
der Anteil
share / proportion
A part of a whole that belongs to a person or thing or is attributed to them.
Der Anteil der Frauen in Führungspositionen ist gestiegen.
The proportion of women in leadership positions has increased.
share / proportion
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share / proportion
A part of a whole that belongs to a person or thing or is attributed to them.
Der Anteil der Frauen in Führungspositionen ist gestiegen.
The proportion of women in leadership positions has increased.

to show sympathy
In a fixed expression: to show sympathy for or interest in another person's fate or feelings.
Alle Kollegen nahmen großen Anteil an seiner schwierigen Situation.
All his colleagues showed great sympathy for his difficult situation.

share
A security that represents an ownership stake in a company; a share of stock.
Er hat seine Anteile an der Firma mit großem Gewinn verkauft.
He sold his shares in the company at a large profit.
The word 'Anteil' (share / proportion) can be easily understood from its components 'an' (at/on) and 'Teil' (part). It literally describes a part that is attached to or belongs to a larger whole.
Jeder Erbe erhielt seinen Anteil am Vermögen.
Each heir received their share of the fortune.
To name the whole of which something is a part, German uses the preposition 'an' followed by the dative. This structure is very common in statistics and reports.
Der Anteil der erneuerbaren Energien an der Stromerzeugung wächst.
The share of renewable energy in electricity generation is growing.
The expression 'Anteil nehmen' (to show sympathy) means to show compassion. It is always used with the preposition 'an' and the dative. The person showing sympathy is the subject of the sentence.
Viele Freunde und Nachbarn nahmen an ihrem Schicksal Anteil.
Many friends and neighbors showed sympathy for her fate.
In the context of business, finance, and companies, 'Anteil' (share) almost always means a share of stock or an ownership stake in a company. Typical verbs in this context are 'kaufen' (to buy), 'verkaufen' (to sell), or 'halten' (to hold).
Sie hat ihre Anteile an dem Technologie-Startup verkauft.
She sold her shares in the technology startup.
part
Both words refer to a part of a whole. „Teil“ is general and can simply mean a segment or component, whereas „Anteil“ typically means the assigned or measurable part that belongs to or is attributed to a person or thing. In contexts involving distribution or ownership, „Anteil“ is therefore more precise.

Mein Anteil am Kuchen liegt auf diesem Teller.
My share of the cake is on this plate.
Dieser Teil des Kuchens liegt noch auf dem Teller.
This part of the cake is still on the plate.