first we want to simplify the denominator
[tex] \frac{1}{4} - \frac{5}{2} [/tex]
to subtract, we convert 5/2 to have a denominator of 4
[tex] \frac{1}{4} - \frac{10}{4} [/tex]
[tex] - \frac{9}{4} [/tex]
now we can put this back into the original problem
[tex] \frac{4}{ - \frac{9}{4} } [/tex]
this equation can also be read as
[tex]4 \div - \frac{9}{4} [/tex]
when dividing, we flip the right side and switch to multiplication
[tex] \frac{4}{1} \times - \frac{4}{9} = - \frac{16}{9} [/tex]
[tex]answer = - \frac{16}{9} [/tex]
