Question
At a workplace 153 of the 225 employees attended a meeting which statement shows value that are all equivalent to the fraction of employees who attended the meeting B 225/153 = 25/17 = 1.47 = 147%
Answers
GPT-4o mini
To determine which statement shows values that are all equivalent to the fraction of employees who attended the meeting, we need to first convert the attendance into a fraction:
The fraction of employees who attended the meeting can be calculated as:
\[ \text{Fraction} = \frac{\text{Number of attendees}}{\text{Total number of employees}} = \frac{153}{225}. \]
Now, we can simplify this fraction and convert it to different forms:
1. **Simplifying the Fraction:**
The fraction \( \frac{153}{225} \) can be simplified. The greatest common divisor (GCD) of 153 and 225 is 51.
So,
\[
\frac{153 \div 51}{225 \div 51} = \frac{3}{5}.
\]
2. **Calculating Percentage:**
To find the percentage of employees who attended:
\[
\text{Percentage} = \left( \frac{153}{225} \right) \times 100 \approx 68\%.
\]
3. **Decimal Form:**
Dividing 153 by 225 gives:
\[
\frac{153}{225} \approx 0.68.
\]
4. **Reciprocal:**
The reciprocal of the fraction \( \frac{153}{225} \) would be \( \frac{225}{153} \).
\[
\frac{225}{153} \approx 1.47.
\]
5. **Expressing as Percent:**
As mentioned previously, \( \frac{153}{225} \) as a ratio is approximately \( 68\% \), so \( \frac{225}{153} \) can also be represented in percentage terms:
\[
\frac{225}{153} \approx 1.47 \approx 147\%.
\]
So if the original statement provided claims that all those values are equivalent, the claim that "225/153 = 25/17 = 1.47 = 147%" is only partly true.
- \( \frac{153}{225} \) simplifies to \( \frac{3}{5} \) which is the fraction of employees that attended.
- Only the portion regarding \( \frac{225}{153} \) is accurate in summarizing the attendance relative to non-attendance.
Therefore, a more careful analysis shows that the values presented are related but not equivalent to \( \frac{153}{225} \). The correct equivalents of that fraction are \( \frac{3}{5} \) or 68% in decimal form (approx. 0.68), as opposed to the values listed, which relate to the overall figure but don’t represent the meeting attendance ratio directly.
The fraction of employees who attended the meeting can be calculated as:
\[ \text{Fraction} = \frac{\text{Number of attendees}}{\text{Total number of employees}} = \frac{153}{225}. \]
Now, we can simplify this fraction and convert it to different forms:
1. **Simplifying the Fraction:**
The fraction \( \frac{153}{225} \) can be simplified. The greatest common divisor (GCD) of 153 and 225 is 51.
So,
\[
\frac{153 \div 51}{225 \div 51} = \frac{3}{5}.
\]
2. **Calculating Percentage:**
To find the percentage of employees who attended:
\[
\text{Percentage} = \left( \frac{153}{225} \right) \times 100 \approx 68\%.
\]
3. **Decimal Form:**
Dividing 153 by 225 gives:
\[
\frac{153}{225} \approx 0.68.
\]
4. **Reciprocal:**
The reciprocal of the fraction \( \frac{153}{225} \) would be \( \frac{225}{153} \).
\[
\frac{225}{153} \approx 1.47.
\]
5. **Expressing as Percent:**
As mentioned previously, \( \frac{153}{225} \) as a ratio is approximately \( 68\% \), so \( \frac{225}{153} \) can also be represented in percentage terms:
\[
\frac{225}{153} \approx 1.47 \approx 147\%.
\]
So if the original statement provided claims that all those values are equivalent, the claim that "225/153 = 25/17 = 1.47 = 147%" is only partly true.
- \( \frac{153}{225} \) simplifies to \( \frac{3}{5} \) which is the fraction of employees that attended.
- Only the portion regarding \( \frac{225}{153} \) is accurate in summarizing the attendance relative to non-attendance.
Therefore, a more careful analysis shows that the values presented are related but not equivalent to \( \frac{153}{225} \). The correct equivalents of that fraction are \( \frac{3}{5} \) or 68% in decimal form (approx. 0.68), as opposed to the values listed, which relate to the overall figure but don’t represent the meeting attendance ratio directly.