Question Number 119814 by bemath last updated on 27/Oct/20
$${If}\:{a},{b},{c}\:{and}\:{d}\:{is}\:{real}\:{numbers} \\ $$$${satisfy}\:\frac{{a}}{{b}}=\frac{\mathrm{2}}{\mathrm{3}},\:\frac{{c}}{{d}}=\frac{\mathrm{4}}{\mathrm{5}},\:\frac{{d}}{{b}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${then}\:\frac{{a}}{{c}}\:=? \\ $$
Answered by Olaf last updated on 27/Oct/20
$${a}\:=\:\frac{\mathrm{2}}{\mathrm{3}}{b} \\ $$$${c}\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{d}\:=\:\frac{\mathrm{4}}{\mathrm{5}}\left(\frac{\mathrm{6}}{\mathrm{7}}{b}\right)\:=\:\frac{\mathrm{24}}{\mathrm{35}}{b} \\ $$$$ \\ $$$$\frac{{a}}{{c}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}{b}×\frac{\mathrm{35}}{\mathrm{24}{b}}\:=\:\frac{\mathrm{35}}{\mathrm{36}} \\ $$
Answered by talminator2856791 last updated on 27/Oct/20
$$\:\frac{\:\:\frac{{a}}{{b}}\:\:}{\:\frac{{c}}{{d}}}\:\:=\:\:\frac{{a}}{\:\:\frac{{bc}}{{d}}\:\:}\:\:=\:\:\frac{\:\:{ad}\:\:}{{bc}}\:\:=\:\:\frac{\frac{\mathrm{2}}{\mathrm{3}}}{\:\:\frac{\mathrm{4}}{\mathrm{5}}\:\:} \\ $$$$\:\frac{{a}}{{c}}\:\:=\:\:\frac{{ad}}{{bc}\:}\:\boldsymbol{\div}\:\frac{{d}}{{b}}\:\:=\:\:\frac{\frac{\mathrm{2}}{\mathrm{3}}}{\:\:\frac{\mathrm{4}}{\mathrm{5}}\:\:}\:\boldsymbol{\div}\:\frac{\mathrm{6}}{\mathrm{7}}\:\:=\:\:\frac{\mathrm{35}}{\mathrm{36}} \\ $$
Answered by $@y@m last updated on 27/Oct/20
$$\frac{{a}}{{c}}=\frac{{a}}{{b}}×\frac{{b}}{{d}}×\frac{{d}}{{c}}=\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{7}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{4}}=\frac{\mathrm{35}}{\mathrm{36}} \\ $$