Re-write each value as an improper fraction by multiplying the denominator by the whole number and adding the the numerator, then placing the result over the denominator.
#color(white)("XXX")color(blue)(2 1/2)=color(blue)((2xx2+1)/2)=color(blue)(5/2)#
and
#color(white)("XXX")color(green)(2 6/7)=color(green)((7xx2+6)/7)=color(green)(20/7)#
So
#color(white)("XXX")color(blue)(2 1/2) div color(green)(2 6/7)#
is the same as
#color(white)("XXX")color(blue)(5/2) div color(green)(20/7)#
Next remember that (in general)
#color(white)("XXX")#dividing by #a/b#
is the same as
#color(white)("XXX")#multiplying by #b/a#
Therefore
#color(white)("XXX")color(blue)(5/2)divcolor(green)(20/7)#
#color(white)("XXX")=color(blue)(5/2) xx color(green)(7/20)#
#color(white)("XXX")=(color(red)(cancel(color(blue)5))xxcolor(green)7)/(color(blue)2xxcolor(red)(cancel(color(green)20)_4#
#color(white)("XXX")=color(magenta)(7/8#
