Solve The Following Mathematical Expressions: (i) NB 18-33 X 11 45, (ii) -105 18 X 72 15, (iii) -7 -1 X 17 10, (iv) 13 120 X 100 16.

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Navigating the Realm of Mathematical Expressions

In this comprehensive exploration, we embark on a journey to dissect and decipher a series of mathematical expressions. These expressions, presented as NB 18-33 X 11 45, -105 18 X 72 15, -7 -1 X 17 10, and 13 120 X 100 16, represent a diverse range of arithmetic operations that demand careful attention to detail and a systematic approach to problem-solving. Our primary objective is to unravel the intricacies of each expression, step by step, while adhering to the fundamental principles of mathematics. By meticulously analyzing the components and applying the correct order of operations, we aim to arrive at accurate and meaningful solutions. This journey through these mathematical expressions will not only enhance our understanding of numerical computations but also reinforce the importance of precision and clarity in mathematical endeavors. Let's begin this exploration with a clear focus on the first expression, ensuring we lay a solid foundation for tackling the challenges ahead.

Deciphering the First Expression: NB 18-33 X 11 45

Our initial focus is on the expression NB 18-33 X 11 45. At first glance, this expression appears to contain a typographical error, specifically the "NB" prefix. In mathematical expressions, each symbol and number serves a specific purpose, and an unidentifiable element like "NB" can introduce ambiguity and hinder our ability to solve the problem correctly. Therefore, we must first address this ambiguity. A reasonable assumption is that "NB" might be a misplaced or misinterpreted symbol. Without further context, it is challenging to definitively determine the original intent. However, for the sake of proceeding with the calculation, we will assume that "NB" is an extraneous element and can be disregarded. This assumption allows us to focus on the numerical components and the mathematical operations involved. With this assumption in place, the expression transforms into a more familiar arithmetic structure: 18 - 33 X 11 45. Now, we can proceed to apply the order of operations, a fundamental principle in mathematics that dictates the sequence in which operations should be performed. The order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), provides a clear roadmap for simplifying complex expressions. In this case, multiplication takes precedence over subtraction. Therefore, our next step is to perform the multiplication operation: 33 multiplied by 11. This calculation sets the stage for the subsequent subtraction, bringing us closer to the final solution of the expression. As we delve deeper into the calculations, we remain mindful of the importance of each step and the logical progression that leads us to the ultimate answer.

Step-by-Step Breakdown of 18 - 33 X 11 45

To effectively solve the expression 18 - 33 X 11 45, we must adhere to the order of operations, which prioritizes multiplication before subtraction. This principle is crucial in ensuring that we arrive at the correct answer. Ignoring this order would lead to a different result, highlighting the significance of following mathematical conventions. Let's break down the steps involved:

  1. Multiplication First: We begin by multiplying 33 by 11. This is a straightforward multiplication operation that can be performed using basic arithmetic principles. The result of 33 multiplied by 11 is 363. This intermediate result is a key component in the overall calculation.
  2. Substituting the Result: Now that we have the result of the multiplication, we substitute it back into the original expression. This transforms the expression from 18 - 33 X 11 45 to 18 - 363 45. This substitution allows us to simplify the expression further and move towards the final subtraction step.
  3. Subtraction Operation: Next, we perform the subtraction operation. We subtract 363 from 18. This subtraction involves dealing with a larger number being subtracted from a smaller number, which will result in a negative value. The result of 18 minus 363 is -345. This negative value is an important aspect of the solution.
  4. Final Subtraction: Finally, we subtract 45 from -345. This last subtraction operation combines two negative numbers, resulting in a more negative value. The final result of -345 minus 45 is -390. This is the ultimate solution to the expression 18 - 33 X 11 45, taking into account the assumption that "NB" was an extraneous element.

Therefore, based on our assumption and the correct application of the order of operations, the solution to the expression NB 18-33 X 11 45 is -390. This step-by-step breakdown illustrates the importance of methodical calculation and adherence to mathematical rules in arriving at accurate solutions. Each step, from multiplication to substitution and finally subtraction, plays a crucial role in the overall process.

