SOLUTION: if a:b=2:3, b:c=4:5, c:d= 6:7 so find a:b:c:d?

Question 761707: if a:b=2:3, b:c=4:5, c:d= 6:7 so find a:b:c:d?
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
A . . . .2 . . . . .B . . . 4 . . . . . C . . . 6
-- . = . --- . . . . -- . = . -- . . . . . -- .= .----
B . . . .3 . . . . .C . . . 5 . . . . . D . . . 7

The best way I think I can explain this is first to find the LCM of , and , which, of course, is .
Now express each of the fractions above with a denominator of .
So,

. . . . . . . . . ( 1 )
In the last ratio, we have as . How can we express as ?
Well,
, so if we want to express this as, then

So
Therefore we can express as . . . . . . . . ( 2 )
We have that , and now we want to get it so that is .
So
Hence
Therefore we can express as . . . . . . . . ( 3 )
Collecting the three ratios ( 1 ), ( 2 ) and ( 3 ) together, we have
A . . . 48 . . . . . B . . . .72 . . . . . C . . . 90
-- . = . ---- . . . . --- . = . ---- . . . . . -- .= .-----
B . . . 72 . . . . . C . . . .90 . . . . . D . . .105
From which you can see that
or, dividing by , you get in lowest terms

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