Question

Create three fractions whose product is -5/24. You may only use fractions between -8/9 to 8/9 and you can only use a fraction once.

Answer 1

`-(5)/(6),(1)/(3), \;and\:(3)/(4)`

Explanation:

We are required to create three fractions whose product is
`-(5)/(24)` where each fraction x is such that:
`-(8)/(9)<x< (8)/(9)`

Consider the fractions:

`-(5)/(6),(1)/(3), \;and\:(3)/(4)`

Each fraction lies in the interval
`-(8)/(9)<x< (8)/(9)`

Their product:

`-(5)/(6)*(1)/(3)*(3)/(4)=(-5*1*3)/(6*3*4)\\=-(15)/(72)\\=-(5)/(24)`