How do you add two fractions? I have a fraction I am trying to solve. I know the answer already, as Wolfram says it is $\frac{143}{300}$.
The fraction is:
$$\frac{5}{12} + \frac{3}{50} = \space ?$$ Please explain why and how your method works.

If $a=b$ then for any function $f(a)=f(b)$. Suppose 
$\displaystyle x=\frac{5}{12}+\frac{3}{50}$. Then 
$\displaystyle (12\cdot 50)\cdot x=(12\cdot 50)\cdot\left(\frac{5}{12}+\frac{3}{50}\right)$, so 
$\displaystyle 600x=\frac{12\cdot 50\cdot 5}{12}+\frac{12\cdot 50\cdot 3 }{50}=$
$=50\cdot 5+12\cdot 3=286$, why $\displaystyle x=\frac{286}{600}=\frac{143}{300}$.
