The Rule of Subtraction for Negative Numbers

Oct 13, 2025 by miodeya.com 3 views

Understanding the Problem

When dealing with negative numbers, it's essential to understand the concept of subtraction. In this case, we're asked to find the value of $-12.48 - (-9.08)$ . To solve this problem, we need to apply the rules of subtraction for negative numbers.

The Rule of Subtraction for Negative Numbers

The rule of subtraction for negative numbers states that when we subtract a negative number from another number, it's equivalent to adding the absolute value of the first number to the second number. In other words, $a - (-b) = a + b$ .

Applying the Rule to the Problem

Using the rule of subtraction for negative numbers, we can rewrite the expression $-12.48 - (-9.08)$ as $-12.48 + 9.08$ . Now, we can add the two numbers together.

Adding the Numbers

To add the numbers, we need to align the decimal points and add the corresponding digits. Here's the calculation:

$-12.48$ $+ 9.08$ $-----$ $-3.40$

Conclusion

Therefore, the value of $-12.48 - (-9.08)$ is $-3.40$ . This means that the correct answer is option B.

Why is this Important?

Understanding the concept of subtraction for negative numbers is crucial in mathematics, particularly in algebra and calculus. It's essential to apply this rule correctly to solve equations and inequalities involving negative numbers.

Real-World Applications

The concept of subtraction for negative numbers has numerous real-world applications. For example, in finance, it's used to calculate the difference between two negative numbers, such as the loss of money in a business. In science, it's used to calculate the difference between two negative values, such as the temperature difference between two locations.

Common Mistakes

When dealing with negative numbers, it's easy to make mistakes. One common mistake is to forget to change the sign when subtracting a negative number. For example, $-12.48 - (-9.08)$ is not equal to $-12.48 + 9.08$ . Instead, it's equal to $-12.48 + 9.08$ , which is $-3.40$ .

Tips and Tricks

To avoid making mistakes when dealing with negative numbers, it's essential to follow the rule of subtraction for negative numbers. Here are some tips and tricks to help you:

Always change the sign when subtracting a negative number.
Use the rule of subtraction for negative numbers to rewrite the expression.
Add the absolute value of the first number to the second number.
Align the decimal points and add the corresponding digits.

Conclusion

In conclusion, the value of $-12.48 - (-9.08)$ is $-3.40$ . This means that the correct answer is option B. Understanding the concept of subtraction for negative numbers is crucial in mathematics, particularly in algebra and calculus. It's essential to apply this rule correctly to solve equations and inequalities involving negative numbers.

Frequently Asked Questions

Q: What is the rule of subtraction for negative numbers? A: The rule of subtraction for negative numbers states that when we subtract a negative number from another number, it's equivalent to adding the absolute value of the first number to the second number.
Q: How do I apply the rule of subtraction for negative numbers? A: To apply the rule, rewrite the expression by changing the sign of the second number and then add the absolute value of the first number to the second number.
Q: What are some common mistakes to avoid when dealing with negative numbers? A: One common mistake is to forget to change the sign when subtracting a negative number.

Q&A Article

In this article, we'll answer some frequently asked questions about the subtraction of negative numbers. Whether you're a student, teacher, or simply someone who wants to understand this concept better, this article is for you.

Q1: What is the rule of subtraction for negative numbers?

A1: The rule of subtraction for negative numbers states that when we subtract a negative number from another number, it's equivalent to adding the absolute value of the first number to the second number. In other words, $a - (-b) = a + b$ .

Q2: How do I apply the rule of subtraction for negative numbers?

A2: To apply the rule, rewrite the expression by changing the sign of the second number and then add the absolute value of the first number to the second number. For example, $-12.48 - (-9.08)$ can be rewritten as $-12.48 + 9.08$ .

Q3: What are some common mistakes to avoid when dealing with negative numbers?

A3: One common mistake is to forget to change the sign when subtracting a negative number. For example, $-12.48 - (-9.08)$ is not equal to $-12.48 + 9.08$ . Instead, it's equal to $-12.48 + 9.08$ , which is $-3.40$ .

Q4: How do I handle subtraction of negative numbers with decimals?

A4: When subtracting negative numbers with decimals, follow the same steps as before. For example, $-12.48 - (-9.08)$ can be rewritten as $-12.48 + 9.08$ . Then, align the decimal points and add the corresponding digits.

Q5: Can I use a calculator to solve subtraction of negative numbers?

A5: Yes, you can use a calculator to solve subtraction of negative numbers. However, make sure to understand the concept behind the calculation. A calculator can help you verify your answer, but it's essential to understand the rule of subtraction for negative numbers.

Q6: How do I apply the rule of subtraction for negative numbers in real-world scenarios?

A6: The rule of subtraction for negative numbers has numerous real-world applications. For example, in finance, it's used to calculate the difference between two negative numbers, such as the loss of money in a business. In science, it's used to calculate the difference between two negative values, such as the temperature difference between two locations.

Q7: Can I use the rule of subtraction for negative numbers to solve equations and inequalities?

A7: Yes, you can use the rule of subtraction for negative numbers to solve equations and inequalities. For example, $x - (-3) = 5$ can be rewritten as $x + 3 = 5$ . Then, solve for x by subtracting 3 from both sides.

Q8: How do I handle subtraction of negative numbers with fractions?

A8: When subtracting negative numbers with fractions, follow the same steps as before. For example, $-\frac{3}{4} - (-\frac{1}{4})$ can be rewritten as $-\frac{3}{4} + \frac{1}{4}$ . Then, find a common denominator and add the fractions.

Q9: Can I use the rule of subtraction for negative numbers to solve word problems?

A9: Yes, you can use the rule of subtraction for negative numbers to solve word problems. For example, "Tom lost $12.48 and then found $9.08. How much money does Tom have now?" can be rewritten as $-12.48 - (-9.08)$ . Then, apply the rule of subtraction for negative numbers to find the answer.

Q10: How do I practice and improve my understanding of subtraction of negative numbers?

A10: To practice and improve your understanding of subtraction of negative numbers, try the following:

Practice solving problems with negative numbers.
Use online resources, such as calculators and worksheets.
Ask your teacher or tutor for help.
Join a study group or online community to discuss and learn from others.

By following these tips and practicing regularly, you'll become more confident and proficient in solving subtraction of negative numbers.