Question

What is 7 2/3-(1 2/4+3 6/8)? And how do you get to the answer

Answer 1

in essence, PEMDAS, but let's firstly convert the mixed fractions to improper fractions.

`\stackrel{mixed}{7(2)/(3)}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} ~\hfill \stackrel{mixed}{1(2)/(4)} \implies \cfrac{1\cdot 4+2}{4} \implies \stackrel{improper}{\cfrac{6}{4}} \\\\\\ \stackrel{mixed}{3(6)/(8)}\implies \cfrac{3\cdot 8+6}{8}\implies \stackrel{improper}{\cfrac{30}{8}} \\\\[-0.35em] ~\dotfill`

`\cfrac{23}{3}-\left(\cfrac{6}{4}+\cfrac{30}{8} \right)\implies \cfrac{23}{3}-\left( \cfrac{(2)6~~ + ~~(1)30}{\underset{\textit{using this LCD}}{8}} \right)\implies \cfrac{23}{3}-\left( \cfrac{12+30}{8} \right)`

`\cfrac{23}{3}-\left( \cfrac{42}{8} \right)\implies \cfrac{23}{3}- \cfrac{42}{8}\implies \cfrac{(8)23~~ - ~~(1)42}{\underset{\textit{using this LCD}}{24}}\implies \cfrac{184-42}{24} \\\\\\ \cfrac{142}{24}\implies \cfrac{2\cdot 71}{2\cdot 12}\implies \cfrac{2}{2}\cdot \cfrac{71}{12}\implies \cfrac{71}{12}\implies 5(11)/(12)`