Ratio Inequality

How can I prove that,

$\frac{{a}_{1}+{a}_{2}+\cdots +{a}_{n}}{{b}_{1}+{b}_{2}+\cdots +{b}_{n}}\le \underset{i}{max}\left\{\frac{{a}_{i}}{{b}_{i}}\right\}$

where $1\le i\le n$, and ${a}_{i}\ne {a}_{j}$ and ${b}_{i}\ne {b}_{j},\mathrm{\forall}i\ne j$

Edit I have figured out that the above assumptions about ${a}_{i}$, and ${b}_{i}$ are not needed.

How can I prove that,

$\frac{{a}_{1}+{a}_{2}+\cdots +{a}_{n}}{{b}_{1}+{b}_{2}+\cdots +{b}_{n}}\le \underset{i}{max}\left\{\frac{{a}_{i}}{{b}_{i}}\right\}$

where $1\le i\le n$, and ${a}_{i}\ne {a}_{j}$ and ${b}_{i}\ne {b}_{j},\mathrm{\forall}i\ne j$

Edit I have figured out that the above assumptions about ${a}_{i}$, and ${b}_{i}$ are not needed.