Question

What is 3 - 2 1/3 x 3/14 + 1 1/3 ÷ 4/5

Answer 1

let's firstly convert the mixed fractions to improper fractions, and then let's process them by PEMDAS.

`\stackrel{mixed}{2(1)/(3)}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}}~\hfill \stackrel{mixed}{1(1)/(3)} \implies \cfrac{1\cdot 3+1}{3} \implies \stackrel{improper}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ 3-2(1)/(3) * \cfrac{3}{14} + 1(1)/(3) / \cfrac{4}{5}\implies 3-\cfrac{7}{3} * \cfrac{3}{14} + \cfrac{4}{3} / \cfrac{4}{5}\implies 3-\cfrac{7}{14} * \cfrac{3}{3} + \cfrac{4}{3} / \cfrac{4}{5}`

`3-\cfrac{1}{2} * 1 + \cfrac{4}{3} / \cfrac{4}{5}\implies 3-\cfrac{1}{2} + \cfrac{4}{3} / \cfrac{4}{5}\implies 3-\cfrac{1}{2} + \cfrac{4}{3} * \cfrac{5}{4}\implies 3-\cfrac{1}{2} + \cfrac{4}{4} * \cfrac{5}{3} \\\\\\ 3-\cfrac{1}{2} + 1 * \cfrac{5}{3}\implies 3-\cfrac{1}{2} + \cfrac{5}{3}\implies \cfrac{(6)3~~ - ~~(3)1~~ + ~~(2)5}{\underset{\textit{using this LCD}}{6}} \\\\\\ \cfrac{18-3+10}{6}\implies \cfrac{15}{6}\implies \cfrac{5}{2}\implies 2(1)/(5)`