Inclined to cry about R number based on three ... (7)
I believe the answer is:
ternary
'based on three' is the definition.
(ternary means based on the number 3)
'inclined to cry about r number' is the wordplay.
'inclined to cry' becomes 'teary' (likely to burst into tears).
'about' indicates putting letters inside.
'number' becomes 'n' (n can represent any number).
'r'+'n'='rn'
'teary' going around 'rn' is 'TERNARY'.
(Other definitions for ternary that I've seen before include "Relating to a third order" , "Composed of three parts" .)