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If a over b equals c over d then is it possible that a plus b equals c plus d If not then give Mathematical Reason for that?
Wiki User
∙ 13y ago
a/b=c/d
=>ad=bc
=>a =bc/d
b =ad/c
c =ad/b
d =bc/a
so if a+b=c+d is true
=> (bc/d)+(ad/c)=(ad/b)+(bc/a)
=> (bc2+ad2)/dc=(da2+cb2)/ab
=> ab(bc2+ad2)=dc(da2+cb2)
and since ad=bc,
=> ab(adc+add) =dc(ada+adc)
=> abadc+abadd =dcada + dcadc
=> abadc-dcadc =dcada-abadd
=> (ab-dc)adc =(dc-ab)add
ad cancels out
=> (ab-dc)c =(dc-ab)d
=> -(dc-ab)c =(dc-ab)d
=> -c = d
so there's your answer :)
Wiki User
∙ 13y ago
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