Question

Determine two fractions that are each greater than 2/5 whose product is less than 2/5

Answer 1

The possible two fractions are
`(1)/(2)` and
`(1)/(2)`

Explanation:

Consider the provided information.

We need to determine two fractions that are each greater than 2/5 whose product is less than 2/5.

Let the first fraction is
`(a)/(b)` and the second fraction is
`(c)/(d)`

It is given that
`(a)/(b)>(2)/(5)` and
`(c)/(d)>(2)/(5)` but
`(a)/(b)* (c)/(d)<(2)/(5)`

Condition I:

`(a)/(b)>(2)/(5)`

`5a>2b`

Condition II:

`(c)/(d)>(2)/(5)`

`5c>2d`

Condition III:

`(a)/(b)* (c)/(d)<(2)/(5)`

`5ac<2bd`

Substitute a = 2 in
`5a>2b`

`10>2b`

Substitute c = 2 in
`5c>2d`

`10>2d`

Substitute a = 2 and c = 2 in
`5ac<2bd`

`10<bd`

Now we need to select the value of b and d so that above 3 conditions are satisfied.

For this substitute b = 4 in
`10>2b`

`10>8` Which is true.

For this substitute d = 4 in
`10>2d`

`10>8` Which is true.

For this substitute b = 4 and d = 4 in
`10<bd`

`10<16` Which is true.

So, the possible two fractions are
`(2)/(4)` and
`(2)/(4)` or
`(1)/(2)` and
`(1)/(2)`