Question

What is (7 5/6−5 1/3)+1 1/9 ?

Answer 1

let's firstly convert all 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{we'll be using this LCD}}{18}} \\\\\\ \cfrac{141~~ - ~~96~~ + ~~20}{18}\implies \cfrac{65}{18}\implies {\Large \begin{array}{llll} 3(11)/(18) \end{array}}`