First, we must convert these mixed fractions into improper fractions by multiplying the integer portion by the correct form of #1# and then adding the result to the fraction:

#(2 1/3)/(1 2/5) = ((3/3 xx 2) + 1/3)/((5/5 xx 1)+ 2/5) = (6/3 + 1/3)/(5/5 + 2/5) = (7/3)/(7/5)#

We can now divide this expression using this rule for dividing fractions:

#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#

Substituting the values from our previous calculation gives:

#(color(red)(7)/color(blue)(3))/(color(green)(7)/color(purple)(5)) = (color(red)(7) xx color(purple)(5))/(color(blue)(3) xx color(green)(7))= (cancel(color(red)(7)) xx color(purple)(5))/(color(blue)(3) xx cancel(color(green)(7))) = 5/3#

Or

#5/3 = (3 +2)/3 = 3/3 + 2/3 = 1 + 2/3 = 1 2/3#