Question 774031: Can someone please explain to me how to find the missing numerator in the equation,
2/3x=?/12x^3
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! You are seeming to want to find c in an equation,  .
The left side is EQUAL to the right hand side. If we multply both sides of the equation by the same factor, then we still have equality. We can undo the division by  on the right side by MULTIPLYING by . We must do this to both the left hand member AND the right hand member.
ANOTHER WAY BUT NOT WHAT YOU NEED FOR YOUR QUESTION:
If you multiply the left side member by 1, then this does not change the meaning or value of the left side member. How do we do this so the denominator will be ?
Denominator on the left member is 3*x
Denominator on the right member is 3*4*x*x*x
What factors and their counts are missing from the left hand side member? It needs 4, x, and another x.
We want a factor of 1 in the form of 
Now we can do this multiplication by 1:
and remember we are trying to multiply here to obtain the right hand side,
 , the equivalent fraction.
So our value for c, the numerator, is 
This is the usual way you would look for equivalent fractions in elementary school education, but once we become acquainted with using variables, we can often more easily use the idea of reciprocals, or multiplicative inverses for proportions.
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