Question

What is the sum of the two largest numbers in the list

$$\frac 13,~\frac 27,~\frac 3{10},~\frac 4{13},~\frac 5{17}~?$$Express your answer in simplest form.

Answer 1

`(25)/(39)`

Explanation:

The given numbers are

`\frac 13,~\frac 27,~\frac 3{10},~\frac 4{13},~\frac 5{17}`

We need to find the sum of the two largest numbers in the list.

The values of each number are

`(1)/(3)=0.33..`

`(2)/(7)\approx 0.286`

`(3)/(10)=0.3`

`(4)/(13)\approx 0.308`

`(5)/(17)\approx 0.294`

Using these we can say that

`(2)/(7)<(5)/(17)< (3)/(10)< (4)/(13)< (1)/(3)`

It means two largest numbers in the list are
`(4)/(13)\text{ and } (1)/(3)`.

The sum of these two number is

`Sum=(4)/(13)+(1)/(3)`

`Sum=(4\cdot 3+1\cdot 13)/(39)`

`Sum=(25)/(39)`

Therefore, the sum of the two largest numbers in the list is
`(25)/(39)`.