There's a question asking me how many 2/3 fit into 6. I don't even know where to begin. Can someone help?

Question

anonymous · Answer

$$\frac{ 2 }{ 3 } \times x=6$$
$$x=\frac{ 6\times3 }{ 2 }=\frac{ 18 }{2 }=9$$

naveen · Answer

Wow.  I never thought of doing that.  Thanks.  This is reallyhelpful.

anonymous · Answer

no problem :)

naveen · Answer

Are you in college? You seem very smart.

anonymous · Answer

I am in university :)

nubeer · Answer

that's cool.. :)

anonymous · Answer

Why are you allowed to move the x to the other side? 
How come there's a 2 on the bottom now?

anonymous · Answer

@cthomasknight, the easy way to remember what to do is to keep in mind that 'dividing by a fraction is the same as multiplying by the inverse of the fraction'. That's what Gretacig does in her response:

2/3 * x = 6 but you need an equation with a shape like x = ....

This can only be achieved by dividing left and right by 2/3. Now apply the rule above, about multiplying by the inverse of the fraction (so dividing by 2/3 is multiplying by 3/2).

2/3 * 2/3 * x = 3/2 * 6, where 3/2 * 2/3 = 1, leading to

1*x = 2/3 * 6 ==> x = 18