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

$\frac{\frac{1}{4}}{x}>\frac{1}{4}$

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

$\frac{1}{4}>\frac{1}{4}\cdot x$

and finally,

$\begin{gathered} \frac{\frac{1}{4}}{\frac{1}{4}}>x \\ 1>x \end{gathered}$

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

$\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{1\cdot2}{4\cdot1}=\frac{2}{4}=\frac{1}{2}$

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

$\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{1\cdot3}{4\cdot1}=\frac{3}{4}$

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