#4 3/10# can be written as an improper fraction
#color(white)("XXX")(4xx10+3)/10=43/10#
#3 3/5# can be written as an improper fraction
#color(white)("XXX")(3xx5+3)/5=(18/5)#
#18/5# can be written with a denominator of #10# to match the #4 3/10=43/10# term
#color(white)("XXX")(18xx2)/(5xx2)=36/10#
Therefore
#color(white)("XXX")4 3/10 - 3 3/5#
is equivalent to
#color(white)("XXX")43/10 - 36/10#
#color(white)("XXX")=7/10#