Question

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

Answer 1

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.

`\stackrel{mixed}{2(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(9)/(20)=r`

Answer 2

`r=(21)/(20)`

Explanation:

Given the following question:


`(1)/(4) =r-(4)/(5)`
Add 4/5s on both sides:

`-(4)/(5) +(4)/(5) =0`

`(1)/(4) +(4)/(5)`
Find the LCM:

`(5)/(20)+(16)/(20)`

`(5+16)/(20)`

`(21)/(20)`

`r=(21)/(20)`

Hope this helps.