Division is the inverse operation of multiplication

Oct 13, 2025 by recoveryshake.com 1 views

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Introduction

When it comes to division, we often focus on the rules for positive numbers. However, when dealing with negative numbers, things can get a bit more complicated. In this article, we will explore the concept of dividing negative numbers and provide a step-by-step guide on how to solve the equation $-150 \div -25$ .

Understanding Negative Numbers

Before we dive into the solution, let's take a moment to understand the concept of negative numbers. A negative number is a number that is less than zero. It is denoted by a minus sign (-) preceding the number. For example, -5 is a negative number, as it is less than zero.

The Rules of Division

When it comes to division, there are two main rules to keep in mind:

Division is the inverse operation of multiplication: This means that if we have a division problem, we can multiply the dividend (the number being divided) by the reciprocal of the divisor (the number by which we are dividing).
The order of operations: When we have multiple operations in an expression, we need to follow the order of operations (PEMDAS):
1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Solving the Equation

Now that we have a solid understanding of negative numbers and the rules of division, let's tackle the equation $-150 \div -25$ .

Step 1: Identify the Dividend and Divisor

In this equation, the dividend is -150, and the divisor is -25.

Step 2: Apply the Rules of Division

Since we are dividing two negative numbers, we can use the rule that states that when we divide two negative numbers, the result is a positive number.

Step 3: Multiply the Dividend by the Reciprocal of the Divisor

To solve the equation, we can multiply the dividend (-150) by the reciprocal of the divisor (-25). The reciprocal of -25 is -1/25.

Step 4: Simplify the Expression

Now, let's multiply -150 by -1/25:

-150 \times -1/25 = 150/25 = 6

Step 5: Write the Final Answer

Therefore, the final answer to the equation $-150 \div -25$ is 6.

Conclusion

In this article, we explored the concept of dividing negative numbers and provided a step-by-step guide on how to solve the equation $-150 \div -25$ . By following the rules of division and applying the concept of negative numbers, we were able to arrive at the final answer of 6.

Frequently Asked Questions

Q: What is the rule for dividing two negative numbers?

A: When we divide two negative numbers, the result is a positive number.

Q: How do we multiply a negative number by a fraction?

A: To multiply a negative number by a fraction, we can multiply the negative number by the numerator and then divide by the denominator.

Q: What is the final answer to the equation $-150 \div -25$ ?

A: The final answer to the equation $-150 \div -25$ is 6.

Additional Resources

For more information on division and negative numbers, check out the following resources:

Khan Academy: Division of Negative Numbers
Mathway: Division of Negative Numbers
Wolfram Alpha: Division of Negative Numbers

Final Thoughts

Division of negative numbers can be a bit tricky, but by following the rules and applying the concept of negative numbers, we can arrive at the correct answer. Remember to always follow the order of operations and to multiply the dividend by the reciprocal of the divisor. With practice and patience, you'll become a pro at dividing negative numbers in no time!

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Introduction

In our previous article, we explored the concept of dividing negative numbers and provided a step-by-step guide on how to solve the equation $-150 \div -25$ . However, we know that there are many more questions and concerns that readers may have. In this article, we will address some of the most frequently asked questions about division of negative numbers.

Q&A

Q: What is the rule for dividing two negative numbers?

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

Q: How do I know when to change the sign of the result?

A: When you divide two negative numbers, you should change the sign of the result to positive. However, when you divide a negative number by a positive number, the result will be negative. And when you divide a positive number by a negative number, the result will also be negative.

Q: Can you give me an example of dividing two negative numbers?

A: Let's say we want to divide -12 by -3. To solve this problem, we can multiply the dividend (-12) by the reciprocal of the divisor (-3). The reciprocal of -3 is -1/3. So, we multiply -12 by -1/3 to get:

-12 \times -1/3 = 12/3 = 4

As you can see, the result is a positive number.

Q: What if I have a problem with a negative number and a fraction?

A: When you have a problem with a negative number and a fraction, you can multiply the negative number by the numerator and then divide by the denominator. For example, let's say we want to divide -15 by 1/2. To solve this problem, we can multiply -15 by 2 (the reciprocal of 1/2) to get:

-15 \times 2 = -30

Then, we can divide -30 by 1 to get:

-30 \div 1 = -30

As you can see, the result is a negative number.

Q: Can you explain the concept of negative reciprocals?

A: A negative reciprocal is a fraction that has a negative numerator and a positive denominator, or a positive numerator and a negative denominator. For example, the negative reciprocal of 2 is -1/2, and the negative reciprocal of -2 is 1/2.

Q: How do I know when to use a negative reciprocal?

A: You should use a negative reciprocal when you are dividing a negative number by a positive number, or a positive number by a negative number. For example, let's say we want to divide -12 by 3. To solve this problem, we can multiply -12 by the negative reciprocal of 3, which is -1/3. So, we multiply -12 by -1/3 to get:

-12 \times -1/3 = 12/3 = 4

As you can see, the result is a positive number.

Conclusion

In this article, we addressed some of the most frequently asked questions about division of negative numbers. We hope that this article has been helpful in clarifying any confusion you may have had. Remember to always follow the rules of division and to use negative reciprocals when necessary. With practice and patience, you'll become a pro at dividing negative numbers in no time!

Additional Resources

For more information on division and negative numbers, check out the following resources:

Khan Academy: Division of Negative Numbers
Mathway: Division of Negative Numbers
Wolfram Alpha: Division of Negative Numbers