Rules of Signs for Division

Oct 13, 2025 by recoveryshake.com 16 views

Understanding the Problem

When dealing with division, it's essential to remember the rules of signs. The expression $-18 \div (-9)$ involves two negative numbers, which can lead to confusion. To simplify this expression, we need to understand the concept of dividing negative numbers.

Rules of Signs for Division

When dividing two negative numbers, the result is always positive. This is because the negative signs cancel each other out. On the other hand, when dividing a negative number by a positive number, the result is always negative.

Evaluating the Expression

Let's evaluate the expression $-18 \div (-9)$ step by step:

We know that when dividing two negative numbers, the result is always positive.
To simplify the expression, we can multiply both the numerator and the denominator by $-1$ to make the division easier.
This gives us: $-18 \div (-9) = -18 \times (-1) \div (-9) \times (-1)$
Now, we can simplify the expression by canceling out the negative signs: $-18 \times (-1) \div (-9) \times (-1) = 18 \div 9$
Finally, we can evaluate the expression: $18 \div 9 = 2$

Comparing the Options

Now that we have evaluated the expression $-18 \div (-9)$ , let's compare it with the given options:

A. $-18 \div 2$ : This option is incorrect because the expression $-18 \div 2$ is not equal to $-18 \div (-9)$ .
B. $-12 + (-3)$ : This option is also incorrect because the expression $-12 + (-3)$ is not equal to $-18 \div (-9)$ .
C. $-10 \div 5$ : This option is incorrect because the expression $-10 \div 5$ is not equal to $-18 \div (-9)$ .
D. $-8 \div (-4)$ : This option is correct because the expression $-8 \div (-4)$ is equal to $-18 \div (-9)$ .

Conclusion

In conclusion, the expression that has the same value as $-18 \div (-9)$ is $-8 \div (-4)$ . This is because both expressions involve dividing two negative numbers, which results in a positive value. By understanding the rules of signs for division, we can simplify the expression and evaluate it correctly.

Frequently Asked Questions

What is the rule for dividing negative numbers?
When dividing two negative numbers, the result is always positive.
What is the result of $-18 \div (-9)$ ?
The result of $-18 \div (-9)$ is 2.
Which expression has the same value as $-18 \div (-9)$ ?
The expression $-8 \div (-4)$ has the same value as $-18 \div (-9)$ .

Final Answer

The final answer is D. $-8 \div (-4)$ .

Introduction

Division with negative numbers can be a challenging concept to grasp, especially when it comes to understanding the rules of signs. In this article, we will address some of the most frequently asked questions related to division with negative numbers.

Q&A

Q1: What is the rule for dividing negative numbers?

A1: When dividing two negative numbers, the result is always positive. This is because the negative signs cancel each other out.

Q2: What is the result of $-18 \div (-9)$ ?

A2: The result of $-18 \div (-9)$ is 2. This is because the negative signs cancel each other out, and the result is a positive value.

Q3: What is the result of $-10 \div 5$ ?

A3: The result of $-10 \div 5$ is -2. This is because the negative sign in the numerator is carried over to the result, making it a negative value.

Q4: What is the result of $-8 \div (-4)$ ?

A4: The result of $-8 \div (-4)$ is 2. This is because the negative signs cancel each other out, and the result is a positive value.

Q5: What is the rule for dividing a negative number by a positive number?

A5: When dividing a negative number by a positive number, the result is always negative. This is because the negative sign in the numerator is carried over to the result.

Q6: What is the result of $-12 \div 3$ ?

A6: The result of $-12 \div 3$ is -4. This is because the negative sign in the numerator is carried over to the result, making it a negative value.

Q7: What is the result of $-15 \div (-5)$ ?

A7: The result of $-15 \div (-5)$ is 3. This is because the negative signs cancel each other out, and the result is a positive value.

Q8: What is the rule for dividing a positive number by a negative number?

A8: When dividing a positive number by a negative number, the result is always negative. This is because the negative sign in the denominator is carried over to the result.

Q9: What is the result of $18 \div (-9)$ ?

A9: The result of $18 \div (-9)$ is -2. This is because the negative sign in the denominator is carried over to the result, making it a negative value.

Q10: What is the result of $-20 \div (-5)$ ?

A10: The result of $-20 \div (-5)$ is 4. This is because the negative signs cancel each other out, and the result is a positive value.

Conclusion

In conclusion, division with negative numbers can be a complex concept, but by understanding the rules of signs, we can simplify the process and evaluate expressions correctly. We hope that this article has addressed some of the most frequently asked questions related to division with negative numbers.

Final Answer

The final answer is that division with negative numbers involves understanding the rules of signs, which can be summarized as follows:

When dividing two negative numbers, the result is always positive.
When dividing a negative number by a positive number, the result is always negative.
When dividing a positive number by a negative number, the result is always negative.

By understanding these rules, we can evaluate expressions involving division with negative numbers correctly.