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

Answer 1

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

Answer 2

To find the sum of two and one third plus five sixths of one and two fifths, first convert all the mixed numbers to improper fractions. Two and one third is equivalent to 7/3, one and two fifths is equivalent to 7/5. Next, find five sixths of 7/5 which is 35/30 or 7/6. Finally, add 7/3 and 7/6 to get 21/6 + 7/6 = 28/6 which simplifies to 4 and 2/6 or 4 and 1/3. Therefore, the sum is 4 and 1/3.