Correct Evaluation of the Expression Inside the Parentheses

Oct 13, 2025 by miodeya.com 82 views

Introduction

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. In this article, we will explore an example where Carly attempts to evaluate an expression, but makes a mistake along the way. We will identify the step where Carly first made a mistake and provide a clear explanation of the correct solution.

The Expression

The expression that Carly is trying to evaluate is $24 \div (4 \times 2 - 5)$ . This expression involves multiple operations, including division, multiplication, and subtraction. To evaluate this expression, we need to follow the order of operations, which is a set of rules that dictate the order in which we perform mathematical operations.

Step 1: Evaluating the Expression

Carly's first step is to evaluate the expression inside the parentheses: $4 \times 3$ . However, this is not the correct expression to evaluate. The correct expression to evaluate is $4 \times 2 - 5$ . Let's evaluate this expression correctly.

Correct Evaluation of the Expression Inside the Parentheses

To evaluate the expression $4 \times 2 - 5$ , we need to follow the order of operations. First, we multiply 4 and 2, which gives us 8. Then, we subtract 5 from 8, which gives us 3.

Correct Evaluation of the Original Expression

Now that we have evaluated the expression inside the parentheses, we can evaluate the original expression. The original expression is $24 \div (4 \times 2 - 5)$ . We have already evaluated the expression inside the parentheses, which is equal to 3. Therefore, the original expression becomes $24 \div 3$ .

Step 2: Evaluating the Expression

Carly's second step is to evaluate the expression $24 \div 12$ . However, this is not the correct expression to evaluate. The correct expression to evaluate is $24 \div 3$ .

Correct Evaluation of the Expression

To evaluate the expression $24 \div 3$ , we simply divide 24 by 3, which gives us 8.

Step 3: Evaluating the Expression

Carly's third step is to evaluate the expression $= 2$ . However, this is not the correct expression to evaluate. The correct expression to evaluate is $24 \div 3$ , which we have already evaluated to be 8.

Conclusion

In conclusion, Carly made a mistake in Step 1, where she evaluated the expression $4 \times 3$ instead of the correct expression $4 \times 2 - 5$ . This mistake led to a series of incorrect evaluations in subsequent steps. The correct evaluation of the expression is $24 \div (4 \times 2 - 5) = 24 \div 3 = 8$ .

Key Takeaways

To evaluate an expression, we need to follow the order of operations.
We need to evaluate expressions inside parentheses first.
We need to evaluate multiplication and division operations from left to right.
We need to evaluate addition and subtraction operations from left to right.

Common Mistakes

Evaluating expressions inside parentheses incorrectly.
Failing to follow the order of operations.
Evaluating multiplication and division operations incorrectly.
Evaluating addition and subtraction operations incorrectly.

Tips for Evaluating Expressions

Read the expression carefully and identify the order of operations.
Evaluate expressions inside parentheses first.
Evaluate multiplication and division operations from left to right.
Evaluate addition and subtraction operations from left to right.
Check your work carefully to ensure that you have evaluated the expression correctly.

Practice Problems

Evaluate the expression $12 \div (3 \times 2 - 1)$ .
Evaluate the expression $18 \div (2 \times 3 + 1)$ .
Evaluate the expression $24 \div (4 \times 2 + 3)$ .

Conclusion

Introduction

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. In our previous article, we explored an example where Carly attempted to evaluate an expression, but made a mistake along the way. We identified the step where Carly first made a mistake and provided a clear explanation of the correct solution. In this article, we will provide a Q&A section to help readers better understand the concept of evaluating expressions.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which we perform mathematical operations. The order of operations is:

Parentheses: Evaluate expressions inside parentheses first.
Exponents: Evaluate any exponential expressions next.
Multiplication and Division: Evaluate multiplication and division operations from left to right.
Addition and Subtraction: Evaluate 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 crucial to ensure that we arrive at the correct solution. If we do not follow the order of operations, we may arrive at an incorrect solution.

Q: What happens if I forget to evaluate expressions inside parentheses first?

A: If you forget to evaluate expressions inside parentheses first, you may arrive at an incorrect solution. For example, consider the expression $3 \times (2 + 4)$ . If you forget to evaluate the expression inside the parentheses first, you may evaluate the expression as $3 \times 2 + 4$ , which is incorrect.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. 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 meanings. Multiplication involves adding a number a certain number of times, while division involves finding the quotient of two numbers.

Q: How do I evaluate expressions with fractions?

A: To evaluate expressions with fractions, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. 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 way of expressing a part of a whole, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I convert a fraction to a decimal?

A: To convert a fraction to a decimal, you need to divide the numerator by the denominator.

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

A: A percentage is a way of expressing a number as a part of 100, while a decimal is a way of expressing a number as a sum of powers of 10.

Q: How do I convert a percentage to a decimal?

A: To convert a percentage to a decimal, you need to divide the percentage by 100.

Conclusion

Evaluating expressions is a critical skill in mathematics that requires careful attention to order of operations. By following the order of operations and evaluating expressions correctly, we can ensure that we arrive at the correct solution. In this article, we provided a Q&A section to help readers better understand the concept of evaluating expressions. We hope that this article has been helpful in clarifying any questions or doubts that readers may have had.

Practice Problems

Evaluate the expression $12 \div (3 \times 2 - 1)$ .
Evaluate the expression $18 \div (2 \times 3 + 1)$ .
Evaluate the expression $24 \div (4 \times 2 + 3)$ .

Additional Resources

Khan Academy: Evaluating Expressions
Mathway: Evaluating Expressions
IXL: Evaluating Expressions

Conclusion

Evaluating expressions is a fundamental concept in mathematics that requires careful attention to order of operations. By following the order of operations and evaluating expressions correctly, we can ensure that we arrive at the correct solution. We hope that this article has been helpful in clarifying any questions or doubts that readers may have had.