Use parentheses to group numbers

Oct 13, 2025 by recoveryshake.com 94 views

Understanding the Basics of Parentheses and Exponents

When it comes to evaluating mathematical expressions, understanding the order of operations is crucial. The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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

Evaluating 4(8-12)

To evaluate the expression 4(8-12), we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses.

Subtracting 12 from 8

When we subtract 12 from 8, we get -4.

Multiplying 4 by -4

Now that we have the result of the expression inside the parentheses, we can multiply 4 by -4. Multiplying a positive number by a negative number results in a negative number.

4 × -4 = -16

Therefore, the value of 4(8-12) is -16.

Evaluating 4(5-8)

To evaluate the expression 4(5-8), we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses.

Subtracting 8 from 5

When we subtract 8 from 5, we get -3.

Multiplying 4 by -3

Now that we have the result of the expression inside the parentheses, we can multiply 4 by -3. Multiplying a positive number by a negative number results in a negative number.

4 × -3 = -12

Therefore, the value of 4(5-8) is -12.

Conclusion

In conclusion, evaluating expressions with parentheses and exponents requires a clear understanding of the order of operations. By following the rules of PEMDAS, we can ensure that mathematical expressions are evaluated correctly. In this article, we evaluated two expressions: 4(8-12) and 4(5-8). By following the order of operations, we found that the value of 4(8-12) is -16 and the value of 4(5-8) is -12.

Real-World Applications

Understanding how to evaluate expressions with parentheses and exponents is crucial in many real-world applications, such as:

Science and Engineering: In scientific and engineering applications, mathematical expressions are used to model real-world phenomena. Understanding how to evaluate expressions with parentheses and exponents is essential in these fields.
Finance: In finance, mathematical expressions are used to calculate interest rates, investment returns, and other financial metrics. Understanding how to evaluate expressions with parentheses and exponents is crucial in these applications.
Computer Programming: In computer programming, mathematical expressions are used to perform calculations and make decisions. Understanding how to evaluate expressions with parentheses and exponents is essential in programming.

Tips and Tricks

Here are some tips and tricks to help you evaluate expressions with parentheses and exponents:

Use parentheses to group numbers: When evaluating expressions with parentheses, use parentheses to group numbers together. This will help you avoid confusion and ensure that the expression is evaluated correctly.
Follow the order of operations: When evaluating expressions with parentheses and exponents, always follow the order of operations. This will ensure that the expression is evaluated correctly.
Use a calculator: If you are unsure about how to evaluate an expression with parentheses and exponents, use a calculator to check your work.

Common Mistakes

Here are some common mistakes to avoid when evaluating expressions with parentheses and exponents:

Not following the order of operations: Failing to follow the order of operations can result in incorrect answers.
Not using parentheses to group numbers: Failing to use parentheses to group numbers together can result in confusion and incorrect answers.
Not checking your work: Failing to check your work can result in incorrect answers.

Conclusion

Understanding the Basics of Parentheses and Exponents

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

Q&A: Evaluating 4(8-12)

Q: What is the value of 4(8-12)?

A: To evaluate the expression 4(8-12), we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses. When we subtract 12 from 8, we get -4. Then, we multiply 4 by -4. Multiplying a positive number by a negative number results in a negative number. Therefore, the value of 4(8-12) is -16.

Q: Why do we need to follow the order of operations?

A: Following the order of operations ensures that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may get incorrect answers.

Q: What happens if we don't use parentheses to group numbers?

A: If we don't use parentheses to group numbers, we may get confused and evaluate the expression incorrectly. For example, if we don't use parentheses to group numbers in the expression 4(8-12), we may evaluate it as 4 × 8 - 12, which is incorrect.

Q&A: Evaluating 4(5-8)

Q: What is the value of 4(5-8)?

A: To evaluate the expression 4(5-8), we need to follow the order of operations. The first step is to evaluate the expression inside the parentheses. When we subtract 8 from 5, we get -3. Then, we multiply 4 by -3. Multiplying a positive number by a negative number results in a negative number. Therefore, the value of 4(5-8) is -12.

Q: Why do we need to follow the order of operations?

A: Following the order of operations ensures that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may get incorrect answers.

Q: What happens if we don't use parentheses to group numbers?

A: If we don't use parentheses to group numbers, we may get confused and evaluate the expression incorrectly. For example, if we don't use parentheses to group numbers in the expression 4(5-8), we may evaluate it as 4 × 5 - 8, which is incorrect.

Common Q&A

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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

Q: Why do we need to follow the order of operations?

A: Following the order of operations ensures that mathematical expressions are evaluated correctly. If we don't follow the order of operations, we may get incorrect answers.