to remove / pay off / wear out
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to remove
To remove or tear down something layer by layer, for example soil, an old building, or a mountain.
Die Arbeiter trugen die oberste Erdschicht ab, um das Fundament zu legen.
The workers removed the top layer of soil in order to lay the foundation.
'Abtragen' (to remove / pay off / wear out) is a separable verb. In a main clause, the prefix 'ab-' goes at the end. In subordinate clauses or in the infinitive with 'zu', the verb stays together.
Die Firma trägt das alte Fabrikgebäude ab.
The company is tearing down the old factory building.
The word is made up of 'ab-' and 'tragen' (to carry/wear). The prefix 'ab-' here means 'away' or 'becoming less'. So you 'carry away' something layer by layer, carry away a debt, or wear clothing until it is 'gone', meaning worn out.
Der Bagger trug die oberste Schicht des Bodens ab.
The excavator removed the top layer of the ground.
You can easily recognize the meaning of 'abtragen' (to remove / pay off / wear out) from the object: with soil or buildings, it is about removing. With debts or loans, it is about paying. With clothing, it is about becoming worn out.
Man muss den alten Schuppen abtragen, bevor man neu bauen kann.
You have to tear down the old shed before you can build something new.
In a financial context, 'abtragen' (to pay off) is almost always combined with liabilities. Typical phrases are: 'Schulden abtragen' (to pay off debts), 'einen Kredit abtragen' (to pay off a loan), or 'eine Hypothek abtragen' (to pay off a mortgage).
Wie lange werdet ihr brauchen, um die Hypothek für das Haus abzutragen?
How long will you need to pay off the mortgage on the house?
In the meaning 'to wear out clothing', the past participle 'abgetragen' is often used like an adjective to describe old, frequently worn clothing.
Er trug eine abgetragene Jeans und ein altes T-Shirt.
He wore worn-out jeans and an old T-shirt.
to wear / carry
'tragen' and 'abtragen' look similar, and both can have to do with clothing. 'tragen' simply means that you have clothing, jewelry, or glasses on your body. With clothing, 'abtragen' means something more specific: you wear a piece of clothing until it is old or worn out. So you cannot replace every 'tragen' with 'abtragen'. If you only want to say what someone is wearing today, use 'tragen'. If it is about old clothing that is still being used up, 'abtragen' fits.
Die alten Arbeitshosen trägt er im Garten noch ab.
He still wears out the old work pants in the garden.
Frau Neumann trägt heute eine blaue Jacke und bequeme Schuhe.
Ms. Neumann is wearing a blue jacket and comfortable shoes today.