Question

What is the exact value of 5 5/6-(1 1/4+3 7/8)

Answer 1

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

`\stackrel{mixed}{5(5)/(6)}\implies \cfrac{5\cdot 6+5}{6}\implies \stackrel{improper}{\cfrac{35}{6}} ~\hfill \stackrel{mixed}{1(1)/(4)} \implies \cfrac{1\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{5}{4}} \\\\\\ \stackrel{mixed}{3(7)/(8)}\implies \cfrac{3\cdot 8+7}{8}\implies \stackrel{improper}{\cfrac{31}{8}} \\\\[-0.35em] ~\dotfill`

`\cfrac{35}{6}-\left( \cfrac{5}{4}+\cfrac{31}{8} \right)\implies \cfrac{35}{6}-\cfrac{5}{4}-\cfrac{31}{8}\implies \cfrac{(8)35~~ - ~~(12)5~~ - ~~(6)31}{\underset{\textit{using this LCD}}{48}} \\\\\\ \cfrac{280~~ - ~~60~~ - ~~186}{48}\implies \cfrac{34}{48}\implies \cfrac{17}{24}`