SOLUTION: 5/3 is to 1/5 as 5 is to what does this mean ?

Question 765341: 5/3 is to 1/5 as 5 is to what does this mean ?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the problem states:
5/3 is to 1/5 as 5 is to what?
replace what with x and you get:
5/3 is to 1/5 as 5 is to x.
this is a proportion formula that can also be expressed as:
(5/3) / (1/5) = 5 / x
in a proportion formula, the ratios on the left side of the equation have to be equal to the ratios on the right side of the equatioln.
the ratio on the left side of the equation is (5/3) / (1/5).
the ratio on the right side of the equation is (5/x).
you need to solve for the value of x that makes these ratios equal to each other.
you can cross multiply to get:
(5/3) * x = (1/5 * 5
this simplifies to:
5/3 * x = 1
divide both sides of this equation to get:
x = 1 / (5/3) which is the same as:
x = 1 * (3/5) which simplifies to:
x = (3/5)
your ratio formula of:
(5/3 / (1/5) = 5 / (3/5)
in termsof the original problem statement, this ratio becomes:
5/3 is to 1/5 as 5 is to (3/5)
if the ratio holds, then (5/3) / (1/5) should be the same as 5 / (3/5)
take 5/3 and divide it by (1/5) and you get (5/3 * 5) = 25/3.
take 5 and divide it by (3/5) and you get (5 * (5/3) = 25/3.
the ratios are the same which means that your value of x = (3/5) is good.

proportions mean that the ratios expressed in the proportion are equal.
proportions are expressed in any of the following ways:

a is to b as c is to d
a/b = c/d
a:b = c:d

all these different forms mean the same thing.

your equation stated the proportion in the first way which was translated to the second way.
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