First, convert each mixed number to an improper fraction:
#-(7 + 1/6) + (3 + 5/6) =>#
#-([6/6 xx 7] + 1/6) + ([6/6 xx 3] + 5/6) =>#
#-(42/6 + 1/6) + (18/6 + 5/6) =>#
#-(42+ 1)/6 + (18 + 5)/6 =>#
#-43/6 + 23/6 =>#
#(-43 + 23)/6 =>#
#-20/6#
We can now convert this to a mixed number:
#-(18 + 2)/6 =>#
#-(18/6 + 2/6) =>#
#-(3 + 2/(3 xx 2)) =>#
#-(3 + color(red)(cancel(color(black)(2)))/(3 xx color(red)(cancel(color(black)(2))))) =>#
#-(3 + 1/3) =>#
#-3 1/3#
Another process starts with rewrite the expression as:
#-(7 + 1/6) + (3 + 5/6) =>#
#3 - 7 + 5/6 - 1/6 =>#
#-4 + (5 - 1)/6#
#-4 + 4/6 =>#
#-(6/6 xx 4) + 4/6 =>#
#-24/6 + 4/6 =>#
#(-24 + 4)/6 =>#
#-20/6#
We can now convert this to a mixed number:
#-(18 + 2)/6 =>#
#-(18/6 + 2/6) =>#
#-(3 + 2/(3 xx 2)) =>#
#-(3 + color(red)(cancel(color(black)(2)))/(3 xx color(red)(cancel(color(black)(2))))) =>#
#-(3 + 1/3) =>#
#-3 1/3#
