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Question Number 119814 by bemath last updated on 27/Oct/20

If a,b,c and d is real numbers  satisfy (a/b)=(2/3), (c/d)=(4/5), (d/b)=(6/7)  then (a/c) =?

$${If}\:{a},{b},{c}\:{and}\:{d}\:{is}\:{real}\:{numbers} \\ $$$${satisfy}\:\frac{{a}}{{b}}=\frac{\mathrm{2}}{\mathrm{3}},\:\frac{{c}}{{d}}=\frac{\mathrm{4}}{\mathrm{5}},\:\frac{{d}}{{b}}=\frac{\mathrm{6}}{\mathrm{7}} \\ $$$${then}\:\frac{{a}}{{c}}\:=? \\ $$

Answered by Olaf last updated on 27/Oct/20

a = (2/3)b  c = (4/5) d = (4/5)((6/7)b) = ((24)/(35))b    (a/c) = (2/3)b×((35)/(24b)) = ((35)/(36))

$${a}\:=\:\frac{\mathrm{2}}{\mathrm{3}}{b} \\ $$$${c}\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{d}\:=\:\frac{\mathrm{4}}{\mathrm{5}}\left(\frac{\mathrm{6}}{\mathrm{7}}{b}\right)\:=\:\frac{\mathrm{24}}{\mathrm{35}}{b} \\ $$$$ \\ $$$$\frac{{a}}{{c}}\:=\:\frac{\mathrm{2}}{\mathrm{3}}{b}×\frac{\mathrm{35}}{\mathrm{24}{b}}\:=\:\frac{\mathrm{35}}{\mathrm{36}} \\ $$

Answered by talminator2856791 last updated on 27/Oct/20

 ((  (a/b)  )/( (c/d)))  =  (a/(  ((bc)/d)  ))  =  ((  ad  )/(bc))  =  ((2/3)/(  (4/5)  ))   (a/c)  =  ((ad)/(bc )) ÷ (d/b)  =  ((2/3)/(  (4/5)  )) ÷ (6/7)  =  ((35)/(36))

$$\:\frac{\:\:\frac{{a}}{{b}}\:\:}{\:\frac{{c}}{{d}}}\:\:=\:\:\frac{{a}}{\:\:\frac{{bc}}{{d}}\:\:}\:\:=\:\:\frac{\:\:{ad}\:\:}{{bc}}\:\:=\:\:\frac{\frac{\mathrm{2}}{\mathrm{3}}}{\:\:\frac{\mathrm{4}}{\mathrm{5}}\:\:} \\ $$$$\:\frac{{a}}{{c}}\:\:=\:\:\frac{{ad}}{{bc}\:}\:\boldsymbol{\div}\:\frac{{d}}{{b}}\:\:=\:\:\frac{\frac{\mathrm{2}}{\mathrm{3}}}{\:\:\frac{\mathrm{4}}{\mathrm{5}}\:\:}\:\boldsymbol{\div}\:\frac{\mathrm{6}}{\mathrm{7}}\:\:=\:\:\frac{\mathrm{35}}{\mathrm{36}} \\ $$

Answered by $@y@m last updated on 27/Oct/20

(a/c)=(a/b)×(b/d)×(d/c)=(2/3)×(7/6)×(5/4)=((35)/(36))

$$\frac{{a}}{{c}}=\frac{{a}}{{b}}×\frac{{b}}{{d}}×\frac{{d}}{{c}}=\frac{\mathrm{2}}{\mathrm{3}}×\frac{\mathrm{7}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{4}}=\frac{\mathrm{35}}{\mathrm{36}} \\ $$

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