Question

Paige decided to paint 45
of the rooms in her home last year.  By the end of the year, Paige completed 23
of the rooms.  How much of Paige’s home was painted last year?(1 point)
Responses

815
8 over 15

29
2 ninths

615
6 over 15

13

Answers

GPT-4o mini
To determine how much of Paige's home was painted, we need to set up the problem with the information provided.

Paige intended to paint \( \frac{4}{5} \) of the rooms (which is equivalent to a fraction form, 45) but completed \( \frac{2}{3} \) of them (which is equivalent to a fraction form, 23).

To find out how much of her home was painted, we can express it as:

\[
\text{Amount Painted} = \text{Completed Rooms} \div \text{Total Rooms} = \frac{23}{45}
\]

To express \( \frac{23}{45} \) as a simplified fraction, we can look for the greatest common divisor (GCD) of 23 and 45. Since 23 is a prime number and does not divide 45, \( \frac{23}{45} \) is already in its simplest form.

Looking at the provided responses, it seems the closest option that matches is \( 23 \) out of a total of \( 45 \) rooms, which does not explicitly appear in the form of a fraction.

Paige painted \( \frac{23}{45} \) of her home last year.

Regarding the listed responses:
- 815
- 8 over 15
- 29
- 2 ninths
- 615
- 6 over 15
- 13

None of those options directly represent \( \frac{23}{45} \). If any of those need to be simplified, for example, \( 8/15 \) (which is less than \( 23/45 \)) is not correct, nor does any others simplify accordingly.

Thus, the painting completion answer is \( \frac{23}{45} \), but it does not appear among your provided options. If you stand with \( 8/15 \), \( 6/15 \) represent incorrect parts of painted homes as compared with \( 23/45 \) amount painted by Paige.