Understanding Integer Operations

Oct 13, 2025 by wbrum.org 20 views

Introduction

In mathematics, integer operations are fundamental concepts that form the basis of arithmetic. When dealing with integers, it's essential to understand the rules governing their operations, including addition, subtraction, multiplication, and division. In this article, we will focus on solving a simple integer operation: $ (+9) - (+5) = $. We will break down the problem step by step, explaining the reasoning behind each step.

Understanding Integer Operations

Before we dive into the solution, let's briefly review the rules governing integer operations. When dealing with positive integers, the rules are straightforward:

Addition: When adding two positive integers, the result is always a positive integer.
Subtraction: When subtracting a smaller positive integer from a larger positive integer, the result is always a positive integer.
Multiplication: When multiplying two positive integers, the result is always a positive integer.
Division: When dividing a positive integer by a non-zero positive integer, the result is always a positive integer.

Solving the Integer Operation

Now that we have reviewed the rules governing integer operations, let's solve the given problem: $ (+9) - (+5) = $. To solve this problem, we need to follow the rules of subtraction.

Step 1: Identify the Minuend and Subtrahend

In the given problem, $ (+9) - (+5) = $, the minuend is $ (+9) $ and the subtrahend is $ (+5) $.

Step 2: Subtract the Subtrahend from the Minuend

To subtract the subtrahend from the minuend, we need to perform the following operation:

$ (+9) - (+5) = (+9) + (-5) $

Step 3: Simplify the Expression

To simplify the expression, we need to combine the terms:

$ (+9) + (-5) = (+9) + (-5) = (+9) + (-5) = (+4) $

Step 4: Write the Final Answer

The final answer is $ (+4) $.

Conclusion

In this article, we solved a simple integer operation: $ (+9) - (+5) = $. We broke down the problem step by step, explaining the reasoning behind each step. By following the rules of subtraction, we arrived at the final answer: $ (+4) $. This problem demonstrates the importance of understanding integer operations and how to apply them to solve mathematical problems.

Frequently Asked Questions

What is the result of $ (+9) - (+5) = $?
- The result is $ (+4) $.
What are the rules governing integer operations?
- The rules are:
- Addition: When adding two positive integers, the result is always a positive integer.
- Subtraction: When subtracting a smaller positive integer from a larger positive integer, the result is always a positive integer.
- Multiplication: When multiplying two positive integers, the result is always a positive integer.
- Division: When dividing a positive integer by a non-zero positive integer, the result is always a positive integer.

References

[1] Khan Academy. (n.d.). Integer Operations. Retrieved from https://www.khanacademy.org/math/integer-operations
[2] Mathway. (n.d.). Integer Operations. Retrieved from https://www.mathway.com/integer-operations
[3] Wolfram MathWorld. (n.d.). Integer Operations. Retrieved from https://mathworld.wolfram.com/IntegerOperations.html

Introduction

In our previous article, we solved a simple integer operation: $ (+9) - (+5) = $. We also reviewed the rules governing integer operations and provided a step-by-step solution to the problem. In this article, we will answer some frequently asked questions (FAQs) related to integer operations.

Q&A: Integer Operations

Q1: What is the result of $ (+3) - (+2) = $?

A1: To solve this problem, we need to follow the rules of subtraction. The minuend is $ (+3) $ and the subtrahend is $ (+2) $. We need to subtract the subtrahend from the minuend:

$ (+3) - (+2) = (+3) + (-2) = (+1) $

The final answer is $ (+1) $.

Q2: What is the result of $ (+5) - (+8) = $?

A2: To solve this problem, we need to follow the rules of subtraction. The minuend is $ (+5) $ and the subtrahend is $ (+8) $. We need to subtract the subtrahend from the minuend:

$ (+5) - (+8) = (+5) + (-8) = (-3) $

The final answer is $ (-3) $.

Q3: What is the result of $ (-3) - (+2) = $?

A3: To solve this problem, we need to follow the rules of subtraction. The minuend is $ (-3) $ and the subtrahend is $ (+2) $. We need to subtract the subtrahend from the minuend:

$ (-3) - (+2) = (-3) + (-2) = (-5) $

The final answer is $ (-5) $.

Q4: What is the result of $ (+4) - (-3) = $?

A4: To solve this problem, we need to follow the rules of subtraction. The minuend is $ (+4) $ and the subtrahend is $ (-3) $. We need to subtract the subtrahend from the minuend:

$ (+4) - (-3) = (+4) + (+3) = (+7) $

The final answer is $ (+7) $.

Q5: What are the rules governing integer operations?

A5: The rules governing integer operations are:

Addition: When adding two positive integers, the result is always a positive integer.
Subtraction: When subtracting a smaller positive integer from a larger positive integer, the result is always a positive integer.
Multiplication: When multiplying two positive integers, the result is always a positive integer.
Division: When dividing a positive integer by a non-zero positive integer, the result is always a positive integer.

Conclusion

In this article, we answered some frequently asked questions related to integer operations. We provided step-by-step solutions to various problems and reviewed the rules governing integer operations. By following these rules, you can solve a wide range of integer operation problems.

Frequently Asked Questions

What is the result of $ (+3) - (+2) = $?
- The result is $ (+1) $.
What is the result of $ (+5) - (+8) = $?
- The result is $ (-3) $.
What is the result of $ (-3) - (+2) = $?
- The result is $ (-5) $.
What is the result of $ (+4) - (-3) = $?
- The result is $ (+7) $.
What are the rules governing integer operations?
- The rules are:
- Addition: When adding two positive integers, the result is always a positive integer.
- Subtraction: When subtracting a smaller positive integer from a larger positive integer, the result is always a positive integer.
- Multiplication: When multiplying two positive integers, the result is always a positive integer.
- Division: When dividing a positive integer by a non-zero positive integer, the result is always a positive integer.

References

[1] Khan Academy. (n.d.). Integer Operations. Retrieved from https://www.khanacademy.org/math/integer-operations
[2] Mathway. (n.d.). Integer Operations. Retrieved from https://www.mathway.com/integer-operations
[3] Wolfram MathWorld. (n.d.). Integer Operations. Retrieved from https://mathworld.wolfram.com/IntegerOperations.html