Adding the Negative Number

Oct 13, 2025 by wbrum.org 73 views

Understanding the Problem

When solving the expression 5^2 + (-3), we need to follow the order of operations, which is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

In this expression, we have an exponent (5^2) and a subtraction operation. We need to follow the order of operations to evaluate the expression correctly.

Evaluating the Exponent

The first step is to evaluate the exponent 5^2. This means that we need to raise 5 to the power of 2. To do this, we multiply 5 by itself: 5 * 5 = 25.

Adding the Negative Number

Now that we have evaluated the exponent, we can add the negative number -3 to the result. When we add a negative number, we need to change the sign of the number we are adding to. So, -3 becomes +3.

Performing the Addition

Now we can perform the addition: 25 + 3 = 28.

Conclusion

Therefore, the final result of the expression 5^2 + (-3) is 28.

Why is Following the Order of Operations Important?

Following the order of operations is important because it helps us to evaluate expressions correctly and avoid errors. If we don't follow the order of operations, we may get the wrong answer. For example, if we were to evaluate the expression 5^2 + (-3) without following the order of operations, we might get the wrong answer.

Real-World Applications of the Order of Operations

The order of operations is used in many real-world applications, such as:

Science and Engineering: The order of operations is used to evaluate complex mathematical expressions that are used to model real-world phenomena.
Computer Programming: The order of operations is used in programming languages to evaluate expressions and perform calculations.
Finance: The order of operations is used to evaluate financial expressions and perform calculations.

Tips for Solving Expressions

Here are some tips for solving expressions:

Read the expression carefully: Before you start solving the expression, read it carefully to make sure you understand what it says.
Follow the order of operations: Make sure to follow the order of operations to evaluate the expression correctly.
Use parentheses: Use parentheses to group numbers and operations together and make it easier to evaluate the expression.
Check your work: Once you have solved the expression, check your work to make sure you got the right answer.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving expressions:

Not following the order of operations: Failing to follow the order of operations can lead to errors and incorrect answers.
Not using parentheses: Failing to use parentheses can make it difficult to evaluate the expression correctly.
Not checking your work: Failing to check your work can lead to errors and incorrect answers.

Conclusion

In conclusion, solving the expression 5^2 + (-3) requires following the order of operations and evaluating the exponent and the addition correctly. By following the order of operations and using parentheses, we can ensure that we get the right answer.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when there are multiple operations in an expression. The order of operations is often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Q: Why is following the order of operations important?

A: Following the order of operations is important because it helps us to evaluate expressions correctly and avoid errors. If we don't follow the order of operations, we may get the wrong answer.

Q: How do I evaluate an exponent?

A: To evaluate an exponent, we need to raise the base number to the power of the exponent. For example, to evaluate 5^2, we need to multiply 5 by itself: 5 * 5 = 25.

Q: How do I add a negative number?

A: When we add a negative number, we need to change the sign of the number we are adding to. So, -3 becomes +3.

Q: What is the difference between addition and subtraction?

A: Addition and subtraction are both operations that involve combining numbers. However, addition involves combining numbers by adding them together, while subtraction involves combining numbers by subtracting one number from another.

Q: How do I use parentheses to group numbers and operations together?

A: To use parentheses to group numbers and operations together, we need to surround the numbers and operations we want to group with parentheses. For example, to group the numbers 2 and 3 together, we would write (2 + 3).

Q: Why is it important to check my work?

A: Checking our work is important because it helps us to catch errors and ensure that we get the right answer. If we don't check our work, we may get the wrong answer.

Q: What are some common mistakes to avoid when solving expressions?

A: Some common mistakes to avoid when solving expressions include:

Not following the order of operations
Not using parentheses
Not checking our work

Q: How can I practice solving expressions?

A: There are many ways to practice solving expressions, including:

Working on math problems and exercises
Using online resources and tools to practice solving expressions
Asking a teacher or tutor for help and guidance

Q: What are some real-world applications of the order of operations?

A: The order of operations is used in many real-world applications, including:

Science and engineering
Computer programming
Finance

Q: Why is the order of operations important in science and engineering?

A: The order of operations is important in science and engineering because it helps us to evaluate complex mathematical expressions that are used to model real-world phenomena.

Q: Why is the order of operations important in computer programming?

A: The order of operations is important in computer programming because it helps us to evaluate expressions and perform calculations.

Q: Why is the order of operations important in finance?

A: The order of operations is important in finance because it helps us to evaluate financial expressions and perform calculations.

Conclusion

In conclusion, solving expressions requires following the order of operations and evaluating the exponent and the addition correctly. By following the order of operations and using parentheses, we can ensure that we get the right answer.