Question

(7 5/6 - 5 1/3) + 1 1/9

Answer 1

let's firstly convert the mixed fractions to improper fractions.

`\stackrel{mixed}{7(5)/(6)}\implies \cfrac{7\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{47}{6}} ~\hfill \stackrel{mixed}{5(1)/(3)} \implies \cfrac{5\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{16}{3}} \\\\\\ \stackrel{mixed}{1(1)/(9)}\implies \cfrac{1\cdot 9+1}{9}\implies \stackrel{improper}{\cfrac{10}{9}} \\\\[-0.35em] ~\dotfill`

`\left( \cfrac{47}{6}-\cfrac{16}{3} \right)+\cfrac{10}{9}\implies \cfrac{47}{6}-\cfrac{16}{3}+\cfrac{10}{9}\implies \cfrac{(3)47~~ - ~~(6)16~~ + ~~(2)10}{\underset{\textit{using this LCD}}{18}} \\\\\\ \cfrac{141-96+20}{18}\implies \cfrac{65}{18}\implies {\Large \begin{array}{llll} 3(11)/(18) \end{array}}`