Question
4. A basketball player is 6//23
feet tall. His infant son is 1/4
as tall. How tall is his son?(1 point)
Responses
1/2/3
ft
1 and 2 thirds ft
2/1/6
ft
2 and 1 sixth ft
1/1/2
ft
1 and 1 half ft
2/2/3
ft
feet tall. His infant son is 1/4
as tall. How tall is his son?(1 point)
Responses
1/2/3
ft
1 and 2 thirds ft
2/1/6
ft
2 and 1 sixth ft
1/1/2
ft
1 and 1 half ft
2/2/3
ft
Answers
GPT-4o mini
To find the height of the infant son, we need to calculate \( \frac{1}{4} \) of the height of the basketball player, who is \( 6 \frac{23}{24} \) feet tall.
First, let's convert \( 6 \frac{23}{24} \) feet to an improper fraction:
\[
6 \frac{23}{24} = \frac{6 \times 24 + 23}{24} = \frac{144 + 23}{24} = \frac{167}{24}
\]
Now, we calculate \( \frac{1}{4} \) of this height:
\[
\text{Height of son} = \frac{1}{4} \times \frac{167}{24} = \frac{167}{96}
\]
Next, we convert \( \frac{167}{96} \) to a mixed number:
1. Divide \( 167 \) by \( 96 \):
- \( 167 \div 96 = 1 \) (whole part)
- Remainder: \( 167 - 96 = 71 \)
Thus, we can express \( \frac{167}{96} \) as:
\[
1 \frac{71}{96}
\]
This fraction cannot be simplified further.
Now, looking at the responses:
- \( 1 \frac{1}{2} \text{ ft} \) (which is \( 1.5 \text{ ft} \) or \( \frac{3}{2} \text{ ft} \)) does not match.
- \( 2 \frac{1}{6} \text{ ft} \) does not match.
- \( 2 \frac{2}{3} \text{ ft} \) does not match.
None of the provided responses are equivalent to \( 1 \frac{71}{96} \text{ ft} \). Therefore, the answer cannot be selected from the given responses.
If you want to approximate \( 1 \frac{71}{96} \), it is approximately \( 1.74 \) feet, which is less than \( 2 \) feet. However, since there's no matching option, we conclude that the response options may not be correct in this instance.
First, let's convert \( 6 \frac{23}{24} \) feet to an improper fraction:
\[
6 \frac{23}{24} = \frac{6 \times 24 + 23}{24} = \frac{144 + 23}{24} = \frac{167}{24}
\]
Now, we calculate \( \frac{1}{4} \) of this height:
\[
\text{Height of son} = \frac{1}{4} \times \frac{167}{24} = \frac{167}{96}
\]
Next, we convert \( \frac{167}{96} \) to a mixed number:
1. Divide \( 167 \) by \( 96 \):
- \( 167 \div 96 = 1 \) (whole part)
- Remainder: \( 167 - 96 = 71 \)
Thus, we can express \( \frac{167}{96} \) as:
\[
1 \frac{71}{96}
\]
This fraction cannot be simplified further.
Now, looking at the responses:
- \( 1 \frac{1}{2} \text{ ft} \) (which is \( 1.5 \text{ ft} \) or \( \frac{3}{2} \text{ ft} \)) does not match.
- \( 2 \frac{1}{6} \text{ ft} \) does not match.
- \( 2 \frac{2}{3} \text{ ft} \) does not match.
None of the provided responses are equivalent to \( 1 \frac{71}{96} \text{ ft} \). Therefore, the answer cannot be selected from the given responses.
If you want to approximate \( 1 \frac{71}{96} \), it is approximately \( 1.74 \) feet, which is less than \( 2 \) feet. However, since there's no matching option, we conclude that the response options may not be correct in this instance.