Calculating the Product Range

Oct 13, 2025 by recoveryshake.com 94 views

Introduction

In mathematics, multiplication is a fundamental operation that involves finding the product of two or more numbers. When dealing with decimals, it's essential to understand how to multiply them to obtain a specific product range. In this discussion, we will focus on selecting decimals that, when multiplied by 8, result in a product that falls between 4 and 6.

Understanding the Problem

To solve this problem, we need to find the decimals that satisfy the given condition. We are looking for decimals that, when multiplied by 8, result in a product between 4 and 6. This means we need to find the range of decimals that, when multiplied by 8, will give us a value between 4 and 6.

Calculating the Product Range

To find the product range, we need to multiply the given range by 8. The given range is between 4 and 6. When we multiply 4 by 8, we get 32. When we multiply 6 by 8, we get 48. Therefore, the product range is between 32 and 48.

Selecting Decimals

Now that we have the product range, we can select the decimals that satisfy the given condition. We need to find the decimals that, when multiplied by 8, result in a product between 32 and 48.

Option A: 0.49

When we multiply 0.49 by 8, we get 3.92. This product is less than 32, so option A is not a valid choice.

Option B: 0.52

When we multiply 0.52 by 8, we get 4.16. This product is between 32 and 48, so option B is a valid choice.

Option C: 0.66

When we multiply 0.66 by 8, we get 5.28. This product is between 32 and 48, so option C is a valid choice.

Option D: 0.78

When we multiply 0.78 by 8, we get 6.24. This product is greater than 48, so option D is not a valid choice.

Option E: 0.8

When we multiply 0.8 by 8, we get 6.4. This product is greater than 48, so option E is not a valid choice.

Conclusion

In conclusion, the decimals that, when multiplied by 8, result in a product between 4 and 6 are 0.52 and 0.66. These decimals satisfy the given condition and fall within the product range of 32 and 48.

Key Takeaways

To solve this problem, we need to find the decimals that satisfy the given condition.
We need to find the product range by multiplying the given range by 8.
We can select the decimals that satisfy the given condition by finding the decimals that, when multiplied by 8, result in a product between 32 and 48.
The decimals that satisfy the given condition are 0.52 and 0.66.

Final Answer

The final answer is:

Option B: 0.52
Option C: 0.66
Frequently Asked Questions (FAQs) =====================================

Q: What is the main condition for selecting decimals in this problem?

A: The main condition is that the product of the decimal and 8 must fall between 4 and 6.

Q: How do we find the product range?

A: To find the product range, we multiply the given range by 8. In this case, the given range is between 4 and 6, so we multiply 4 by 8 to get 32 and multiply 6 by 8 to get 48.

Q: Why is it essential to find the product range?

A: Finding the product range helps us determine the range of decimals that satisfy the given condition. This range is between 32 and 48.

Q: How do we select the decimals that satisfy the given condition?

A: We select the decimals that, when multiplied by 8, result in a product between 32 and 48. We can do this by multiplying each option by 8 and checking if the product falls within the given range.

Q: What is the significance of the product range in this problem?

A: The product range is crucial in this problem because it helps us determine the range of decimals that satisfy the given condition. Without the product range, we would not be able to identify the correct decimals.

Q: Can we use any decimal to solve this problem?

A: No, we cannot use any decimal to solve this problem. We need to select decimals that, when multiplied by 8, result in a product between 32 and 48.

Q: How do we know which decimals to select?

A: We know which decimals to select by multiplying each option by 8 and checking if the product falls within the given range. If the product falls within the range, we select that decimal.

Q: What is the final answer to this problem?

A: The final answer is 0.52 and 0.66, as these decimals satisfy the given condition and fall within the product range of 32 and 48.

Q: Can we use a calculator to solve this problem?

A: Yes, we can use a calculator to solve this problem. However, it's essential to understand the concept behind the problem and how to select the correct decimals.

Q: Is there a shortcut to solving this problem?

A: No, there is no shortcut to solving this problem. We need to follow the steps outlined above to select the correct decimals.

Q: Can we apply this concept to other problems?

A: Yes, we can apply this concept to other problems that involve multiplying decimals by a specific number to obtain a product within a given range.

Q: What is the key takeaway from this problem?

A: The key takeaway from this problem is that we need to find the product range and select decimals that satisfy the given condition. This involves multiplying each option by 8 and checking if the product falls within the given range.