Simplifying Expressions Using Order Of Operations PEMDAS BODMAS

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In the realm of mathematics, precision and order are paramount. When faced with complex expressions involving multiple operations, understanding and applying the order of operations is crucial for arriving at the correct solution. Often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), this set of rules provides a standardized approach to simplifying mathematical expressions. In this comprehensive guide, we will delve into the intricacies of the order of operations, illustrating its application with a specific example: (2-1)+3^2 ÷ 3. By meticulously dissecting each step, we will not only arrive at the correct answer but also gain a deeper understanding of the underlying principles that govern mathematical computations. This exploration will empower you to confidently tackle a wide range of mathematical problems, ensuring accuracy and efficiency in your calculations. Whether you're a student grappling with algebra or simply someone seeking to refresh your mathematical skills, this guide will serve as a valuable resource in your journey towards mathematical proficiency.

Before we dive into the specifics of our example, let's solidify our understanding of the fundamental principles that govern the order of operations. The acronym PEMDAS (or BODMAS) serves as a mnemonic device to help us remember the correct sequence in which operations should be performed. Each letter represents a specific type of operation, and the order in which they appear dictates the priority in which they should be executed. Let's break down each component of PEMDAS/BODMAS:

  • Parentheses (or Brackets): The first step in simplifying any mathematical expression is to address the operations enclosed within parentheses (or brackets). This means performing any calculations within the parentheses before moving on to other operations. Parentheses act as grouping symbols, indicating that the enclosed expressions should be treated as a single entity.
  • Exponents (or Orders): Next, we tackle exponents (or orders), which represent repeated multiplication. Exponents indicate the number of times a base number is multiplied by itself. For instance, in the expression 3^2, the exponent 2 indicates that the base 3 should be multiplied by itself twice (3 * 3 = 9). Exponents take precedence over multiplication, division, addition, and subtraction.
  • Multiplication and Division: Multiplication and division hold equal precedence and are performed from left to right. This means that if both operations appear in an expression, we evaluate them in the order they occur, moving from left to right. For example, in the expression 12 ÷ 3 * 2, we would first perform the division (12 ÷ 3 = 4) and then the multiplication (4 * 2 = 8).
  • Addition and Subtraction: Similar to multiplication and division, addition and subtraction also share equal precedence and are performed from left to right. If both operations are present, we evaluate them in the order they appear, progressing from left to right. For instance, in the expression 5 + 3 - 2, we would first perform the addition (5 + 3 = 8) and then the subtraction (8 - 2 = 6).

By adhering to the order of operations, we ensure consistency and accuracy in our mathematical calculations. This standardized approach eliminates ambiguity and guarantees that everyone arrives at the same correct answer when simplifying expressions. Now that we have a solid grasp of PEMDAS/BODMAS, let's apply these principles to our specific example.

Now, let's apply the rules of order of operations to simplify the expression (2-1)+3^2 ÷ 3. We will meticulously walk through each step, explaining the reasoning behind each operation and highlighting the importance of adhering to PEMDAS/BODMAS. By breaking down the problem into manageable steps, we can gain a clear understanding of the simplification process and avoid potential errors.

Step 1: Parentheses

According to PEMDAS/BODMAS, the first operation we should address is the one enclosed within parentheses. In our expression, we have (2-1). Performing this subtraction, we get:

(2-1) = 1

Now, our expression becomes:

1 + 3^2 ÷ 3

Step 2: Exponents

Next, we move on to exponents. In our simplified expression, we have 3^2, which represents 3 raised to the power of 2. This means we need to multiply 3 by itself:

3^2 = 3 * 3 = 9

Substituting this result back into our expression, we get:

1 + 9 ÷ 3

Step 3: Division

Now, we encounter division. We have 9 ÷ 3, which yields:

9 ÷ 3 = 3

Our expression is now further simplified to:

1 + 3

Step 4: Addition

Finally, we perform the addition:

1 + 3 = 4

Therefore, the simplified value of the expression (2-1)+3^2 ÷ 3 is 4.

In this comprehensive guide, we have meticulously explored the application of the order of operations (PEMDAS/BODMAS) to simplify the mathematical expression (2-1)+3^2 ÷ 3. By systematically addressing each operation in the correct sequence, we have arrived at the solution: 4. The process began with simplifying the expression within parentheses, followed by evaluating the exponent, performing the division, and finally, carrying out the addition. Each step was carefully explained to reinforce the importance of adhering to the established rules of order of operations. Mastering these rules is essential for success in mathematics, as it ensures consistency and accuracy in calculations. By consistently applying PEMDAS/BODMAS, you can confidently tackle complex mathematical expressions and arrive at the correct solutions. This understanding not only enhances your problem-solving skills but also provides a solid foundation for more advanced mathematical concepts. Remember, practice is key to mastering any mathematical skill, so continue to apply these principles to various problems to solidify your understanding and build your confidence. The ability to accurately simplify expressions using the order of operations is a fundamental skill that will serve you well in your mathematical journey.

Final Answer: D) 4