SOLUTION: Can someone please explain to me how to find the missing numerator in the equation, 2/3x=?/12x^3

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.
RELATED QUESTIONS
2x/2x-3 = ?/8x-27 Could someone please help me find the missing numerator? (answered by Theo)

Can someone please help me with this? Thank you in advance. 1. True or False: (answered by stanbon)

Can someone please help me with the following: What are all the possible rational roots... (answered by venugopalramana)

Hello. Can you help me to find the missing value in this equation: 2x+9=6x+? (x=-3/2) (answered by rothauserc)

Can someone please explain to me how to do this problem? Find the domain of the... (answered by jim_thompson5910)

Fill in the missing terms in the numerator, and then use long division to find the... (answered by rfer)

Rationalize each numerator. Simplify, if possible. 94.) √(5/3) Can someone (answered by Fombitz)

Please help me solve this equation: I have to find the missing expression. The letter... (answered by ankor@dixie-net.com)

Find the missing coordinate to complete the ordered pair solution to the given linear... (answered by checkley77)