Calculating the Enlarged Height

Oct 13, 2025 by wbrum.org 71 views

Understanding the Problem

When a customer requests to enlarge a photo to a specific height, it's essential to understand the mathematical concept behind the enlargement. In this scenario, the customer wants the photo to be enlarged to ${$ \frac{23}{4}$}$ its current height. The photo's current height is ${$ \frac{31}{4}$}$ inches. To determine the new height, we need to calculate the enlarged height based on the given ratio.

Calculating the Enlarged Height

To find the enlarged height, we need to multiply the current height by the ratio given by the customer. The ratio is ${$ \frac{23}{4}$}$, which means the new height will be ${$ \frac{23}{4}$}$ times the current height.

Step 1: Convert the Current Height to a Decimal

First, let's convert the current height from a fraction to a decimal. The current height is ${$ \frac{31}{4}$}$ inches, which is equivalent to 7.75 inches.

Step 2: Multiply the Current Height by the Ratio

Now, let's multiply the current height by the ratio. The ratio is ${$ \frac{23}{4}$}$, which is equivalent to 5.75. Multiply the current height (7.75 inches) by the ratio (5.75):

7.75 x 5.75 = 44.5625

Step 3: Convert the Result to a Mixed Number

The result (44.5625) can be converted to a mixed number. To do this, we need to divide the decimal part (0.5625) by the denominator (4):

0.5625 ÷ 4 = 0.140625

Since 0.140625 is equivalent to ${$ \frac{3}{16}$}$, we can rewrite the result as a mixed number:

44.5625 = 44 ${$ \frac{3}{16}$}$

Conclusion

Based on the customer's request, the enlarged height of the photo should be ${ $6 \frac{3}{16}\$}$ inches.

Answer

The correct answer is:

B. ${ $6 \frac{3}{16}\$}$

Discussion

Understanding the Problem

Calculating the Enlarged Height

Step 1: Convert the Current Height to a Decimal

First, let's convert the current height from a fraction to a decimal. The current height is ${$ \frac{31}{4}$}$ inches, which is equivalent to 7.75 inches.

Step 2: Multiply the Current Height by the Ratio

Now, let's multiply the current height by the ratio. The ratio is ${$ \frac{23}{4}$}$, which is equivalent to 5.75. Multiply the current height (7.75 inches) by the ratio (5.75):

7.75 x 5.75 = 44.5625

Step 3: Convert the Result to a Mixed Number

The result (44.5625) can be converted to a mixed number. To do this, we need to divide the decimal part (0.5625) by the denominator (4):

0.5625 ÷ 4 = 0.140625

Since 0.140625 is equivalent to ${$ \frac{3}{16}$}$, we can rewrite the result as a mixed number:

44.5625 = 44 ${$ \frac{3}{16}$}$

Conclusion

Based on the customer's request, the enlarged height of the photo should be ${ $6 \frac{3}{16}\$}$ inches.

Answer

The correct answer is:

B. ${ $6 \frac{3}{16}\$}$

Discussion

This problem requires a basic understanding of fractions and decimals. The customer's request is to enlarge the photo to ${$ \frac{23}{4}$}$ its current height. To calculate the new height, we need to multiply the current height by the ratio given by the customer. The result is a mixed number, which can be converted to a decimal or a fraction. In this case, the correct answer is ${ $6 \frac{3}{16}\$}$ inches.

Q&A

Q: What is the customer's request?

A: The customer wants the photo to be enlarged to ${$ \frac{23}{4}$}$ its current height.

Q: What is the current height of the photo?

A: The current height of the photo is ${$ \frac{31}{4}$}$ inches.

Q: How do we calculate the new height?

A: To calculate the new height, we need to multiply the current height by the ratio given by the customer.

Q: What is the ratio given by the customer?

A: The ratio given by the customer is ${$ \frac{23}{4}$}$.

Q: What is the result of multiplying the current height by the ratio?

A: The result is 44.5625 inches.

Q: How do we convert the result to a mixed number?

A: To convert the result to a mixed number, we need to divide the decimal part by the denominator.

Q: What is the correct answer?

A: The correct answer is ${ $6 \frac{3}{16}\$}$ inches.

Q: What is the importance of understanding fractions and decimals in this problem?

A: Understanding fractions and decimals is essential in this problem because the customer's request is to enlarge the photo to a specific height, and the result is a mixed number that can be converted to a decimal or a fraction.

Q: What is the final answer?

A: The final answer is ${ $6 \frac{3}{16}\$}$ inches.

Conclusion

In conclusion, the customer's request to enlarge the photo to ${$ \frac{23}{4}$}$ its current height requires a basic understanding of fractions and decimals. By multiplying the current height by the ratio given by the customer, we can calculate the new height. The result is a mixed number that can be converted to a decimal or a fraction. In this case, the correct answer is ${ $6 \frac{3}{16}\$}$ inches.