Answer:
   appropriately writing the proportion can reduce or eliminate steps required to solve it
Step-by-step explanation:
The proportion ...
   
is equivalent to the equation obtained by "cross-multiplying:"
   AD = BC
This equation can be written as proportions in 3 other ways:
   
   Effectively, the proportion can be written upside-down and sideways, as long as the corresponding parts are kept in the same order.
I find this most useful to ...
   a) put the unknown quantity in the numerator
   b) give that unknown quantity a denominator of 1, if possible.
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The usual method recommended for solving proportions is to form the cross-product, as above, then divide by the coefficient of the variable. If the variable is already in the numerator, you can simply multiply the proportion by its denominator.
<u>Example</u>:
   x/4 = 3/2
Usual method:
   2x = 4·3
   x = 12/2 = 6
Multiplying by the denominator:
   x = 4(3/2) = 12/2 = 6 . . . . . . saves the "cross product" step 
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<u>Example 2</u>:
   x/4 = 1/2 . . . . we note that "1" is "sideways" from x, so we can rewrite the proportion as ...
   x/1 = 4/2 . . . . . . written with 1 in the denominator
   x = 2 . . . . simplify
Of course, this is the same answer you would get by multiplying by the denominator, 4. 
The point here is that if you have a choice when you write the initial proportion, you can make the choice to write it with x in the numerator and 1 in the denominator.