Question

Which ratio has the unit rate of 4

Answer 1

`2(1)/(2) ~~ : ~~ \cfrac{5}{8}\implies \cfrac{5}{2} ~~ : ~~ \cfrac{5}{8}\implies \cfrac{ ~~ (5)/(2) ~~ }{(5)/(8)}\implies \cfrac{5}{2}\cdot \cfrac{8}{5}\implies 4 ~~ \checkmark \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1}{8}~~ : ~~1\implies \cfrac{ ~~ (1)/(8)~~ }{1}\implies \cfrac{1}{8} ~~ \bigotimes \\\\[-0.35em] ~\dotfill`

`4~~ : ~~1(1)/(4)\implies 4~~ : ~~(5)/(4)\implies \cfrac{4}{ ~~ (5)/(4) ~~ }\implies \cfrac{4}{1}\cdot \cfrac{4}{5}\implies \cfrac{16}{5}~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ \cfrac{7}{8}~~ : ~~3(1)/(2)\implies \cfrac{7}{8}~~ : ~~\cfrac{7}{2}\implies \cfrac{ ~~ (7)/(8)~~ }{(7)/(2)}\implies \cfrac{7}{8}\cdot \cfrac{2}{7}\implies \cfrac{1}{4}~~ \bigotimes \\\\[-0.35em] ~\dotfill`

`4(1)/(3)~~ : ~~3\implies \cfrac{13}{3}~~ : ~~3\implies \cfrac{ ~~ (13)/(3)~~ }{3}\implies \cfrac{13}{3}\cdot \cfrac{1}{3}\implies \cfrac{13}{9} ~~ \bigotimes \\\\[-0.35em] ~\dotfill\\\\ 2~~ : ~~\cfrac{1}{2}\implies \cfrac{2}{ ~~ (1)/(2) ~~ }\implies \cfrac{2}{1}\cdot \cfrac{2}{1}\implies 4 ~~ \checkmark`