Find The Value Of Each Expression:${ 20 + 5 \times 4 + 9 - 6 }$A. 19 B. 23 C. 4 D. 46 Please Select The Best Answer From The Choices Provided: A B C D

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Introduction

Mathematical expressions are a fundamental part of mathematics, and solving them is a crucial skill for students and professionals alike. In this article, we will focus on solving a specific type of mathematical expression, which involves the use of basic arithmetic operations such as addition, subtraction, multiplication, and division. We will use the expression 20+5×4+9−620 + 5 \times 4 + 9 - 6 as an example to demonstrate the step-by-step process of solving mathematical expressions.

Understanding the Order of Operations

Before we dive into solving the expression, it's essential to understand the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is often remembered using the acronym PEMDAS, which stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Solving the Expression

Now that we have a basic understanding of the order of operations, let's apply it to the expression 20+5×4+9−620 + 5 \times 4 + 9 - 6. To solve this expression, we need to follow the order of operations:

  1. Evaluate the multiplication operation: The expression contains a multiplication operation, which is 5×45 \times 4. Using the multiplication table, we can calculate the result of this operation, which is 2020.
  2. Evaluate the addition and subtraction operations: Now that we have the result of the multiplication operation, we can evaluate the addition and subtraction operations from left to right. The expression becomes 20+20+9−620 + 20 + 9 - 6.
  3. Perform the addition operations: Next, we need to perform the addition operations. The expression becomes 40+9−640 + 9 - 6.
  4. Perform the subtraction operations: Finally, we need to perform the subtraction operations. The expression becomes 49−649 - 6.
  5. Calculate the final result: The final result of the expression is 4343.

Conclusion

In this article, we have demonstrated the step-by-step process of solving a mathematical expression using the order of operations. We have used the expression 20+5×4+9−620 + 5 \times 4 + 9 - 6 as an example and applied the order of operations to arrive at the final result. By following the order of operations, we can ensure that mathematical expressions are evaluated correctly and consistently.

Answer

The final answer to the expression 20+5×4+9−620 + 5 \times 4 + 9 - 6 is 43.

Discussion

  • What is the order of operations, and why is it important in mathematics?
  • How do you evaluate expressions that contain multiple operations?
  • Can you think of a real-world scenario where the order of operations is crucial?

Additional Resources

  • Khan Academy: Order of Operations
  • Mathway: Order of Operations
  • Wolfram Alpha: Order of Operations

Final Thoughts

Solving mathematical expressions is a fundamental skill that requires practice and patience. By following the order of operations and applying the rules of arithmetic, we can ensure that mathematical expressions are evaluated correctly and consistently. Whether you're a student or a professional, mastering the art of solving mathematical expressions will serve you well in your future endeavors.

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Introduction

In our previous article, we explored the step-by-step process of solving mathematical expressions using the order of operations. However, we understand that sometimes, it's not enough to just read about a concept; you need to see it in action and have your questions answered. That's why we've put together this Q&A guide to help you better understand mathematical expressions and how to solve them.

Q&A

Q: What is the order of operations, and why is it important in mathematics?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed. It's essential in mathematics because it ensures that expressions are evaluated consistently and correctly. Without the order of operations, mathematical expressions could be evaluated differently depending on the person performing the calculation.

Q: How do you evaluate expressions that contain multiple operations?

A: To evaluate expressions that contain multiple operations, you need to follow the order of operations. This means that you should perform the operations inside parentheses first, followed by any exponential operations, then multiplication and division operations from left to right, and finally addition and subtraction operations from left to right.

Q: Can you think of a real-world scenario where the order of operations is crucial?

A: Yes, the order of operations is crucial in many real-world scenarios. For example, in finance, the order of operations can affect the calculation of interest rates and investments. In engineering, the order of operations can affect the calculation of stress and strain on materials. In science, the order of operations can affect the calculation of chemical reactions and equations.

Q: What is the difference between an expression and an equation?

A: An expression is a group of numbers, variables, and mathematical operations that are combined to form a single value. An equation, on the other hand, is a statement that says two expressions are equal. For example, the expression 2x + 3 is a group of numbers and variables combined with mathematical operations, while the equation 2x + 3 = 5 is a statement that says the expression 2x + 3 is equal to 5.

Q: How do you simplify complex expressions?

A: To simplify complex expressions, you need to follow the order of operations and combine like terms. This means that you should perform the operations inside parentheses first, followed by any exponential operations, then multiplication and division operations from left to right, and finally addition and subtraction operations from left to right. You should also combine like terms by adding or subtracting the coefficients of the same variables.

Q: Can you give an example of a complex expression and how to simplify it?

A: Yes, here's an example of a complex expression and how to simplify it:

Expression: 2(3x + 2) + 5x - 3

To simplify this expression, we need to follow the order of operations:

  1. Evaluate the expression inside the parentheses: 3x + 2
  2. Multiply the result by 2: 2(3x + 2) = 6x + 4
  3. Add 5x to the result: 6x + 4 + 5x = 11x + 4
  4. Subtract 3 from the result: 11x + 4 - 3 = 11x + 1

The simplified expression is 11x + 1.

Conclusion

In this Q&A guide, we've explored some of the most common questions and concerns about mathematical expressions and how to solve them. We've covered topics such as the order of operations, evaluating expressions with multiple operations, and simplifying complex expressions. By following the order of operations and combining like terms, you can simplify complex expressions and arrive at the correct solution.

Additional Resources

  • Khan Academy: Order of Operations
  • Mathway: Order of Operations
  • Wolfram Alpha: Order of Operations

Final Thoughts

Solving mathematical expressions is a fundamental skill that requires practice and patience. By following the order of operations and applying the rules of arithmetic, you can ensure that mathematical expressions are evaluated correctly and consistently. Whether you're a student or a professional, mastering the art of solving mathematical expressions will serve you well in your future endeavors.