Current Height of the Photo

Oct 13, 2025 by talynt.org 38 views

Understanding the Problem

In this problem, we are tasked with enlarging a photo to a specific scale. The customer wants the photo to be enlarged to $2 \frac{3}{4}$ times its current height. To solve this problem, we need to understand the concept of scaling and how to apply it to the given dimensions.

Current Height of the Photo

The current height of the photo is given as $3 \frac{1}{4}$ inches. To work with this measurement, we need to convert it to an improper fraction. We can do this by multiplying the whole number part (3) by the denominator (4) and then adding the numerator (1).

$3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$

Scaling the Photo

The customer wants the photo to be enlarged to $2 \frac{3}{4}$ times its current height. To find the enlarged height, we need to multiply the current height by the scaling factor.

Scaling factor = $2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

Enlarged height = current height × scaling factor = $\frac{13}{4} \times \frac{11}{4}$ = $\frac{13 \times 11}{4 \times 4}$ = $\frac{143}{16}$

Converting the Enlarged Height to a Mixed Number

To convert the enlarged height to a mixed number, we need to divide the numerator (143) by the denominator (16).

$143 ÷ 16 = 8$ with a remainder of $15$

So, the enlarged height can be written as:

$\frac{143}{16} = 8 \frac{15}{16}$

Conclusion

In conclusion, the enlarged height of the photo should be $8 \frac{15}{16}$ inches.

Answer

The correct answer is:

Understanding the Problem

Current Height of the Photo

$3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$

Scaling the Photo

The customer wants the photo to be enlarged to $2 \frac{3}{4}$ times its current height. To find the enlarged height, we need to multiply the current height by the scaling factor.

Scaling factor = $2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}$

Enlarged height = current height × scaling factor = $\frac{13}{4} \times \frac{11}{4}$ = $\frac{13 \times 11}{4 \times 4}$ = $\frac{143}{16}$

Converting the Enlarged Height to a Mixed Number

To convert the enlarged height to a mixed number, we need to divide the numerator (143) by the denominator (16).

$143 ÷ 16 = 8$ with a remainder of $15$

So, the enlarged height can be written as:

$\frac{143}{16} = 8 \frac{15}{16}$

Conclusion

In conclusion, the enlarged height of the photo should be $8 \frac{15}{16}$ inches.

Answer

The correct answer is:

C. $8 \frac{15}{16}$

Q: What is the current height of the photo?

A: The current height of the photo is $3 \frac{1}{4}$ inches.

Q: What is the scaling factor for the photo?

A: The scaling factor for the photo is $2 \frac{3}{4}$ .

Q: How do I convert the current height to an improper fraction?

A: To convert the current height to an improper fraction, multiply the whole number part (3) by the denominator (4) and then add the numerator (1).

$3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}$

Q: How do I find the enlarged height of the photo?

A: To find the enlarged height, multiply the current height by the scaling factor.

Enlarged height = current height × scaling factor = $\frac{13}{4} \times \frac{11}{4}$ = $\frac{13 \times 11}{4 \times 4}$ = $\frac{143}{16}$

Q: How do I convert the enlarged height to a mixed number?

A: To convert the enlarged height to a mixed number, divide the numerator (143) by the denominator (16).

$143 ÷ 16 = 8$ with a remainder of $15$

So, the enlarged height can be written as:

$\frac{143}{16} = 8 \frac{15}{16}$

Q: What is the correct answer for the enlarged height of the photo?

A: The correct answer is:

C. $8 \frac{15}{16}$