Patrick Tried To Evaluate The Expression $7 \times (8 - 3 \times 2$\]. His Work Is Below:Step 1: $= 7 \times (5 \times 2$\] Step 2: $= 7 \times 10$ Step 3: $= 70$In Which Step Did Patrick First Make A Mistake?Choose

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Introduction

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. In this article, we will explore a common mistake made by students when evaluating expressions and provide a step-by-step guide on how to evaluate expressions correctly.

The Problem

Patrick tried to evaluate the expression 7×(8−3×2)7 \times (8 - 3 \times 2). His work is below:

Step 1: =7×(5×2)= 7 \times (5 \times 2)

Step 2: =7×10= 7 \times 10

Step 3: =70= 70

Where Did Patrick Go Wrong?

Let's analyze Patrick's work and identify where he made a mistake.

Step 1: Incorrect Application of Order of Operations

In the first step, Patrick incorrectly applied the order of operations. He multiplied 5 and 2, which is not the correct order of operations. The correct order of operations is to evaluate the expression inside the parentheses first, which is 8−3×28 - 3 \times 2. Patrick should have evaluated this expression first before multiplying 7 by the result.

Step 2: Correct Application of Order of Operations

Let's re-evaluate the expression using the correct order of operations.

Step 1: Evaluate the expression inside the parentheses

8−3×2=8−6=28 - 3 \times 2 = 8 - 6 = 2

Step 2: Multiply 7 by the result

7×2=147 \times 2 = 14

Step 3: Correct Answer

The correct answer is 14, not 70.

Conclusion

Evaluating expressions requires careful attention to order of operations. Patrick's mistake was in the first step, where he incorrectly applied the order of operations. By following the correct order of operations, we can evaluate expressions accurately and avoid mistakes.

Tips for Evaluating Expressions

  1. Follow the order of operations: Evaluate expressions inside parentheses first, then exponents, multiplication and division, and finally addition and subtraction.
  2. Use parentheses to clarify: Use parentheses to clarify the order of operations and avoid confusion.
  3. Check your work: Double-check your work to ensure that you have evaluated the expression correctly.

By following these tips and practicing regularly, you can become proficient in evaluating expressions and solve mathematical problems with confidence.

Common Mistakes to Avoid

  1. Incorrect application of order of operations: Make sure to evaluate expressions inside parentheses first, then exponents, multiplication and division, and finally addition and subtraction.
  2. Not using parentheses: Use parentheses to clarify the order of operations and avoid confusion.
  3. Not checking work: Double-check your work to ensure that you have evaluated the expression correctly.

By avoiding these common mistakes, you can ensure that you are evaluating expressions accurately and avoiding mistakes.

Practice Problems

  1. Evaluate the expression 4×(6−2×3)4 \times (6 - 2 \times 3).
  2. Evaluate the expression 9×(8+2×3)9 \times (8 + 2 \times 3).
  3. Evaluate the expression 6×(4−2×2)6 \times (4 - 2 \times 2).

By practicing regularly, you can become proficient in evaluating expressions and solve mathematical problems with confidence.

Conclusion

Introduction

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. In this article, we will provide a Q&A section to help you better understand how to evaluate expressions and answer common questions.

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 any 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 important because it ensures that you evaluate expressions accurately and avoid mistakes. If you don't follow the order of operations, you may get different answers or even incorrect answers.

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 parentheses?

A: To evaluate expressions with parentheses, you need to follow the order of operations. First, evaluate any expressions inside the parentheses, then evaluate any exponential expressions, and finally evaluate any multiplication and division operations from left to right.

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

A: An expression is a mathematical statement that contains numbers, variables, and operations, but it does not have an equal sign (=). An equation, on the other hand, is a mathematical statement that contains an equal sign (=) and is used to solve for a variable.

Q: How do I evaluate expressions with variables?

A: To evaluate expressions with variables, you need to follow the order of operations and substitute the value of the variable into the expression.

Q: What is the difference between a variable and a constant?

A: A variable is a letter or symbol that represents a value that can change, while a constant is a value that does not change.

Q: How do I simplify expressions?

A: To simplify expressions, you need to follow the order of operations and combine like terms.

Q: What is the difference between like terms and unlike terms?

A: Like terms are terms that have the same variable and exponent, while unlike terms are terms that have different variables or exponents.

Q: How do I evaluate expressions with exponents?

A: To evaluate expressions with exponents, you need to follow the order of operations and evaluate the exponential expression first.

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

A: A positive exponent is an exponent that is greater than 0, while a negative exponent is an exponent that is less than 0.

Conclusion

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. By following the correct order of operations and avoiding common mistakes, you can evaluate expressions accurately and solve mathematical problems with confidence. Remember to practice regularly and use parentheses to clarify the order of operations. With practice and patience, you can become proficient in evaluating expressions and achieve success in mathematics.

Practice Problems

  1. Evaluate the expression 4×(6−2×3)4 \times (6 - 2 \times 3).
  2. Evaluate the expression 9×(8+2×3)9 \times (8 + 2 \times 3).
  3. Evaluate the expression 6×(4−2×2)6 \times (4 - 2 \times 2).

By practicing regularly, you can become proficient in evaluating expressions and solve mathematical problems with confidence.

Additional Resources

  • Math textbooks: Check out your math textbook for additional practice problems and examples.
  • Online resources: Visit online resources such as Khan Academy, Mathway, or Wolfram Alpha for additional practice problems and examples.
  • Math tutors: Consider hiring a math tutor to help you with difficult concepts and provide additional practice problems.

By using these resources and practicing regularly, you can become proficient in evaluating expressions and achieve success in mathematics.