expressions can appear daunting, but they become manageable when you follow the correct order of operations. Let's break down a complex expression step-by-step to understand how to solve it.

Given Expression: 72 - 3(224 ÷ 4) × 3 - 2 × 2 8

In this expression, we will follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Step-by-Step Solution

Solve the bracket: First, we solve the division inside the parentheses. 224 ÷ 4 56 Substitute back into the expression: 72 - 3(56) × 3 - 2 × 2 8 Multiplication: Next, we perform the multiplications. 3 × 56 168 2 × 2 4 Substitute back into the expression: 72 - 168 × 3 - 4 8 Further Multiplication: 168 × 3 504 Substitute back into the expression: 72 - 504 - 4 8 Subtraction and Addition: Finally, we perform the subtraction and addition from left to right. 72 - 504 -432 -432 - 4 -436 -436 8 -428

Therefore, the result of the expression 72 - 3(224 ÷ 4) × 3 - 2 × 2 8 is -428.

Understanding the Order of Operations

To solve such complex expressions, understanding the order of operations is crucial. Here's a quick overview of PEMDAS:

Parentheses (P): Solve any expressions inside parentheses first. Exponents (E): Evaluate any exponents next. Multiplication and Division (MD): Perform multiplication and division from left to right. Addition and Subtraction (AS): Perform addition and subtraction from left to right.

By following these steps, you can systematically and accurately solve complex arithmetic expressions.

Conclusion

Mastering the order of operations is a fundamental skill in mathematics. Not only does it simplify complex expressions, but it also enhances your problem-solving abilities. If you found this article helpful, please consider giving it a like or upvote.