Question

Judy is playing a card game. She needs to select two cards below that have a sum greater

than 5. Which two cards should she select? Prove it.

`2 (2)/(5)`


`2 (2)/(7)`


`1 (7)/(8)`


`2 (1)/(10)`


`2 (5)/(8)`
​​
(posted again to put this in the right subject)

Answer 1

`2(2)/(5)  + 2(5)/(8) \simeq 5`

`2(2)/(7)  + 2(5)/(8)  \simeq 5`

Explanation:

Mixed fraction
`a(b)/(c)` can be converted into like or unlike fractions.

Here,
`a(b)/(c) =  (ac +b)/(b)`

So, convert all the given fractions as follows:

`2(2)/(5) =  (2(5) +2)/(5) = (12)/(5)  =2.4`

`2(2)/(7) =  (2(7) +2)/(7) = (16)/(7)  =2.4`

`1(7)/(8) =  (1(8) +7)/(8) = (15)/(8)  =1.8`

`2(1)/(10) =  (2(10) + 1)/(10) = (21)/(10)  =2.1`

`2(5)/(8) =  (2(8) +5)/(8) = (21)/(8)  =2.6`

Here, No Two fractions on addition gives a sum greater than 5.

But an approximate sum of 5 is given by adding 2.4 + 2.6 = 5

⇒
`2(2)/(5)  + 2(5)/(8) \simeq 5`

or ⇒
`2(2)/(7)  + 2(5)/(8)  \simeq 5`