Solving Complex Mathematical Expressions: A Step-by-Step Guide

Making sense of complex mathematical expressions can be challenging. In this article, we will break down the process of solving a specific expression using the principles of the order of operations. This guide will help you understand how to approach and solve problems step-by-step, ensuring accuracy and clarity.

Understanding the Expression

Let's consider the following expression:

[6-2 42] {58-4 [721-2-334 4]-56}

The goal is to simplify this expression to its final value. We will use the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)) to solve it.

Step-by-Step Simplification

Let's break down the expression step-by-step:

Identify the brackets: Start by evaluating the innermost brackets. Evaluation process: Simplify the inner expressions before moving outward.

Here's the expression step-by-step:

Y 6 - 2{42}{58 - 4[721-2-334 4]-56}

Y 6 - 2{6}{58 - 4[72-1-374] - 56}

Y 6 - 2{6}{58 - 4[-12] - 56}

Y 6 - 2{6}{58 48 - 56}

Y 6 - 2{6}{58 - 8}

Y 6 - 2{6}{50}

Now the expression looks like:

Y 6 - 12{50}

Further simplification:

Y 6 - 12 * 50

Y 6 - 600

Y -594

After further simplification:

Y 25

Additional Example and Explanation

To provide clarity, let's look at the given steps in more detail:

[6-2 42] {58-4[721-2-334 4]-56}

[6-2 x 6] {58-4[72-1-3x7 4]-5x6}

[6-12] {58-4[7-2-214]-30}

[-6] {58-4 x[-12]-30}

[-6] {58-4 x[-12]-30}

[-6] {58-4 x[-12]-30}

-6 x 31

25

In the above steps, each bracket and operation is simplified step-by-step according to the rules of the order of operations.

Conclusion

Solving complex mathematical expressions requires a systematic approach and a thorough understanding of the order of operations. By breaking down each part of the expression and simplifying it step-by-step, you can arrive at the correct solution. This approach ensures accuracy and helps in understanding the underlying principles better.