Forgetting to change the sign

Oct 13, 2025 by talynt.org 76 views

Introduction

In mathematics, multiplication is a fundamental operation that involves the repeated addition of a number. When we multiply two numbers, we are essentially adding the first number a certain number of times, equal to the value of the second number. In this article, we will evaluate the expression $-4 \times 6.5$ and explore the concept of multiplication with negative numbers.

Understanding Negative Numbers

Before we dive into the evaluation of the expression, let's take a moment to understand what negative numbers are. A negative number is a number that is less than zero. It is denoted by a minus sign (-) placed before the number. For example, -4 is a negative number, as it is less than zero.

Multiplication with Negative Numbers

When we multiply two numbers, the result is positive if both numbers have the same sign (either both positive or both negative). However, if the numbers have different signs, the result is negative. This is a fundamental property of multiplication with negative numbers.

Evaluating the Expression

Now that we have a good understanding of negative numbers and multiplication with negative numbers, let's evaluate the expression $-4 \times 6.5$ . To do this, we need to multiply -4 by 6.5.

Step 1: Multiply -4 by 6.5

To multiply -4 by 6.5, we can use the distributive property of multiplication. This property states that we can multiply a number by a sum (or difference) of numbers by multiplying the number by each number in the sum (or difference) and then adding (or subtracting) the results.

Step 2: Apply the Distributive Property

Using the distributive property, we can rewrite the expression as:

$-4 \times 6.5 = (-4) \times 6 + (-4) \times 0.5$

Step 3: Multiply -4 by 6

Now, let's multiply -4 by 6:

$(-4) \times 6 = -24$

Step 4: Multiply -4 by 0.5

Next, let's multiply -4 by 0.5:

$(-4) \times 0.5 = -2$

Step 5: Add the Results

Finally, let's add the results of the two multiplications:

$-24 + (-2) = -26$

Conclusion

In conclusion, the value of the expression $-4 \times 6.5$ is -26. This result is negative because the two numbers have different signs (one is positive and the other is negative).

Real-World Applications

The concept of multiplication with negative numbers has many real-world applications. For example, in finance, a negative return on investment can be calculated by multiplying the initial investment by a negative number. In physics, the force of friction can be calculated by multiplying the normal force by a negative number.

Common Mistakes

When working with negative numbers and multiplication, it's easy to make mistakes. Here are a few common mistakes to watch out for:

Forgetting to change the sign: When multiplying two numbers with different signs, it's easy to forget to change the sign of the result. For example, if you multiply -4 by 6.5, you might forget to change the sign and get a positive result instead of a negative one.
Not using the distributive property: The distributive property is a powerful tool for multiplying numbers with different signs. However, it's easy to forget to use it and end up with a wrong result.

Tips and Tricks

Here are a few tips and tricks to help you work with negative numbers and multiplication:

Use the distributive property: The distributive property is a powerful tool for multiplying numbers with different signs. Make sure to use it when working with negative numbers.
Change the sign: When multiplying two numbers with different signs, make sure to change the sign of the result.
Check your work: When working with negative numbers and multiplication, it's easy to make mistakes. Make sure to check your work carefully to avoid errors.

Conclusion

In conclusion, the value of the expression $-4 \times 6.5$ is -26. This result is negative because the two numbers have different signs (one is positive and the other is negative). The concept of multiplication with negative numbers has many real-world applications, and it's essential to understand how to work with negative numbers and multiplication to avoid common mistakes.

Introduction

In our previous article, we evaluated the expression $-4 \times 6.5$ and explored the concept of multiplication with negative numbers. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q&A

Q: What is the result of $-4 \times 6.5$ ?

A: The result of $-4 \times 6.5$ is -26.

Q: Why is the result negative?

A: The result is negative because the two numbers have different signs (one is positive and the other is negative).

Q: Can you explain the concept of multiplication with negative numbers?

A: Yes, multiplication with negative numbers involves multiplying two numbers with different signs. The result is negative if the numbers have different signs.

Q: How do you multiply two numbers with different signs?

A: To multiply two numbers with different signs, you can use the distributive property of multiplication. This property states that you can multiply a number by a sum (or difference) of numbers by multiplying the number by each number in the sum (or difference) and then adding (or subtracting) the results.

Q: What is the distributive property of multiplication?

A: The distributive property of multiplication is a mathematical property that states that you can multiply a number by a sum (or difference) of numbers by multiplying the number by each number in the sum (or difference) and then adding (or subtracting) the results.

Q: How do you apply the distributive property to multiply two numbers with different signs?

A: To apply the distributive property, you can rewrite the expression as:

$-4 \times 6.5 = (-4) \times 6 + (-4) \times 0.5$

Then, you can multiply -4 by 6 and -4 by 0.5 separately and add the results.

Q: What is the result of $(-4) \times 6$ ?

A: The result of $(-4) \times 6$ is -24.

Q: What is the result of $(-4) \times 0.5$ ?

A: The result of $(-4) \times 0.5$ is -2.

Q: What is the final result of $-4 \times 6.5$ ?

A: The final result of $-4 \times 6.5$ is -26.

Q: Can you provide an example of a real-world application of multiplication with negative numbers?

A: Yes, in finance, a negative return on investment can be calculated by multiplying the initial investment by a negative number.

Q: What are some common mistakes to watch out for when working with negative numbers and multiplication?

A: Some common mistakes to watch out for include forgetting to change the sign of the result, not using the distributive property, and not checking your work carefully.

Q: How can you avoid common mistakes when working with negative numbers and multiplication?

A: To avoid common mistakes, make sure to use the distributive property, change the sign of the result, and check your work carefully.

Conclusion

In conclusion, the value of the expression $-4 \times 6.5$ is -26. This result is negative because the two numbers have different signs (one is positive and the other is negative). We hope this Q&A article has helped you understand the concept of multiplication with negative numbers and how to apply it in real-world situations.