What we have here is:
$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{4}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}$$
The easiest method to do this is to convert them all to even denominators.
We can do that by multiplying them by multiples of two.
$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ * $${\frac{{\mathtt{4}}}{{\mathtt{4}}}}$$ = $${\frac{{\mathtt{4}}}{{\mathtt{8}}}}$$
$${\frac{{\mathtt{1}}}{{\mathtt{4}}}}$$ * $${\frac{{\mathtt{2}}}{{\mathtt{2}}}}$$ = $${\frac{{\mathtt{2}}}{{\mathtt{8}}}}$$
Now that they all have a denominator of eight, we can esily add the numerators:
$${\frac{{\mathtt{4}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}$$ = $${\frac{{\mathtt{7}}}{{\mathtt{8}}}}$$
.