Divide: \[$-15 \div 3\$\]A. -12 B. -5 C. -18 D. 45

Feb 26, 2025 by ADMIN 56 views

Divide: ${$ -15 \div 3$}$ - Understanding the Concept of Division with Negative Numbers

Division is a fundamental operation in mathematics that involves sharing a certain quantity into equal parts or groups. When it comes to dividing negative numbers, it's essential to understand the concept and apply the rules correctly to arrive at the right answer. In this article, we'll delve into the world of division with negative numbers and explore how to solve the given problem: Divide: ${$ -15 \div 3$}$.

Understanding Division with Negative Numbers

When we divide two negative numbers, the result is always positive. This is because the negative signs cancel each other out, leaving us with a positive quotient. On the other hand, when we divide a negative number by a positive number, the result is always negative. This is because the negative sign in the dividend (the number being divided) remains, resulting in a negative quotient.

The Rules of Division with Negative Numbers

To solve division problems involving negative numbers, we need to follow these rules:

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.

Applying the Rules to the Given Problem

Now that we've understood the rules of division with negative numbers, let's apply them to the given problem: Divide: ${$ -15 \div 3$}$.

In this problem, we have a negative dividend (-15) and a positive divisor (3). According to the rules we've learned, when dividing a negative number by a positive number, the result is always negative. Therefore, the correct answer is:

-5

Why is the Answer -5?

To understand why the answer is -5, let's break down the division process:

We start with the dividend, which is -15.
We divide -15 by 3, which means we're sharing -15 into 3 equal parts.
To find the quotient, we divide -15 by 3, which gives us -5.

Therefore, the correct answer is -5.

Conclusion

In conclusion, division with negative numbers requires a clear understanding of the rules and how to apply them. By following the rules and breaking down the division process, we can arrive at the correct answer. In this article, we've explored the concept of division with negative numbers and applied the rules to the given problem: Divide: ${$ -15 \div 3$}$. We've learned that the correct answer is -5, and we've understood why it's the correct answer.

Common Mistakes to Avoid

When working with division and negative numbers, it's essential to avoid common mistakes. Here are some common mistakes to watch out for:

Not following the rules: Make sure to follow the rules of division with negative numbers, which we've discussed in this article.
Not breaking down the division process: Take the time to break down the division process and understand how to arrive at the correct answer.
Not checking the answer: Always check your answer to ensure it's correct.

Practice Problems

To reinforce your understanding of division with negative numbers, try solving the following practice problems:

Divide: ${$ -20 \div 4$}$
Divide: ${$ -30 \div 6$}$
Divide: ${$ -40 \div 8$}$

By practicing these problems, you'll become more confident in your ability to solve division problems involving negative numbers.

Final Thoughts

Division with negative numbers may seem challenging at first, but with practice and a clear understanding of the rules, you'll become proficient in solving these types of problems. Remember to follow the rules, break down the division process, and check your answer to ensure it's correct. With time and practice, you'll become a master of division with negative numbers.
Divide: ${$ -15 \div 3$}$ - Q&A

In our previous article, we explored the concept of division with negative numbers and applied the rules to the given problem: Divide: ${$ -15 \div 3$}$. We've learned that the correct answer is -5, and we've understood why it's the correct answer. In this article, we'll address some common questions and concerns related to division with negative numbers.

Q: What happens when we divide two negative numbers?

A: When we divide two negative numbers, the result is always positive. This is because the negative signs cancel each other out, leaving us with a positive quotient.

Q: What happens when we divide a negative number by a positive number?

A: When we divide a negative number by a positive number, the result is always negative. This is because the negative sign in the dividend (the number being divided) remains, resulting in a negative quotient.

Q: What happens when we divide a positive number by a negative number?

A: When we divide a positive number by a negative number, the result is always negative. This is because the negative sign in the divisor (the number by which we're dividing) remains, resulting in a negative quotient.

Q: How do we handle division with zero?

A: When we divide a number by zero, the result is undefined. This is because division by zero is not a valid mathematical operation.

Q: Can we divide a negative number by a negative number?

A: Yes, we can divide a negative number by a negative number. In this case, the result is always positive.

Q: Can we divide a negative number by a positive number and get a positive result?

A: No, we cannot divide a negative number by a positive number and get a positive result. When we divide a negative number by a positive number, the result is always negative.

Q: Can we divide a positive number by a negative number and get a positive result?

A: No, we cannot divide a positive number by a negative number and get a positive result. When we divide a positive number by a negative number, the result is always negative.

Q: How do we handle decimal numbers in division?

A: When we divide decimal numbers, we can use a calculator or perform long division to find the quotient.

Q: Can we divide a negative number by a fraction?

A: Yes, we can divide a negative number by a fraction. In this case, we need to follow the rules of division with negative numbers and fractions.

Q: Can we divide a fraction by a negative number?

A: Yes, we can divide a fraction by a negative number. In this case, we need to follow the rules of division with fractions and negative numbers.