Float - rule for positioning depended on something, so you will never align object without that something.
So, you should use following sequence:
<div style="background-color:Aqua">
<div style="float:right;max-width:50%;">Right</div><!-- 100% by default -->
<div>Left</div>
<div style="clear:right;"></div><!-- closing the floating -->
</div>
and otherwise:
<div style="background-color:Aqua">
<div style="float:left;max-width:50%;">Left</div>
<div>Right</div>
<div style="clear:left;"></div>
</div>
or both:
<div style="background-color:Aqua">
<div style="float:left;max-width:30%;">Left</div>
<div style="float:right;max-width:30%;">Right</div>
<div>Center</div>
<div style="clear:both;"></div>
</div>