Question

Write an expression si that when you divide 1/4 by a number the quotient will be greater than 1/4

Answer 1

we have a number x which divide 1/4, such that the quotient will be greater than 1/4.

This can be written mathematically as

`((1)/(4))/(x)>(1)/(4)`

If we move x to the right hand side, we obtain

`(1)/(4)>(1)/(4)\cdot x`

and finally,

`\begin{gathered} ((1)/(4))/((1)/(4))>x \\ 1>x \end{gathered}`

this means that, the number x must be less than one. For instance, if x=1/2, we have

`((1)/(4))/((1)/(2))=(1\cdot2)/(4\cdot1)=(2)/(4)=(1)/(2)`

and 1/2 is greater tha 1/4. Let us see another example, for instance, x=1/3

`((1)/(4))/((1)/(3))=(1\cdot3)/(4\cdot1)=(3)/(4)`

and 3/4 is greater than 1/4. And so on.