Question

Explain how you can find the missing number and 3 4/5 divided by something equals 2 5/7 then find the missing number

Answer 1

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

$\bf \stackrel{mixed}{3\frac{4}{5}}\implies \cfrac{3\cdot 5+4}{5}\implies \stackrel{improper}{\cfrac{19}{5}} ~\hfill \stackrel{mixed}{2\frac{5}{7}}\implies \cfrac{2\cdot 7+5}{7}\implies \stackrel{improper}{\cfrac{19}{7}} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \cfrac{~~\frac{19}{5}~~}{x}=\cfrac{19}{7}\implies \cfrac{~~\frac{19}{5}~~}{\frac{x}{1}}=\cfrac{19}{7}\implies \cfrac{19}{5}\cdot \cfrac{1}{x}=\cfrac{19}{7}\implies \cfrac{19}{5x}=\cfrac{19}{7} \\\\\\ \stackrel{}{\cfrac{7}{5x}=\cfrac{19}{19}}\implies \cfrac{7}{5x}=1\implies 7=5x\implies \cfrac{7}{5}=x\implies 1\frac{2}{5}=x$