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 A 153/225 = 17/25 = 0.68 = 68% and why
Answers
GPT-4o mini
To determine if the provided statement shows values that are all equivalent to the fraction of employees who attended the meeting, we start with the fraction itself:
\[
\frac{153}{225}
\]
Now, let’s simplify this fraction:
1. **Finding the GCD**: The greatest common divisor (GCD) of 153 and 225 is 9.
2. **Simplifying the fraction**:
\[
\frac{153 \div 9}{225 \div 9} = \frac{17}{25}
\]
So, \(\frac{153}{225} = \frac{17}{25}\) is correct.
Next, we convert \(\frac{17}{25}\) into decimal form:
\[
\frac{17}{25} = 17 \div 25 = 0.68
\]
We can also convert it to a percentage:
\[
0.68 \times 100 = 68\%
\]
Putting it all together, we find:
- \( \frac{153}{225} = \frac{17}{25} = 0.68 = 68\% \)
Thus, the statement **A** is indeed correct as it shows that all values presented (\(\frac{153}{225}\), \(\frac{17}{25}\), \(0.68\), and \(68\%\)) are equivalent.
**Why it’s correct:**
All these values represent the same quantity, indicating that 68% of the employees attended the meeting. The fraction \(\frac{153}{225}\) simplifies correctly, and both the decimal and percentage forms accurately represent the fraction.
\[
\frac{153}{225}
\]
Now, let’s simplify this fraction:
1. **Finding the GCD**: The greatest common divisor (GCD) of 153 and 225 is 9.
2. **Simplifying the fraction**:
\[
\frac{153 \div 9}{225 \div 9} = \frac{17}{25}
\]
So, \(\frac{153}{225} = \frac{17}{25}\) is correct.
Next, we convert \(\frac{17}{25}\) into decimal form:
\[
\frac{17}{25} = 17 \div 25 = 0.68
\]
We can also convert it to a percentage:
\[
0.68 \times 100 = 68\%
\]
Putting it all together, we find:
- \( \frac{153}{225} = \frac{17}{25} = 0.68 = 68\% \)
Thus, the statement **A** is indeed correct as it shows that all values presented (\(\frac{153}{225}\), \(\frac{17}{25}\), \(0.68\), and \(68\%\)) are equivalent.
**Why it’s correct:**
All these values represent the same quantity, indicating that 68% of the employees attended the meeting. The fraction \(\frac{153}{225}\) simplifies correctly, and both the decimal and percentage forms accurately represent the fraction.