Solving the Mathematical Expression 212 × 4 – 1/6 – 3/2 – 1

Introduction

The mathematical expression 212 × 4 – 1/6 – 3/2 – 1 presents a unique challenge that requires a careful application of the order of operations. This article delves into the step-by-step process of solving this problem and explores the importance of adhering to the order of operations in ensuring accurate results.

Understanding the Expression

The given expression is:

Z 212 × 4 – 1/6 – 3/2 – 1

The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), is crucial in solving this problem. Let's break it down step-by-step.

Step-by-Step Solution

Multiplication: Subtracting fractions and integers: Evaluating the expression:

Multiplication

First, we handle the multiplication:

Z 212 × 4 – 1/6 – 3/2 – 1

Solving 212 × 4:

Z 848 – 1/6 – 3/2 – 1

Subtracting Fractions and Integers

Next, we need to subtract the fractions and integers. To do this, we find a common denominator and combine the terms:

Z 848 – (1/6 3/2 – 1)

Z 848 – (1/6 9/6 – 1)

Z 848 – (10/6 – 1)

Z 848 – (10/6 – 6/6)

Z 848 – (4/6)

Z 848 – (2/3)

Now, we convert 848 to a fraction with a denominator of 3 to facilitate the subtraction:

Z 2544/3 – 2/3

Combining these terms:

Z (2544 – 2)/3

Z 2542/3

Finally, converting 2542/3 to a mixed number:

Z 847 1/3

Evaluating the Expression

Let's re-evaluate the initial expression using a more straightforward approach:

Z 212 × 4 – 1/6 – 3/2 – 1

Z 848 – 1/6 – 3/2 – 1

Z 848 – (1/6 3/2 – 1)

Z 848 – (1/6 9/6 – 1)

Z 848 – (10/6 – 1)

Z 848 – (4/6)

Z 848 – (2/3)

Z 847 1/3

Conclusion

By following the order of operations and carefully managing the fractions, we arrive at the solution:

Z 847 1/3

Using a calculator or manual calculation, the exact result is:

Z 847.333333333

Additional Insights and Considerations

Understanding the solution to this mathematical expression is not just an exercise in arithmetic. It also highlights the importance of clear notation and the order of operations. In complex mathematical expressions, adhering to these rules ensures accurate and consistent results. This principle is crucial in various fields, including engineering, physics, and technology, where precise calculations are essential.

Related Keywords and SEO Optimizations

Mathematical expression Order of operations (PEMDAS) Google SEO

Final Thoughts

By mastering the order of operations and understanding how to handle fractions and integers, you can solve a wide range of mathematical problems. Whether you're working on a complex calculation or a simpler expression like this, adhering to the correct steps will lead you to the right answer.