Crossword Genius

Quietly did sums as they walked about (6)

Ross

I believe the answer is:

padded

I'm a little stuck... Click here to teach me more about this clue!

'walked about' is the definition.
'padded' can be an answer for 'walked' (padding is a kind of walking). I am not sure about the 'about' bit.

'quietly did sums as they' is the wordplay.
I cannot quite understand how this works, but
'quietly' could be 'p' (p for piano and quiet) and 'p' is present in the answer.
'did sums' could be 'added' (I've seen this in another clue) and 'added' is found within the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for padded that I've seen before include "Covered with anything soft; stuffed" , "Covered with thick material" , "Filled with wadding" , "Covered in soft material" , "Kind of cell for violent prisoners" .)

I've seen this clue in The Irish Times.
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