I guess some will smile about this post. But for me it wasn't that trivial to cut an object exactly in half with Inkscape. Maybe there are better ways to do that, but here is my simple one.
Let us assume that we have a yellow circle like this.
We will use the Align and Distribute tools to cut the object in half. Important for the Align tool is the the option Relative to. I like always to use Last selected, but you can choose what ever you want. This option means that my last selected object is always the anchor.
We will create a red rectangle that is higher and a little bit wider than the half of the circle.
After that we will select first the red rectangle and after that the yellow circle. Let us push the button Align left edges of objects to the right edge of the anchor in the Align and Distribute tools. That should be the button with the yellow square in the left upper corner. The red rectangle should be moved exactly to the right side of the yellow circle.
Let us duplicate the red rectanlge and fill it with the color blue. I have moved the blue rectangle a little bit more left after all.
Let us select all three objects. After that we can push the button Distribute left edges equidistantly. That should be the first button in the Distribute section. The left edge of blue rectangle should be on the half of the circle after all.
We can select the yellow circle and the blue rectanlge. Let us cut the blue rectangle out of the yellow circle. That can be done with Difference in the menu item Path. I have also removed the red rectangle. After all we should have a exactly halved yellow circle.
This is a fast and easy way to bisect objects in Inkscape. I hope it is clear that we could also cut objects in thirds with the same method.