Answer: Fuchsia can certainly be rooted from tip cuttings. You will need to start with freshly cut tips so the foliage is not wilted. Here are some general directions on how to do that, with illustrations. (You may need to cut and paste the complete url into your browser to make it work correctly.)
In general you will want to keep your fuchsia in morning only sun or bright dappled light all day so it is in the coolest possible location during the summer. (Once the weather turns too hot, it will stop blooming.) Water to keep the soil evenly moist but not saturated/sopping wet, and fertilize regularly with a water soluble fertilizer per the label directions. In the fall, bring it indoors for the winter if you want to keep it for next year.
Here are some additional pointers on fuchsia.
Enjoy your plant!
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