Solving Mathematical Expressions Using PEMDAS/BODMAS: A Case Study

Mathematics often involves complex expressions that can be simplified using specific rules. One important rule is the order of operations, abbreviated as PEMDAS in the United States and BODMAS in the UK. This rule ensures that mathematical problems are solved consistently and correctly. In this article, we will apply PEMDAS/BODMAS to solve a specific mathematical expression and understand each step of the process.

Understanding PEMDAS/BODMAS

PEMDAS and BODMAS are mnemonics used to remember the order of operations in mathematics. Both acronyms stand for the same principles, though the terms used may differ slightly based on regional education systems.

P/Brackets: Parentheses/Brackets (do all calculations inside parentheses first) E/Orders: Exponents/Orders (evaluate all exponents, roots, etc.) Multiplication and Division: Perform multiplication and division from left to right A/Authentication: Addition and Subtraction (solve addition and subtraction from left to right)

A Specific Mathematical Expression

Consider the mathematical expression: 7 - 6 - 8 - 99 - 768

Step-by-Step Solution

Let's walk through the problem using PEMDAS/BODMAS:

7 - 6: First, we subtract 6 from 7.

Result: 1

1 - 8: Next, we subtract 8 from 1.

Result: -7

-7 - 99: Then, we subtract 99 from -7.

Result: -106

-106 - 768: Finally, we subtract 768 from -106.

Result: -874

Therefore, the final answer is -874.

Revisiting the Given Expression

The expression you provided is: 7 - 6 - 8 - 9 9 - 7 6 8

Separate the spaces to make it 7 - 6 - 8 - 99 - 768

Applying the same steps as before:

7 - 6: 1 1 - 8: -7 -7 - 99: -106 -106 - 768: -874

As before, the final answer is -874.

Conclusion

Solving mathematical expressions correctly is crucial for various applications, from academic assessments to real-world problem-solving scenarios. Understanding and applying the order of operations, as demonstrated by PEMDAS/BODMAS, ensures that such expressions are evaluated accurately and efficiently.

Additional Resources

For further learning and practice, you can explore the following resources:

Practice Problems: Online platforms such as Khan Academy, Coursera, and Udemy offer numerous practice problems and tutorials on mathematical expressions and order of operations. Interactive Tools: Websites like WolframAlpha provide interactive tools to practice and verify your solutions. Educational Videos: YouTube channels such as Math Antics, PatrickJMT, and Numberphile offer detailed explanations and walkthroughs of complex mathematical problems.

Summary

PEMDAS and BODMAS are essential tools in solving mathematical expressions. By following the correct sequence of operations, we can ensure accurate and consistent results. Through practice and additional resources, you can enhance your mathematical problem-solving skills.

Related Keywords

PEMDAS, BODMAS, Mathematical Expressions

Keywords

PEMDAS, BODMAS, Order of Operations, Mathematical Problem-Solving, Academic Assessments, Real-World Problem-Solving