Of this year’s graduating seniors at South High, 9/10 will be going to college, while the rest will be going to four-year college, while the rest will be going to two-year college. What part of the class will be going to two-year colleges?

You know that 9/10 of the class is going to college.
4/5 of those 9/10 will go to a four-year college, while the remaining 1/5 will go to a two-year college.
To determine what part of the class does the 1/5 of 9/10 represent, you have to multiply both fractions:
[tex]\frac{9}{10}\cdot\frac{1}{5}=\frac{9\cdot1}{10\cdot5}=\frac{9}{50}[/tex]9/50 of the graduating seniors will be going to a two-year college.