Answer: Plums should be pruned in late winter to open the center, allowing light to penetrate deep into the center of the tree. During the growing season, you can remove vigorous upright shoots growing into the center of the tree and any suckers that grow from the base.
Fruit should be thinned to about 4" apart when it is "pea sized". Plums need some protective spraying including dormant oil in late winter to control scale, an insecticide to control the plum curculio (the worm in the fruit) from bloom to just before harvest, and a fungicide in the weeks prior to harvest to control brown rot.
Your County Extension Office can assist you with what sprays are labeled for plums and when to apply them.
Plums need some supplemental watering in summer, but also require good drainage. Soggy soils are very detrimental.
Hope this helps!
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