What is the sum of Two and one third plus five sixths of one and two fifths?

x = 2 1/2 + (5/6 x 1 2/5)

convert the 1 2/5 to a fraction in 1/5 only

x = 2 1/2 + (5/6 x 7/5)

separate the 5 from the 1/6

x = 2 1/2 + (5 x 7/5 x 1/6)

5 x 7/5 = 7/1, i.e. the 5's cancel each other out.

x = 2 1/2 + (7 x 1/6)

7 x 1/6 = 7/6

x = 2 1/2 + 7/6

convert the 2 1/2 to a fraction in terms of 1/6, i.e multiply the 1/2 by 3/3 => 3/6 and the whole number by 6 and add them together

x = 15/6 + 7/6

finally add the two fractions

x = 22/6

and reduce....

x = 3 4/6

....to the simplest fraction

x = 3 2/3

QED