Question

Find the quotient 16 2/3 ÷ 5 5/7​

Answer 1

let's convert firstly, the mixed fractions to improper fractions and then divide.

`\bf \stackrel{mixed}{16(2)/(3)}\implies \cfrac{16\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{50}{3}}~\hfill \stackrel{mixed}{5(5)/(7)}\implies \cfrac{5\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{40}{7}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{50}{3}/\cfrac{40}{7}\implies \cfrac{\stackrel{5}{\begin{matrix} 50 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}{3}\cdot \cfrac{7}{\underset{4}{\begin{matrix} 40 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}}\implies \cfrac{35}{12}\implies 2(11)/(12)`

Answer 2

2 11/12

Explanation:

(50/3)/(40/7)

=50/3*7/40

=5/3*7/4

=35/12

=2 11/12