Evaluate $-5 - 3 \times (-9$\].

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Introduction

In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating expressions involves simplifying them to a single value. In this article, we will focus on evaluating the expression −5−3×(−9)-5 - 3 \times (-9), which involves the use of parentheses, multiplication, and subtraction.

Understanding the Order of Operations

When evaluating expressions, it is essential to follow the order of operations (PEMDAS):

  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.

Evaluating the Expression −5−3×(−9)-5 - 3 \times (-9)

To evaluate the expression −5−3×(−9)-5 - 3 \times (-9), we need to follow the order of operations:

  1. Evaluate the expression inside the parentheses: There are no expressions inside parentheses, so we can move on to the next step.
  2. Evaluate the multiplication operation: Multiply 3 and -9: 3×(−9)=−273 \times (-9) = -27
  3. Evaluate the subtraction operation: Subtract -27 from -5: −5−(−27)=−5+27=22-5 - (-27) = -5 + 27 = 22

Conclusion

In conclusion, the expression −5−3×(−9)-5 - 3 \times (-9) simplifies to 22. It is essential to follow the order of operations when evaluating expressions to ensure accurate results.

Common Mistakes to Avoid

When evaluating expressions, it is easy to make mistakes. Here are some common mistakes to avoid:

  • Not following the order of operations: Failing to follow the order of operations can lead to incorrect results.
  • Not evaluating expressions inside parentheses first: Failing to evaluate expressions inside parentheses first can lead to incorrect results.
  • Not multiplying and dividing from left to right: Failing to multiply and divide from left to right can lead to incorrect results.

Real-World Applications

Evaluating expressions is a fundamental concept in mathematics that has real-world applications in various fields, including:

  • Science: Evaluating expressions is essential in scientific calculations, such as calculating the trajectory of a projectile or the energy of a system.
  • Engineering: Evaluating expressions is essential in engineering calculations, such as designing bridges or calculating the stress on a material.
  • Finance: Evaluating expressions is essential in financial calculations, such as calculating interest rates or investment returns.

Practice Problems

To practice evaluating expressions, try the following problems:

  • 2+5×32 + 5 \times 3
  • −3−2×(−4)-3 - 2 \times (-4)
  • 6×2−36 \times 2 - 3

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that requires following the order of operations. By understanding the order of operations and practicing evaluating expressions, you can become proficient in simplifying complex expressions and solving real-world problems.

Additional Resources

For additional resources on evaluating expressions, try the following:

  • Math textbooks: Consult a math textbook for a comprehensive guide to evaluating expressions.
  • Online resources: Visit online resources, such as Khan Academy or Mathway, for interactive lessons and practice problems.
  • Math software: Use math software, such as Mathematica or Maple, to practice evaluating expressions and explore mathematical concepts.
    Evaluating Expressions: A Q&A Guide =====================================

Introduction

In our previous article, we discussed the importance of evaluating expressions in mathematics. In this article, we will provide a Q&A guide to help you understand and evaluate expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells you which operations to perform first when evaluating an expression. The order of operations is:

  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.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential to ensure that you evaluate expressions correctly. If you don't follow the order of operations, you may get incorrect results.

Q: How do I evaluate expressions with parentheses?

A: To evaluate expressions with parentheses, follow these steps:

  1. Evaluate any expressions inside the parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between multiplication and division?

A: Multiplication and division are both operations that involve numbers, but they have different rules. Multiplication involves multiplying two or more numbers together, while division involves dividing one number by another.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, follow these steps:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve numbers, but they have different rules. Addition involves adding two or more numbers together, while subtraction involves subtracting one number from another.

Q: How do I evaluate expressions with negative numbers?

A: To evaluate expressions with negative numbers, follow these steps:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a positive and negative number?

A: A positive number is a number that is greater than zero, while a negative number is a number that is less than zero.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, follow these steps:

  1. Evaluate any expressions inside parentheses first.
  2. Evaluate any exponential expressions next.
  3. Evaluate any multiplication and division operations from left to right.
  4. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between a fraction and a decimal?

A: A fraction is a number that is expressed as a ratio of two numbers, while a decimal is a number that is expressed as a point followed by digits.

Conclusion

In conclusion, evaluating expressions is a fundamental concept in mathematics that requires following the order of operations. By understanding the order of operations and practicing evaluating expressions, you can become proficient in simplifying complex expressions and solving real-world problems.

Additional Resources

For additional resources on evaluating expressions, try the following:

  • Math textbooks: Consult a math textbook for a comprehensive guide to evaluating expressions.
  • Online resources: Visit online resources, such as Khan Academy or Mathway, for interactive lessons and practice problems.
  • Math software: Use math software, such as Mathematica or Maple, to practice evaluating expressions and explore mathematical concepts.