Adding fractions (to find an equal) without known denominator

Question

The question is "Find $v$":

$$\frac {1}{20}=\frac {1}{30}+\frac {1}{v}$$

I have no idea what I'm really doing so if someone could explain in a somewhat easy-to-understand way I'd really appreciate it!

Answer 1

Hint: $$ \dfrac{1}{v}=\dfrac{1}{20}-\dfrac{1}{30} $$ then find the inverse of $\dfrac{1}{v}$.

Answer 2

$$ \frac{1}{20}=\frac{1}{30}+\frac{1}{v}\\ \frac{1}{20}=\frac{v+30}{30v}\\ v+30=\frac{30v}{20}\\ v+30=\frac{3v}{2}\\ 30=\frac{v}{2}\\ v=60 $$

Answer 3

If you multiply both sides of the equation by $v$ you will no longer have an "unknown denominator":

\begin{align} \frac {1}{20} &= \frac {1}{30} + \frac {1}{v} \\ \left(\frac {1}{20}\right) v &= \left(\frac {1}{30} + \frac {1}{v} \right) v\\ \frac {1}{20} v &= \frac {1}{30} v + 1 \end{align}

Now this is in a form you should already know how to solve.

My first thought actually was to do it according to the answer by Emilio Novati (which I think is the answer you should accept) but sometimes if you don't see the "nicest" way to solve something, just trying different things will get you to a point where you know how to continue. The answer by Oussama Boussif is also valid: again, not the neatest solution, but if you just follow through with it, it will work out eventually.