My first jade

I trimmed off half the limbs two months ago, I have new growth but I am afraid the limbs are getting too long, two have fallen off in the last month.
I did just cut off a few branches and booked them into the soil at the base of the mama Jade.
I love this Jade and I want to do right by it. It was given to me by my grandmother.
Any help would be appreciated!
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Also, can anyone tell me the scientific name for my Jade?
https://www.google.com/search?tbm=isch&source=hp&biw=1093&bih=498&ei=KiowWrCcM8X9ac6krsgI&q=Crassula+argentea&oq=Crassula+argentea&gs_l=img.12...3738.9246.0.12333.21.9.0.0.0.0.0.0..0.0....0...1ac.1.64.img..21.0.0.0...0.PiA87lq0NJ8#imgrc=eQK1mrauAS96GM:
The above post shows how your plant should look in ideal conditions ; yours is not getting enough light .
Keep almost dry in the winter , a bright a place as possible is vital .
They can be drastically pruned in the Spring , and will readily regenerate ; just lop all weak and drawn branches . Have you access to a greenhouse or conservatory ; that would be ideal .
PPS Crassula ovata is synonymous with C.argentea