Unraveling the Second Expression: -105 18 X 72 15

The second expression, -105 18 X 72 15, presents a different set of challenges. Similar to the first expression, this one also requires careful interpretation due to the absence of explicit operators between the numbers. In mathematical expressions, the absence of an operator typically implies multiplication. However, to ensure accuracy, we must proceed cautiously and consider the context. If we assume that the missing operators are indeed multiplication signs, the expression can be rewritten as -105 * 18 * 72 * 15. This interpretation provides a clear path forward, allowing us to apply the principles of multiplication to arrive at a solution. The order in which we perform the multiplications does not affect the final result due to the associative property of multiplication, which states that the grouping of factors does not change the product. However, for clarity and consistency, we can proceed from left to right. This systematic approach will help us avoid errors and ensure that we accurately calculate the final value. As we embark on this calculation, we recognize the importance of each multiplication step and the cumulative effect they have on the overall result.

Step-by-Step Solution for -105 * 18 * 72 * 15

To effectively solve the expression -105 * 18 * 72 * 15, we will perform the multiplication operations sequentially, adhering to the associative property of multiplication. This property ensures that the order in which we group the factors does not alter the final product. Let's break down the steps:

  1. First Multiplication: We begin by multiplying -105 by 18. This involves multiplying a negative number by a positive number, which will result in a negative product. The result of -105 multiplied by 18 is -1890. This intermediate result sets the stage for the subsequent multiplications.
  2. Second Multiplication: Next, we multiply the result from the previous step, -1890, by 72. Again, we are multiplying a negative number by a positive number, so the product will be negative. The result of -1890 multiplied by 72 is -136080. This larger negative value represents the cumulative effect of the multiplications performed so far.
  3. Third Multiplication: Finally, we multiply the result from the second multiplication, -136080, by 15. This is the final multiplication step, and it will yield the ultimate solution to the expression. The result of -136080 multiplied by 15 is -2041200. This large negative number is the final answer to the expression -105 * 18 * 72 * 15.

Therefore, based on our assumption that the missing operators are multiplication signs and the correct application of the multiplication operations, the solution to the expression -105 18 X 72 15 is -2041200. This step-by-step breakdown underscores the importance of methodical calculation and the cumulative effect of each multiplication step in arriving at the final solution. The use of the associative property allows us to perform the multiplications in a sequential manner, ensuring accuracy and clarity.

Deconstructing the Third Expression: -7 -1 X 17 10

Moving on to the third expression, -7 -1 X 17 10, we encounter a familiar challenge – the absence of explicit operators between the numbers. This ambiguity necessitates careful interpretation and a thoughtful approach. As with the previous expression, we will assume that the missing operator is a multiplication sign, allowing us to rewrite the expression as -7 -1 * 17 10. However, before we proceed with the calculations, it is crucial to address the potential for misinterpretation. The expression contains both subtraction and implied multiplication, requiring us to adhere strictly to the order of operations (PEMDAS). This order dictates that multiplication must be performed before subtraction. Failing to follow this rule would lead to an incorrect result. Therefore, our first step is to perform the multiplication operation, which involves multiplying -1 by 17. This intermediate result will then be used in the subsequent subtraction operations. As we delve into the calculations, we remain mindful of the importance of each step and the logical progression that leads us to the final answer.

Step-by-Step Solution for -7 -1 X 17 10

To accurately solve the expression -7 -1 X 17 10, we must meticulously follow the order of operations, prioritizing multiplication before subtraction. This principle is fundamental to achieving the correct result. Let's break down the steps involved:

  1. Multiplication First: We begin by performing the multiplication operation: -1 multiplied by 17. The product of a negative number and a positive number is a negative number. Therefore, -1 multiplied by 17 equals -17. This intermediate result is crucial for the subsequent subtraction steps.
  2. Substituting the Result: Now that we have the result of the multiplication, we substitute it back into the original expression. This transforms the expression from -7 -1 X 17 10 to -7 - (-17) 10. It is important to note the double negative, which will play a significant role in the next step.
  3. First Subtraction: Next, we perform the first subtraction operation: -7 minus -17. Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -7 minus -17 is the same as -7 plus 17, which equals 10. This intermediate result simplifies the expression further.
  4. Final Subtraction: Finally, we perform the last subtraction operation: 10 minus 10. This is a straightforward subtraction that yields a result of 0. This is the ultimate solution to the expression -7 -1 X 17 10, taking into account the order of operations and the correct handling of negative numbers.

