Given:
Total number of students at Colfax Middle School = 270
Ratio of boys to girls is 5:4.
Total number of students at Winthrop Middle School = 180
Ratio of boys to girls is 4:5.
The two schools hold a dance and all students from both schools attend.
To find:
The fraction of the students at the dance are girls
Solution:
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.

Number of boys

Number of girls

There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.

Number of boys

Number of girls

Now,
Total number of students in both schools


Total number of girls in both schools


The fraction of the students at the dance are girls is



Therefore, the required fraction is
.