Learn Icelandic: Hann hefur skipt um vinnu.

The verb skipta (to change) is a Group 2 weak verb. Unlike Group 1 verbs which add -að in the supine (like tala becoming talað), Group 2 verbs drop their infinitive ending and add -t, -d, or -ð. Because the root of skipta already ends in a -t sound, the supine is simply skipt.

Why do we need the word um in this sentence?

In English, you directly change a thing, like changing jobs or changing clothes. In Icelandic, when you are replacing one thing with another of the same kind, the verb skipta requires the preposition um.

Why is the word for job spelled vinnu here instead of vinna?

The preposition um requires the noun following it to be in the accusative case. Vinna is a feminine noun, and feminine nouns that end in -a change that ending to -u in the accusative case.

Why does Icelandic use the singular vinnu when the English translation says changed jobs?

English uses the plural jobs because you are moving from one job to a second one. Icelandic logic focuses on the concept or category of what you are swapping, so it keeps the noun in the singular.