Therefore, the solution to the expression -7 -1 X 17 10 is 0. This step-by-step breakdown highlights the importance of adhering to the order of operations and carefully managing negative numbers in mathematical calculations. Each step, from multiplication to substitution and finally subtraction, plays a critical role in arriving at the accurate solution.

Deciphering the Fourth Expression: 13 120 X 100 16

Our final challenge lies in the expression 13 120 X 100 16. This expression, similar to the previous ones, requires careful interpretation due to the absence of explicit operators between the numbers. To proceed, we will make the assumption that the missing operators represent multiplication, allowing us to rewrite the expression as 13 * 120 * 100 * 16. This interpretation provides a clear pathway for applying the principles of multiplication to arrive at a solution. The associative property of multiplication, which we encountered earlier, comes into play once again. This property assures us that the order in which we perform the multiplications will not affect the final result. However, for the sake of clarity and consistency, we will adopt a systematic approach, performing the multiplications from left to right. This methodical approach minimizes the risk of errors and ensures that we accurately calculate the final value. As we embark on this final calculation, we acknowledge the importance of each multiplication step and the cumulative impact they have on the overall result. Let's begin the step-by-step breakdown to unravel the final answer.

Step-by-Step Solution for 13 * 120 * 100 * 16

To effectively solve the expression 13 * 120 * 100 * 16, we will perform the multiplication operations sequentially, adhering to the associative property of multiplication. This property ensures that the order in which we group the factors does not alter the final product. Let's break down the steps:

  1. First Multiplication: We begin by multiplying 13 by 120. This is a straightforward multiplication operation that can be performed using basic arithmetic principles. The result of 13 multiplied by 120 is 1560. This intermediate result sets the stage for the subsequent multiplications.
  2. Second Multiplication: Next, we multiply the result from the previous step, 1560, by 100. Multiplying by 100 is equivalent to adding two zeros to the end of the number. Therefore, 1560 multiplied by 100 equals 156000. This larger value represents the cumulative effect of the multiplications performed so far.
  3. Third Multiplication: Finally, we multiply the result from the second multiplication, 156000, by 16. This is the final multiplication step, and it will yield the ultimate solution to the expression. The result of 156000 multiplied by 16 is 2496000. This large number is the final answer to the expression 13 * 120 * 100 * 16.

Therefore, based on our assumption that the missing operators are multiplication signs and the correct application of the multiplication operations, the solution to the expression 13 120 X 100 16 is 2496000. This step-by-step breakdown underscores the importance of methodical calculation and the cumulative effect of each multiplication step in arriving at the final solution. The use of the associative property allows us to perform the multiplications in a sequential manner, ensuring accuracy and clarity.

Conclusion: Mastering the Art of Mathematical Expressions

In this comprehensive exploration, we have successfully navigated the complexities of four distinct mathematical expressions: NB 18-33 X 11 45, -105 18 X 72 15, -7 -1 X 17 10, and 13 120 X 100 16. Each expression presented its unique challenges, requiring careful interpretation, adherence to the order of operations, and a systematic approach to problem-solving. We meticulously dissected each expression, step by step, making necessary assumptions where ambiguities existed and rigorously applying mathematical principles to arrive at accurate solutions. Through this journey, we have not only enhanced our understanding of numerical computations but also reinforced the importance of precision, clarity, and methodical thinking in mathematical endeavors. The assumption that missing operators represent multiplication played a crucial role in our ability to solve these expressions, highlighting the significance of context and logical reasoning in mathematical problem-solving. Furthermore, the consistent application of the order of operations (PEMDAS) ensured that we performed calculations in the correct sequence, leading us to the accurate final answers. The step-by-step breakdowns provided a clear and transparent pathway for each solution, illustrating the importance of each individual operation and its contribution to the overall result. As we conclude this exploration, we recognize that mastering mathematical expressions is not merely about arriving at the correct answer; it is about developing a deep understanding of the underlying principles and cultivating the ability to approach complex problems with confidence and precision. The skills and insights gained through this exercise will undoubtedly serve us well in future mathematical challenges.