First, convert each mixed number to an improper fraction:
#1 1/15 = 1 + 1/5 = (15/15 xx 1) + 1/15 15/15 + 1/15 = (15 + 1)/15 = 16/15#
#3 3/10 = 3 + 3/10 = (10/10 xx 3) + 3/10 = 30/10 + 3/10 = (30 + 3)/10 = 33/10#
#2 4/5 = 2 + 4/5 = (5/5 xx 2) + 4/5 = 10/5 + 4/5 = (10 + 4)/5 = 14/5#
We can rewrite the expression as:
#16/15 + 33/10 + 14/5#
To add fractions they must be over common denominators. We can multiply each fraction by the appropriate form of #1# and then add the numerators:
#(2/2 xx 16/15) + (3/3 xx 33/10) + (6/6 xx 14/5) =>#
#(2 xx 16)/(2 xx 15) + (3 xx 33)/(3 xx 10) + (6 xx 14)/(6 xx 5) =>#
#32/30 + 99/30 + 84/30 =>#
#(32 + 99 + 84)/30 =>#
#(131 + 84)/30 =>#
#215/30#
If necessary, we can convert this to a mixed number:
#215/30 = (210 + 5)/30 = 210/30 + 5/30 = 7 + 5/30 = 7 + 1/6 = 7 1/6#
