Multiply: − 5 8 ⋅ ( − 3 -\frac{5}{8} \cdot (-3 − 8 5 ​ ⋅ ( − 3 ]Write Your Answer In Simplest Form: □ \square □

Introduction

In mathematics, multiplication is a fundamental operation that involves the combination of two or more numbers to produce a product. When dealing with fractions, multiplication can be a bit more complex, especially when the fractions are negative. In this article, we will explore the multiplication of negative fractions, specifically the product of $-\frac{5}{8}$ and $-3$. We will break down the process into simple steps and provide a clear explanation of each step.

Understanding Negative Fractions

Before we dive into the multiplication process, let's take a moment to understand what negative fractions are. A negative fraction is a fraction that has a negative numerator or a negative denominator. In the case of $-\frac{5}{8}$, the numerator is negative, while the denominator is positive. When we multiply two negative fractions, we need to consider the signs of both fractions.

Multiplying Negative Fractions

Now that we have a basic understanding of negative fractions, let's move on to the multiplication process. To multiply two negative fractions, we follow these steps:

1. Multiply the numerators: Multiply the numerators of both fractions. In this case, we multiply $-5$ and $-3$.
2. Multiply the denominators: Multiply the denominators of both fractions. In this case, we multiply $8$ and $1$ (since $-3$ can be written as $-3 \times 1$).
3. Determine the sign of the product: Since both fractions are negative, the product will be positive.

Step-by-Step Solution

Now that we have a clear understanding of the process, let's apply it to the given problem.

Step 1: Multiply the Numerators

To multiply the numerators, we simply multiply $-5$ and $-3$.

$$-5 \times -3 = 15$$

Step 2: Multiply the Denominators

To multiply the denominators, we multiply $8$ and $1$.

$$8 \times 1 = 8$$

Step 3: Determine the Sign of the Product

Since both fractions are negative, the product will be positive.

The Final Answer

Now that we have completed all the steps, we can write the final answer.

$$-\frac{5}{8} \cdot (-3) = \frac{15}{8}$$

Simplifying the Answer

The answer $\frac{15}{8}$ is already in its simplest form, so we don't need to simplify it further.

Conclusion

In this article, we explored the multiplication of negative fractions, specifically the product of $-\frac{5}{8}$ and $-3$. We broke down the process into simple steps and provided a clear explanation of each step. We also applied the process to the given problem and arrived at the final answer. We hope this article has provided a clear understanding of the multiplication of negative fractions and has helped you to become more confident in your math skills.

Frequently Asked Questions

• Q: What is the product of $-\frac{5}{8}$ and $-3$? A: The product of $-\frac{5}{8}$ and $-3$ is $\frac{15}{8}$.
• Q: How do I multiply negative fractions? A: To multiply negative fractions, you multiply the numerators and denominators separately and then determine the sign of the product.
• Q: What is the simplest form of $\frac{15}{8}$? A: The simplest form of $\frac{15}{8}$ is $\frac{15}{8}$.

Additional Resources

If you are struggling with multiplication of negative fractions or need additional practice, we recommend the following resources:

• Khan Academy: Multiplication of Negative Fractions
• Mathway: Multiplication of Negative Fractions
• IXL: Multiplication of Negative Fractions

Introduction

In our previous article, we explored the multiplication of negative fractions, specifically the product of $-\frac{5}{8}$ and $-3$. We broke down the process into simple steps and provided a clear explanation of each step. However, we know that math can be complex and confusing, and sometimes it's helpful to have a Q&A guide to clarify any doubts. In this article, we will provide a Q&A guide to the multiplication of negative fractions, covering common questions and concerns.

Q&A Guide

Q: What is the product of $-\frac{5}{8}$ and $-3$?

A: The product of $-\frac{5}{8}$ and $-3$ is $\frac{15}{8}$.

Q: How do I multiply negative fractions?

A: To multiply negative fractions, you multiply the numerators and denominators separately and then determine the sign of the product. If both fractions are negative, the product will be positive.

Q: What is the rule for multiplying negative fractions?

A: The rule for multiplying negative fractions is:

• If both fractions are positive, the product is positive.
• If both fractions are negative, the product is positive.
• If one fraction is positive and the other is negative, the product is negative.

Q: Can I simplify the product of two negative fractions?

A: Yes, you can simplify the product of two negative fractions by following the same steps as simplifying a fraction. For example, if the product is $\frac{15}{8}$, you can simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD).

Q: How do I determine the sign of the product of two negative fractions?

A: To determine the sign of the product of two negative fractions, you can use the following rule:

• If both fractions are negative, the product is positive.
• If one fraction is negative and the other is positive, the product is negative.

Q: Can I multiply a negative fraction by a positive fraction?

A: Yes, you can multiply a negative fraction by a positive fraction. To do this, you multiply the numerators and denominators separately and then determine the sign of the product. If the negative fraction is multiplied by a positive fraction, the product will be negative.

Q: How do I multiply a negative fraction by a negative integer?

A: To multiply a negative fraction by a negative integer, you multiply the numerator and denominator separately and then determine the sign of the product. If the negative fraction is multiplied by a negative integer, the product will be positive.

Q: Can I multiply a negative fraction by a positive integer?

A: Yes, you can multiply a negative fraction by a positive integer. To do this, you multiply the numerator and denominator separately and then determine the sign of the product. If the negative fraction is multiplied by a positive integer, the product will be negative.

Common Mistakes

When multiplying negative fractions, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not following the order of operations: Make sure to multiply the numerators and denominators separately before determining the sign of the product.
• Not considering the signs of the fractions: Remember that if both fractions are negative, the product will be positive, and if one fraction is negative and the other is positive, the product will be negative.
• Not simplifying the product: Make sure to simplify the product by dividing both the numerator and denominator by their greatest common divisor (GCD).

Conclusion

In this Q&A guide, we have covered common questions and concerns about the multiplication of negative fractions. We hope this guide has provided a clear understanding of the process and has helped you to become more confident in your math skills. Remember to always follow the order of operations, consider the signs of the fractions, and simplify the product to get the correct answer.

Frequently Asked Questions

• Q: What is the product of $-\frac{5}{8}$ and $-3$? A: The product of $-\frac{5}{8}$ and $-3$ is $\frac{15}{8}$.
• Q: How do I multiply negative fractions? A: To multiply negative fractions, you multiply the numerators and denominators separately and then determine the sign of the product.
• Q: What is the rule for multiplying negative fractions? A: The rule for multiplying negative fractions is:
• If both fractions are positive, the product is positive.
• If both fractions are negative, the product is positive.
• If one fraction is positive and the other is negative, the product is negative.

Additional Resources

If you are struggling with multiplication of negative fractions or need additional practice, we recommend the following resources:

• Khan Academy: Multiplication of Negative Fractions
• Mathway: Multiplication of Negative Fractions
• IXL: Multiplication of Negative Fractions

We hope this Q&A guide has provided a clear understanding of the multiplication of negative fractions and has helped you to become more confident in your math skills.