A House Was Valued At $\$272,000$. Over Several Years, The Value Decreased By $8\%$, Giving The House A New Value.(a) Fill In The Blank To Write The New Value In Terms Of The Old Value. Write Your Answer As A Decimal.New Value =

Introduction

When it comes to real estate, the value of a house can fluctuate over time due to various factors such as market trends, economic conditions, and maintenance costs. In this article, we will explore how to calculate the new value of a house after its value has decreased by a certain percentage. We will use a specific example to illustrate this concept and provide a step-by-step guide on how to fill in the blank to write the new value in terms of the old value.

The Problem

A house was valued at $\$272,000$. Over several years, the value decreased by $8\%$, giving the house a new value. We need to fill in the blank to write the new value in terms of the old value.

Calculating the New Value

To calculate the new value of the house, we need to understand the concept of percentage decrease. When a value decreases by a certain percentage, we can calculate the new value by multiplying the old value by a decimal factor. In this case, the house's value decreased by $8\%$, which means we need to multiply the old value by a decimal factor that represents the remaining percentage after the decrease.

Let's denote the old value as $x$ and the new value as $y$. We know that the house's value decreased by $8\%$, so the new value is $92\%$ of the old value. We can write this as:

$$y = x \times 0.92$$

where $0.92$ represents the remaining percentage after the decrease.

Filling in the Blank

Now that we have the formula for the new value, we can fill in the blank to write the new value in terms of the old value. We are given that the old value is $\$272,000$, so we can substitute this value into the formula:

$$y = 272,000 \times 0.92$$

To calculate the new value, we can multiply the old value by the decimal factor:

$$y = 272,000 \times 0.92 = 250,240$$

Therefore, the new value of the house is $\$250,240$.

Conclusion

In this article, we explored how to calculate the new value of a house after its value has decreased by a certain percentage. We used a specific example to illustrate this concept and provided a step-by-step guide on how to fill in the blank to write the new value in terms of the old value. By understanding the concept of percentage decrease and using the formula for the new value, we can easily calculate the new value of a house.

Real-World Applications

The concept of percentage decrease is not limited to real estate. It can be applied to various fields such as finance, economics, and business. For example, when a company's stock price decreases by a certain percentage, we can calculate the new stock price by multiplying the old stock price by a decimal factor. Similarly, when a country's GDP decreases by a certain percentage, we can calculate the new GDP by multiplying the old GDP by a decimal factor.

Tips and Tricks

When working with percentage decrease, it's essential to remember that the decimal factor represents the remaining percentage after the decrease. For example, if a value decreases by $8\%$, the decimal factor is $0.92$, not $0.08$. By using the correct decimal factor, we can ensure accurate calculations and avoid errors.

Common Mistakes

When calculating the new value of a house or any other value, it's common to make mistakes such as:

• Using the wrong decimal factor
• Not considering the percentage decrease
• Not rounding the answer correctly

To avoid these mistakes, it's essential to double-check our calculations and use the correct decimal factor.

Conclusion

Q&A: Frequently Asked Questions

Q: What is percentage decrease?

A: Percentage decrease is a measure of how much a value has decreased by a certain percentage. For example, if a house's value decreases by $8\%$, it means that the new value is $92\%$ of the old value.

Q: How do I calculate the new value of a house after its value has decreased by a certain percentage?

A: To calculate the new value of a house, you need to multiply the old value by a decimal factor that represents the remaining percentage after the decrease. For example, if a house's value decreases by $8\%$, you would multiply the old value by $0.92$.

Q: What is the formula for the new value?

A: The formula for the new value is:

$$y = x \times (1 - r)$$

where $y$ is the new value, $x$ is the old value, and $r$ is the percentage decrease.

Q: How do I fill in the blank to write the new value in terms of the old value?

A: To fill in the blank, you need to substitute the old value into the formula and calculate the new value. For example, if the old value is $\$272,000$ and the percentage decrease is $8\%$, you would multiply the old value by $0.92$ to get the new value.

Q: What is the new value of a house that was valued at $\$272,000$ and decreased by $8\%$?

A: To calculate the new value, you would multiply the old value by $0.92$:

$$y = 272,000 \times 0.92 = 250,240$$

Therefore, the new value of the house is $\$250,240$.

Q: What are some common mistakes to avoid when calculating the new value of a house?

A: Some common mistakes to avoid include:

• Using the wrong decimal factor
• Not considering the percentage decrease
• Not rounding the answer correctly

Q: How do I avoid making mistakes when calculating the new value of a house?

A: To avoid making mistakes, it's essential to double-check your calculations and use the correct decimal factor. You should also consider the percentage decrease and round the answer correctly.

Q: Can I use the formula for the new value in other situations?

A: Yes, the formula for the new value can be used in other situations where a value decreases by a certain percentage. For example, you can use the formula to calculate the new stock price of a company or the new GDP of a country.

Q: What are some real-world applications of the formula for the new value?

A: Some real-world applications of the formula for the new value include:

• Calculating the new stock price of a company
• Calculating the new GDP of a country
• Calculating the new value of a house or other asset

Conclusion

In conclusion, calculating the new value of a house after its value has decreased by a certain percentage is a straightforward process that involves understanding the concept of percentage decrease and using the formula for the new value. By following the steps outlined in this article and avoiding common mistakes, you can easily fill in the blank to write the new value in terms of the old value and ensure accurate calculations.