Solving (1+1)(2+1) A Step-by-Step Arithmetic Guide
Navigating the realm of basic arithmetic, this article serves as a comprehensive guide to understanding and solving the mathematical expression (1+1)(2+1). We will meticulously dissect each step, ensuring clarity and providing valuable insights into the fundamental principles of arithmetic operations. Whether you're a student seeking to solidify your understanding or simply curious about the process, this guide offers a step-by-step approach to arriving at the correct answer.
Understanding the Basics: Order of Operations
Before diving into the specifics of our problem, it's crucial to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This set of rules dictates the sequence in which mathematical operations should be performed to ensure consistency and accuracy in calculations.
- Parentheses: Operations within parentheses are always performed first.
- Exponents: Next, we address exponents or powers.
- Multiplication and Division: These operations are performed from left to right.
- Addition and Subtraction: Finally, addition and subtraction are carried out from left to right.
In the context of our problem, (1+1)(2+1), we will first focus on the operations within the parentheses before proceeding with multiplication.
Step-by-Step Solution: Deciphering (1+1)(2+1)
Now, let's apply the order of operations to solve the expression (1+1)(2+1). We'll break it down into manageable steps:
Step 1: Solve the Parentheses
Our expression contains two sets of parentheses: (1+1) and (2+1). According to PEMDAS, we must address these first.
- (1+1) = 2
- (2+1) = 3
By performing the addition within each set of parentheses, we simplify the expression to 2 * 3.
Step 2: Multiplication
Having resolved the parentheses, we're left with a simple multiplication problem:
- 2 * 3 = 6
Therefore, the product of (1+1)(2+1) is 6. This straightforward calculation highlights the power of following the order of operations to arrive at the correct solution.
Addressing the Distractors: Why the Other Options are Incorrect
To solidify our understanding, let's examine why the other options provided are incorrect. This will reinforce the importance of accurate calculations and adherence to the order of operations.
- A. 3+21: This option appears to be a misinterpretation of the original expression. It might stem from mistakenly adding the numbers within the parentheses before multiplying, or from an incorrect multiplication process. The fundamental error lies in not following the correct order of operations.
- B. 3=1: This option is not mathematically valid. The equals sign (=) indicates that the values on both sides of the equation are equivalent. However, 3 is not equal to 1. This option suggests a misunderstanding of basic numerical relationships.
- C. 3+1: This option, like option A, represents an incorrect application of arithmetic operations. It's possible that this answer results from adding the results of the parentheses instead of multiplying them. This highlights the critical role of correctly interpreting mathematical symbols and operations.
- D. 1-31: This option is not only numerically incorrect but also illogical in the context of the original expression. The presence of subtraction where multiplication is required indicates a significant misunderstanding of the problem's structure.
- E. 1+31: Similar to options A and C, this option incorrectly combines addition with the results of the parentheses. It underscores the necessity of adhering to the correct order of operations to avoid such errors. The mistake is in adding numbers instead of multiplying.
By analyzing these incorrect options, we gain a deeper appreciation for the importance of precise calculations and the correct application of mathematical principles. Understanding why these options are wrong further clarifies the accuracy of our solution: 6.
Conclusion: Mastering Arithmetic Fundamentals
In conclusion, the product of (1+1)(2+1) is unequivocally 6. This solution is achieved by meticulously following the order of operations (PEMDAS), which guides us to first resolve the parentheses and then perform the multiplication. Through this step-by-step approach, we've not only arrived at the correct answer but also reinforced the fundamental principles of arithmetic.
Understanding the order of operations is not just about solving equations; it's about developing a logical and systematic approach to problem-solving. This skill extends far beyond mathematics, influencing how we approach challenges in various aspects of life.
By carefully dissecting each step and examining the common errors that can arise, we've gained a more profound understanding of the process. This knowledge empowers us to confidently tackle similar problems in the future.
The ability to solve basic arithmetic problems like this forms the bedrock of more advanced mathematical concepts. A solid grasp of these fundamentals is essential for success in algebra, calculus, and beyond. It's like building a house; a strong foundation is crucial for a stable structure.
Furthermore, the principles we've discussed here are not confined to the classroom. They have practical applications in everyday life, from managing finances to planning projects. The ability to accurately calculate and solve problems is a valuable asset in both personal and professional settings.
So, remember, the next time you encounter a mathematical expression, take a deep breath, recall the order of operations, and approach it methodically. With practice and a clear understanding of the fundamentals, you'll be well-equipped to conquer any arithmetic challenge that comes your way.
In summary, the correct answer to the question "What is the product (1+1)(2+1)?" is 6. This article has provided a comprehensive explanation of how to arrive at this solution, highlighting the importance of the order of operations and careful calculation.
