1. just checking

The teacher gives the following homework assignment: You have to write an essay by tomorrow. You may work alone or in boy-girl pairs. As it turned out, 2/3 of the boys and 3/5 of the girls worked in pairs. What fraction of the class worked alone?

3 and 5
lcm=15

3/5=9/15 2/3=10/15

9/15-10/15=1/15

I'm I doing the right thing

2. Hello, mr.toronto!

The teacher gives the following homework assignment: You have to write an essay.
You may work alone or in boy-girl pairs.
As it turned out, 2/3 of the boys and 3/5 of the girls worked in pairs.
What fraction of the class worked alone?

Let $B$ = number of boys in the class.
Let $G$ = number of girls in the class.
\. . Then there are $A+B$ students in the class.

2/3 of the boys worked in pairs: $\frac{2}{3}B$
They paired off with 3/5 of the girls: $\frac{3}{5}G$
. . Hence: . $\frac{2}{3}B = \frac{3}{5}G\quad\Rightarrow\quad B = \frac{9}{10}G\;\;{\color{blue}[1]}$

Then 1/3 of the boys worked alone: . $\frac{1}{3}B$
. . and 2/5 of the girls worked alone: . $\frac{2}{5}G$
The fraction of students working alone is: . $\frac{\frac{1}{3}B + \frac{2}{5}G}{B + G}\;\;{\color{blue}[2]}$

Substitute [1] into [2]: . $\frac{\dfrac{1}{3}\left(\dfrac{9}{10}G\right) + \dfrac{2}{5}G}{\dfrac{9}{10}G + G} \;=\;\frac{\dfrac{7}{10}G}{\dfrac{19}{10}G} \;=\;\boxed{\frac{7}{19} }$