Question

Find the unit rate.
6 2/5 revolutions in 2 2/3 seconds

Answer 1

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

`\stackrel{mixed}{6(2)/(5)}\implies \cfrac{6\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{32}{5}}~\hfill \stackrel{mixed}{2(2)/(3)} \implies \cfrac{2\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{8}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{~~ \stackrel{ revolutions }{( 32)/(5 )} ~~}{\underset{ seconds }{(8)/(3)}}\implies \cfrac{32}{5}\cdot \cfrac{3}{8}\implies \cfrac{32}{8}\cdot \cfrac{3}{5}\implies 4\cdot \cfrac{3}{5}\implies \cfrac{12}{5}\implies 2.4~(revolutions)/(seconds)`