Certainly, let's solve each part of the problem step-by-step.
### Part 1:
In a class, there were 45 students. If [tex]\(\frac{3}{5}\)[/tex] of them were boys, how many were girls?
1. Determine the number of boys:
Given that [tex]\(\frac{3}{5}\)[/tex] of the students were boys:
[tex]\[
\text{Number of boys} = \frac{3}{5} \times 45
\][/tex]
Calculate this:
[tex]\[
\text{Number of boys} = \frac{3}{5} \times 45 = 27
\][/tex]
2. Determine the number of girls:
The total number of students is 45. Therefore, the number of girls will be:
[tex]\[
\text{Number of girls} = 45 - \text{Number of boys} = 45 - 27 = 18
\][/tex]
Therefore, the number of girls in the class is 18.
### Part 2:
[tex]\(\frac{1}{3}\)[/tex] parts of the total students in a school are girls. If the number of girls is 150, find the total number of students.
1. Determine the total number of students:
Given that [tex]\(\frac{1}{3}\)[/tex] of the total students are girls and the number of girls is 150:
[tex]\[
\text{Total students} = 150 \div \frac{1}{3}
\][/tex]
Simplify this:
[tex]\[
\text{Total students} = 150 \times 3 = 450
\][/tex]
Therefore, the total number of students in the school is 450.
### Part 3:
There are 450 boys in a school. If this number is [tex]\(\frac{3}{5}\)[/tex] of the total students, find the number of girls.
1. Determine the total number of students:
Given that 450 boys represent [tex]\(\frac{3}{5}\)[/tex] of the total number of students:
[tex]\[
\text{Total students} = 450 \div \frac{3}{5}
\][/tex]
Simplify this by multiplying by the reciprocal of [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\text{Total students} = 450 \times \frac{5}{3} = 450 \times \frac{5}{3} = 750
\][/tex]
2. Determine the number of girls:
The total number of students is 750. Therefore, the number of girls will be:
[tex]\[
\text{Number of girls} = 750 - 450 = 300
\][/tex]
Therefore, the number of girls in the school is 300.
