Question Solve the equation. −2 1/4=r−4/5 r=

Answer:[tex]r=\frac{21}{20}[/tex]Step-by-step explanation:Given the following question:[tex]\frac{1}{4} =r-\frac{4}{5}[/tex]Add 4/5s on both sides:[tex]-\frac{4}{5} +\frac{4}{5} =0[/tex][tex]\frac{1}{4} +\frac{4}{5}[/tex]Find the LCM:[tex]\frac{5}{20}+\frac{16}{20}[/tex][tex]\frac{5+16}{20}[/tex][tex]\frac{21}{20}[/tex][tex]r=\frac{21}{20}[/tex]Hope this helps.

let's firstly convert the mixed fraction to improper fraction, now keeping in mind that the LCD of the denominators 4 and 5 is 20, let's use that LCD to do away with the denominators.[tex]\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{9}{4}=r-\cfrac{4}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{20}}{20\left( -\cfrac{9}{4} \right)=20\left( r-\cfrac{4}{5} \right)}\implies -45=20r-16 \\\\\\ -29=20r\implies -\cfrac{29}{20}=r\implies -1\frac{9}{20}=r[/tex]