Answer :
Answer:
To find out what fraction of the total number of pupils are girls, we can follow these steps:
1. Let's denote the total number of pupils as \( P \).
2. According to the problem, \( \frac{3}{7} \) of the pupils are boys.
3. This means that \( \frac{4}{7} \) of the pupils are girls because \( 1 - \frac{3}{7} = \frac{4}{7} \).
4. We know there are 324 girls, so \( \frac{4}{7}P = 324 \).
5. To find \( P \), we solve for \( P = \frac{324}{4} \times 7 = 81 \times 7 = 567 \).
Now that we know the total number of pupils (P) is 567, and all of them are either boys or girls, we can confirm that the fraction of pupils who are girls is indeed \( \frac{4}{7} \), since \( 324 \) is \( \frac{4}{7} \) of \( 567 \).
So, the fraction of the total number of pupils that are girls is \( \frac{4}{7} \).
Step-by-step explanation:
Answer:
Step-by-step explanation:
First, let's find the total number of pupils in the school. We know that \(\frac{3}{7}\) of the pupils are boys. Therefore, \(\frac{4}{7}\) of the pupils are girls.
Since we know that there are 324 girls, we can set up the following equation to find the total number of pupils:
\[ \frac{4}{7} \times \text{Total number of pupils} = 324 \]
To solve for the total number of pupils, we multiply both sides by \(\frac{7}{4}\):
\[ \text{Total number of pupils} = \frac{7}{4} \times 324 = 567 \]
Now that we know the total number of pupils, we can find the fraction of the total number of pupils that are girls:
\[ \frac{\text{Number of girls}}{\text{Total number of pupils}} = \frac{324}{567} \]
To simplify this fraction, we can find the greatest common divisor (GCD) of 324 and 567, which is 81. Dividing both the numerator and the denominator by 81:
\[ \frac{324}{567} = \frac{324 \div 81}{567 \div 81} = \frac{4}{7} \]
Therefore, \(\frac{4}{7}\) of the total number of pupils are girls.