>>1742725You don't need to break the gear apart. Make the gear on its own first. Make a circle and fill it. Then add 5 rounded rectangles to represent the gears, select all objects, and unite them. It will make a compound path that represents the gear. Next, make a fill for the purple shapes, but also give them a white stroke. It is difficult to tell since the image is on a white background, but you can tell this is how it is done in the original by looking at the left side with the small shape that goes into the gear.
If you really don't want the purple shapes to have a stroke and you actually want the gear to be all segmented, then you will have to draw shapes around the areas you want deleted in the same layer (but above the compounded path) and ctrl+- it each time. That explanation can be found above in the Inkscape tutorial on page 4.
