Question

Simplify -3 1/9 - (-8 1/3)​

Answer 1

let's firstly convert the mixed fractions to improper fractions and then proceed.

`\stackrel{mixed}{3(1)/(9)}\implies \cfrac{3\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{28}{9}} ~\hfill \stackrel{mixed}{8(1)/(3)}\implies \cfrac{8\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{25}{3}} \\\\[-0.35em] ~\dotfill`

`-\cfrac{28}{9}~~ - ~~\left( -\cfrac{25}{3} \right)\implies -\cfrac{28}{9}~~ + ~~\left( \cfrac{25}{3} \right)\implies -\cfrac{28}{9} + \cfrac{25}{3} \\\\\\ \stackrel{\textit{using the LCD of 9}}{\cfrac{1(-28)~~ + ~~3(25)}{9}}\implies \cfrac{-28+75}{9}\implies \cfrac{-47}{9}\implies {\LARGE \begin{array}{llll} -5(2)/(9) \end{array}}`