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:
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Simplifying the Fraction: The fraction \( \frac{153}{225} \) can be simplified. The greatest common divisor (GCD) of 153 and 225 is 51.
So,
\[ \frac{153 \div 51}{225 \div 51} = \frac{3}{5}. \]
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Calculating Percentage: To find the percentage of employees who attended:
\[ \text{Percentage} = \left( \frac{153}{225} \right) \times 100 \approx 68%. \]
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Decimal Form: Dividing 153 by 225 gives:
\[ \frac{153}{225} \approx 0.68. \]
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Reciprocal: The reciprocal of the fraction \( \frac{153}{225} \) would be \( \frac{225}{153} \).
\[ \frac{225}{153} \approx 1.47. \]
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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.
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